MCAT Review - Relationships

Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding Biology Biology DNA Structure Biology Diffusion Biology Blood Pressure Biology Water Homeostasis Biology Nervous System presence of G-C base pairs DNA stability proportional More GC base pairs increase...

Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding Biology Biology DNA Structure Biology Diffusion Biology Blood Pressure Biology Water Homeostasis Biology Nervous System presence of G-C base pairs DNA stability proportional More GC base pairs increase the stability of DNA and RNA structure because it has 3 hydrogen bonds, as opposed to AT or AU base pairs that only have 2 hydrogen bonds. Strong ex: Demyelination of the axon is a major concern for Multiple Sclerosis (MS) patients. The scavenging of myelin on the axon results in a greater surface area of the neuron exposed for interaction. Thus, there is increased diffusion of electrolytes down their neural concentration gradient. The higher the concentration gradient (aka, the greater the difference in concentration between the high-concentration area vs. low-concentration area), the greater the rate of diffusion). Strong concentration gradient, surface area, kinetic energy (aka temperature) rate of diffusion proportional presence of proteins Oncotic pressure proportional ADH water in urine inverse presence of Myelin conduction speed of an action potential proportional Oncotic pressure defined as a form of osmotic pressure, exerted by proteins. For example, low albumin levels in the blood (due to liver damage because albumin is made in the liver) would cause a low oncotic pressure. Antidiuretic Hormone (ADH) directly increases the ability of the blood to reabsorb water from the nephron by inserting aquaporins on the collecting duct. When an individual's blood becomes hypotonic with respect to filtrate, the body would then aim to increase free water excretion to regain homeostasis. This means that the kidney would decrease the amount of water reabsorbed from the filtrate into the blood. This could be accomplished by decreasing the secretion of ADH, which would promote the loss of more water in the urine, increasing the blood concentration. (tip: Remember that Diuretics, such as coffee and alcohol, make you pee more. Another way to think of a decrease in anti-diuretics is the increase of diuretics. More diuretics = more diluted urine output) Strong Strong Myelin is an insulator that surrounds the axons and helps speed up action potential transmission, similar to how a rubber coating helps conduct and speed up electrical transmission in a wire, like your phone charger. (note that since myelin is a good insulator, this also means that by definition it must be a poor conductor) Strong proportional Secondary structure, which includes α-helices and β-pleated sheets, are stablized by hydrogen bonding between the amine and carbonyl groups of the component amino acids of a polypeptide chain. Strong Heat denatures proteins by increasing their average kinetic energy, thus disrupting hydrophobic interactions. Increasing the amount of solutes or dramatically changing pH denatures proteins by disrupting elements of secondary, tertiary, and quaternary structure because the solutes, H+, or OH- interfere with bonds that maintained the protein's structure. Strong At low (acidic) pH, there is more free H+ floating around to interact with the amino acid to protonate it. At high (basic) pH, there is more free OH- present to deprotonate the amino acid. Strong Biochemistry Amino Acids, Biochemistry Peptides, and Proteins Hydrogen Bonding within a polypeptide chain (between amine and carbonyl groups) Amino Acids, Biochemistry Peptides, and Proteins heat solute concentration change in pH protein denaturation proportional Amino Acids, Biochemistry Peptides, and Proteins pH and pKa protonation state if pH < pKa, then protonated if pH > pKa, then deprotonated Amino Acids, Biochemistry Peptides, and Proteins Biochemistry DNA electrophoresis secondary structure stabliziation according to the rules that: if pH < pI, then the amino acid will be in a protonated state if pI < pH, then the amino acid will be in a depronated state when pH = pI, then the amino acid will be in its zwitterion form and will be stationary protonation state of an amino acid (which depends on the pH of the environment and amino acid's intrinsic pI) size (molecular weight) of a DNA fragment direction of migration in electrophoresis distance migrated in DNA electrophoresis if protonated amino acid (cation) ---> cathode if deprotonated amino acid (anion) ---> anode inverse then: if an amino acid with a pI of 5 is run in an electrophoresis that has a pH environment of 8 (aka pI is less than the pH), the amino acid will be deprotonated. Deprotonated amino acids migrate toward the POSITIVELY CHARGED ANODE. (the reason why the anode is positively charged as opposed to negatively charged is because electrophoresis occurs in an ELECTROLYTIC CELL, not a galvanic/voltaic cell.. so that's why the sign designations are flipped). An easy way to remember this is that cations are always attracted to the cathode, and anions are always attracted to the anode. Smaller fragments (or more compact DNA if under native conditions) travel the FURTHEST because they are easiest to push by an electrical field. The larger fragments so not migrate as far from the well because they are heavier and harder to be affected by the given electric field. https://www.youtube.com/watch?v=_EYsykjsfiY Unsure Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding Biochemistry Ion exchange chromatography Overall positive charge on a protein binding affinity to cationexchange column proportional Proteins with an overall positive charge will bind better to cation-exchange columns. More positive charge = tighter binding to the cation exchange column. Oppositely, proteins with an overall negative charge will bind better to anion-exchange columns, and weaker to a cation-exchange column. More negative charge = tighter binding to the anion exchange column. Biochemistry Ion exchange chromatography | magnitude | of the overall charge on a protein concentration of NaCl required for elution proportional Proteins with a higher magnitude of overall charge (aka more charged proteins, as opposed to moderately charged proteins) require a higher salt concentration for elution. (e.g. a protein with an overall charge of +5 and a protein with an overall charge of –4 would both require a higher concentration of NaCl for elution than a protein with an overall charge of +1) Strong demonstrated in a Michaelis-Menten Plot: An increase in the substrate concentration (while maintaining a constant enzyme concentration), leads to a proportional increase in the rate of the reaction only initially. However, once most of the active sites are occupied, the reaction rate levels off, regardless of further increases in substrate concentration. At high concentrations of substrate, the reaction rate approaches its maximal velocity, called Vmax, and is no longer changed by further increases in substrate concentration. Strong Low Km = high affinity for substrate High Km = low affinity for substrate Competitive inhibitors increases the Km of an enzyme, decreasing the binding affinity for the enzyme and the substrate. Unsure logarithmically proportional Strong Biochemistry Enzyme Kinetics [substrate] reaction velocity Biochemistry Enzyme Kinetics Km binding affinity between an enzyme and its substrate inverse Biochemistry Enzyme Kinetics Kcat catalytic efficiency proportional based on the equation: Catalytic efficiency = (Kcat) / (Km) to help remember which term is in the numerator or denominator, remember the mnemonic: "the cat jumps on top of the mouse" Strong Biochemistry Enzyme Kinetics Km catalytic efficiency inverse based on the equation: Catalytic efficiency = (Kcat) / (Km) to help remember which term is in the numerator or denominator, remember the mnemonic: "the cat jumps on top of the mouse" Strong inverse Kd is the Dissociation constant, which is a measure of how easily the enzyme-substate complex dissociates (breaks apart). A high Kd means that the enzyme-substrate complex dissociates easier (aka the binding affinity is weak). A low Kd means that the enzyme-substrate complex does not readily dissociate (indicating that the binding affinity between the enzyme and substrate is STRONG). Strong Biochemistry Enzyme Kinetics Kd binding affinity Biochemistry Enzyme Inhibitors Km vmax Km vmax proportional Km: no change vmax: ⬇ presence of a NONcompetitive inhibitor slope of a Lineweaver–Burke plot Biochemistry Enzyme Inhibitors Km: ⬆ vmax: no change presence of a Competitive inhibitor slope of a Lineweaver–Burke plot Biochemistry Enzyme Inhibitors (until an asymptotic max value, Vmax is reached) presence of an UNcompetitive inhibitor Km vmax In the presence of a competitive inhibitor, Km increases. Remember that x-intercept of the Lineweaver–Burke Plot corresponds to –1/Km. Therefore, because competitive inhibitor causes Km to increase, the x-intercept will approach zero (moves closer to the right). Because the x-intercept moves closer to the right while the y-intercept (associated with Vmax) is uncharged by competitive inhibitors, the slope of the Lineweaker–Burke Plot will become steeper. (basically rotates counter-clockwise with the y-intercept as the axis of rotation) shortcut: basically the "new line" is rotated counter-clockwise w/ the Y-intercept being the center of rotation. A noncompetitive inhibitor binds to an allosteric site, rather than the active site. Binding of the inhibitor to the allosteric site changes the conformation of the active site, leading to a decrease in efficiency of enzyme catalysis, which results in a decrease in vmax. However, Km will NOT change due to nonncompetitive inhibition because any copies of the enzyme still in the active conformation can bind substrate with the same affinity. in a Lineweaver–Burke plot: compared to the line without inhibitor, the line WITH a noncompetitive inhibitor will have the same x-intercept, but a higher y-intercept. This causes an increase in the slope of the line. (basically rotates counter-clockwise with the x-intercept as the axis of rotation) proportional shortcut: basically the "new line" is rotated counter-clockwise w/ the X-intercept being the center of rotation. Km: ⬇ vmax: ⬇ An uncompetitive inhibitor binds to an allosteric site, but only when the substrate is already bound to the enzyme. This results in an increased inffinity for substrate bound to enzyme and decreased dissociation of the enzyme–substrate complex. Therefore, uncompetitive inhibition results in a decrease in BOTH vmax and Km. In a Lineweaver–Burke plot: compared to the line without an inhibitor, the line with an uncompetitive inhibitor will have a more negative x-intercept and a higher y-intercept––a shift upwards and to the left. (parallel) shortcut: basically the "new line" is parallel and shifted to the LEFT. Unsure Unsure Unsure Unsure Unsure Subject Topic Biochemistry Enzyme Inhibitors Variable X Variable Y Relationship slope of a Lineweaver–Burke plot NO EFFECT in slope, but the entire line shifts to the left presence of an UNcompetitive inhibitor An uncompetitive inhibitor binds to an allosteric site, but only when the substrate is already bound to the enzyme. This results in an increased inffinity for substrate bound to enzyme and Explanation / Example / Application complex. Therefore, uncompetitive inhibition decreased dissociation of the enzyme–substrate results in a decrease in BOTH vmax and Km. In a Lineweaver–Burke plot: compared to the line without an inhibitor, the line with an uncompetitive inhibitor will have a more negative x-intercept and a higher y-intercept––a shift upwards and to the left. (parallel) Understanding Unsure shortcut: basically the "new line" is parallel and shifted to the LEFT. Biochemistry Enzymes charge on an amino acid's sidechain proportional ligand affinity/stabilization (if the ligand has an opposite charge to the sidechain) Ligands that have a negatively charged group, such as phosphate groups, would have a high binding affinity to an enzyme active site that contains positively charged side chains on an enzyme, such as His, Lys, and Arg. (aka ionic interactions; "opposites attract") Strong During hypoventilation, breathing rate is slower than normal, and the lungs are not supplying enough oxygen to meet the body's demands.. and it causes blood pH to be low due to the following reason: less CO2 is exhaled (aka less CO2 leaves the body) than normally ∴ CO2 remains inside the body, aka the [CO2] inside the body is high ∴ according to the equation "CO2 + H2O ⇄ H2CO3 ⇄ H+ + HCO3–" ∴ an increase in [CO2] will shift the equilibrium to the right → according to Le Chatlier's Principle ∴ this shift to the right will cause [H+] to increase ∴ blood pH will decrease (becomes more acidic due to more H+ ions present) (if blood pH becomes too acidic due to low [CO2] , this is refered to as respiratory acidosis) (fun fact: this is why some swimmers try to hyperventilate before starting a race: to minimize the amount of [CO2] IN their body before they begin the dive, so that DURING their dive underwater, they can extend the time before they feel the urge to exhale again due to increasing [CO2] levels as they swim... although this does increase their risk of blacking out and thus drowning lol) Strong Regulation of Biochemistry blood pH by breathing breathing rate (ventilation/respiratory rate) blood pH proportional Regulation of Biochemistry blood pH by breathing [blood CO2] blood pH inverse refer to explanation above: "CO2 + H2O ⇄ H2CO3 ⇄ H+ + HCO3–" Increasing the concentration of CO2 would cause the equilibrium to shift to the right (via Le Châtlier's Principle), thus producing more H+. More H+ in the blood causes blood pH to decrease. Strong degree of fatty acid saturation on the cell membrane fluidity of the cell membrane inverse Saturated fatty acids can pack more tightly against each other and therefore will be more viscous. A cell membrane with unsaturated fatty acids will have higher membrane fluidity because they cannot pack as tightly, becoming less viscous (more fluid-like). Unsure proton-motive force energy available for generating ATP proportional Assuming no inhibition occurs, protons are pumped into the intermembrane space, thereby increasing the proton-motive force. The proton-motive force is directly proportional to the energy stored in the concentration gradient; therefore, the larger the proton-motive force is, the more energy available for generating ATP. Because NADH donates electrons to the ETC at Complex I and FADH2 donates electrons to the ETC at Complex II, this explains why NADH yields more ATP than FADH2. (2.5 vs. 1.5 ATP) Strong Hormonal Biochemistry Regulation of Metabolism insulin glycogen formation (glycogenesis) proportional Hormonal Biochemistry Regulation of Metabolism insulin glycogen breakdown (glycogenolysis) inverse Hormonal Biochemistry Regulation of Metabolism insulin gluconeogenesis (liver) inverse Hormonal Biochemistry Regulation of Metabolism insulin lipolysis (adipocytes) inverse Hormonal Biochemistry Regulation of Metabolism insulin protein synthesis (muscle tissue) proportional Biochemistry Lipids Aerobic Biochemistry Metabolism Strong Insulin is a peptide hormone that is incapable of passively diffusing through the bilayer due to its size and hydrophilicity; its receptors are located in the cell membrane. Insulin has major effects on muscle and adipose tissue. It increases the rate of glucose transport across the cell membrane, decreases the rate of lipolysis, and increases the uptake of triglycerides and some amino acids from the blood. Essentially, insulin functions to ensure that, during times of high glucose availability, the body preferentially uses glucose for energy. Further, insulin signals for increased glucose storage, and decreased use of alternative energy sources during the postprandial state. Strong Strong Strong Glucagon essentially results in the opposite metabolic processes as insulin. Strong General Chemistry General Chemistry Electrons General Chemistry Atomic Structure distance of the electron from the nucleus principle quantum number n (energy level) interaction with the surrounding environment proportional Electrons that are furthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called valence electrons; they are more likely to become involved in bonds with other atoms because they experience the least electrostatic pull form their own nucleus. Strong radius proportional The principal quantum number (n) represents the shell of an atom. The larger the integer value of n, the higher the energy level and thus the higher the radius of the electron's orbit. Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding demonstrated by Bohr's equation for the energy of the electron: E = – RH / n^2 General Chemistry Bohr Model General Chemistry Bohr Model principle quantum number n (energy level) principle quantum number n (energy level) Energy of the electon E proportional wavelength λ absorbed inverse where RH = Rydberg's constant = 2.18e–18 The energy of an electron E increases (aka becomes less negative, approaching zero) the farther out from the nucleus that the electron is located (increasing n). This is an important point: while the magnitude of the fraction is getting smaller, mathematically, the actual value it represents is getting larger because of the negative sign in the equation (becoming less negative). Another way to think of this is that a larger integer value for the principal quantum number n indicates a larger radius, and thus higher energy, analogous to gravitational potential energy: where the higher or farther the object is above Earth, the higher its potential energy will be. Strong The principle quantum number describes the energy level; recall that energy is inversely related to wavelength. For example, the energy level n = 3 absorrbs 656 nm the energy level n = 4 absorbs 486 nm Unsure Strong General Chemistry Atomic Structure isotope number magnetic moment ODD isotope # = ↑ magnetic moment EVEN isotope # = none Isotopes that have a magnetic moment (and can thus be imaged by an MRI) are ones with an ODD atomic mass number. This is because an odd atomic mass number indicates an odd number of neutrons + protons, resulting in the nucleus having a nonzero spin and magnetic moment, thus becoming affected when placed in a magnetic field. (e.g. Carbon-13 and Fluorine-19 can be used in MRI because their atomic mass numbers are odd; Phosphorus-32 and Carbon-12 have mass numbers that are even, and they cannot be used in MRI because they will not be influenced by a magnetic field) General Chemistry Atomic Structure half-life of an isotope stablity of the isotope (and therefore, its abundance in nature) proportional Half-life is a marker of stability, generally. Longer-lasting isotopes are more abundant in nature because they have not decayed as fast. In other words, an isotope with a longer half-life is more stable and is therefore more abundant in nature because the isotope has not completely decayed. Strong proportional By combining the concepts of the Bohr Model and Planck's Equation for the energy of a quantum, the energy associated with a change in the principal quantum number from a higher, initial value to a lower, final value is equal to the energy of the emitted photon. For example, a change in energy level from n=4 to n=1 will emit a photon with a much higher energy than a change in energy level from n=2 to n=1. Conversely, a change in energy level from n=1 to n=4 requires the absorption of a photon with a much higher energy than a change in energy level fron n=1 to n=2. Strong Strong General Chemistry Emission difference in energy between the higher-energy state and the lower-energy state of the electron energy of the emitted/absorbed photon electrostatic force between ions boiling point or melting point proportional Because of the strength of the electrostatic force between the ionic bond constituents of a compound, ionic compounds have very high melting points and boiling points (in fact, much higher than those of covalent bonds). For example, the melting point of NaCl is 801ºC. Covalent compounds like carbon dioxide (CO2) tend to have lower melting and boiling points. Key concept: ionic bonds are stronger and harder to overcome than covalent bonds. bond length inverse Bond length is defined as the average distance between two nuclei of atoms in a bond. As the number of shared electron pairs increases, the two atoms are pulled closer together, resulting in a decrease in bond length. Thus for a given pair of atoms, a triple bond is shorter than a double bond, which is shorter than a single bond. Strong proportional Bond energy is defined as the energy required to break a bond by separating its components into their isolated, gaseous atomic states. The greater the number of pairs of electrons shared between the atomic nuclei, the more energy is required to break the bonds holding them together. Thus, triple bonds have the greatest bond energy, and single bonds have the lowest bond energy. By convention, the greater the bond energy is, the stronger the bond. Strong General Chemistry Ionic Bonds General Chemistry Characteristics of a Covalent Bond General Chemistry Characteristics of a Covalent Bond General Chemistry Characteristics of a Covalent Bond bond length bond energy inverse (explained by combining the two relationships above; e.g. triple bonds have the shortest bond legnth and greatest bond energy) Strong General Chemistry Characteristics of a Covalent Bond electronegativity bond length inverse Bond length decreases with larger difference in electronegativity. In other words, the bond lengths decreases when moving to the right along the Periodic Table's rows because the more electronegative atoms have shorter atomic radii. For example, despite C2H2 and HCN both having triple bonds, the nitrogen in HCN is likely to hold the electrons closer (or in a shorter radius) than the carbons in C2H2 because N is more electronegative. Strong General Chemistry Resonance number of nonzero formal charges present in a resonance structure stability of the resonance structure inverse The most stable resonance structures are those that minimize charge on the atoms in the molecule. As a guideline, a Lewis structure will small or no formal charges is preferred over a Lewis structure with large formal charges. Strong General Chemistry Resonance stability of the resonance structure contribution of the character of the resonance hybrid proportional The nature of the bonds within an actual compound is a hybrid of all of its resonance structures, and the actual structure of the compound is called the resonance hybrid. In general, the more stable the resonance structure, the more it contributes to the character of the resonance hybrid. Minor contributors usually contain formal charges, indicating decreased stability. Strong General Chemistry Intermolecular Forces intermolecular forces boiling point or melting point proportional A compound that exhibits more intermolecular forces will have a higher boiling point and melting point. Also, the stronger the intermolecular forces, such as more hydrogen bonding, the higher the boiling point. Strong number of shared electron pairs in a covalent bond (aka, bond order) number of shared electron pairs in a covalent bond (aka, bond order) bond energy (aka, bond strength) Subject Topic Variable X Variable Y Relationship General Chemistry Intermolecular Forces intermolecular forces surface tension proprotional General Chemistry Intermolecular Forces fluid flow rate intermolecular forces inverse General Chemistry Electrolytes General Chemistry Chemical Kinetics General Chemistry Collision Theory of Chemical Kinetics Explanation / Example / Application Understanding Surface tension is defined as a measure of intermolecular forces (and only intermolecular forces) acting between molecules on the surface of a liquid. (e.g. if molecule A can participate in hydrogen bonding while molecule B cannot, then molecule A will exhibit greater surface tension than molecule B) Strong As flow rate increases, there is greater kinetic energy and therefore the intermolecular forces become weaker and more transient. Strong Strong degree of dissocation of an ionic compound (aka, solvation) strength as an electrolyte proportional Electrolytes are solutes that enable solutions to carry currents. The electrical conducitivity of aqueous solutions is governed by the presence and concentration of ions in solution; a solute is considered a strong electrolyte if it dissociates completely into its constituent ions. Examples of strong electrolytes include certain ionic compounds, such as NaCl and KI, and molecular compounds with highly polar covalent bonds that dissociate into ions when dissolved, such as HCl in water. substrate concentration enzyme turnover rate proportional (until a max rate is reached) High substrate conditions saturate the active sites of the enzyme, leading to maximal turnover. Strong Various theories have been proposed to explain the events that are taking place at the atomic levels through the process of a reaction. The Collision Theory of chemical kinetics states that the rate of a reaction is proportional to the number of collisions per second between the reacting molecules. In other words, for a reaction to occur, molecules must collide with each other effectively... at the correction orientation AND with sufficient energy in order to break their existing bonds and form new ones. Strong number of effective collisions per second between reacting molecules in a reaction rate of reaction proportional based on the Arrhenius equation, which is a sophisticated mathemetical representation of Collision Theory: General Chemistry Collision Theory of Chemical Kinetics frequency factor A rate constant k of a reaction proportional k = Ae^(–Ea / RT) Strong (aka, the rate of reaction) As the frequency factor A, a measure of how often molecules in a certain reaction collide, increases... the rate constant of the reaction also increaces in a direct relationship. based on the Arrhenius equation, which is a sophisticated mathemetical representation of Collision Theory: k = Ae^(–Ea / RT) General Chemistry Collision Theory of Chemical Kinetics General Chemistry 4 Factors that affect Reaction Rate activation energy Ea rate constant k of a reaction inverse (aka, the rate of reaction) concentration of reactants or parital pressure of reactants (aka, the number of molecules in a reaction) rate constant k of a reaction proportional (aka, the rate of reaction) As the magnitude of the exponent gets smaller, it actually moves from a more negative value toward zero (because of the negative sign of the exponent in the equation. Thus, mathematically, as Ea decreases, the rate constant k also increases. This should make sense conceptually because a low activation energy means that the reacting molecules do not need to collide with as much energy, and thus the number of effective collisions and reaction rate increases. Increasing the concentration of reactant will increase reaction rate (except for zero-order reactions) because there are more effective collisions per time. In other words, when there are more molecules, there are more opportunities for collision to occur. For reactions occuring in the gaseous state, the partial pressures of the gas reactants serve as a measure of concentration. Strong Strong based on the Arrhenius equation, which is a sophisticated mathemetical representation of Collision Theory: k = Ae^(–Ea / RT) General Chemistry 4 Factors that affect Reaction Rate General Chemistry 4 Factors that affect Reaction Rate effectiveness of the medium in which a reaction occurs General Chemistry 4 Factors that affect Reaction Rate presence of catalysts temperature T rate constant k of a reaction (aka, the rate of reaction) rate constant k of a reaction proportional (to an extent, until denaturation occurs) (aka, the rate of reaction) Strong proportional Changing the medium in which a reaction occurs can either increase or decrease the reaction rate, depending on how the reactants interact with the medium. The more effective the medium in which a reaction occurs, the greater the rate of reaction in that medium. Generally, polar solvents, such as water, increase the rate of a reaction because their molecular dipole tends to polarize the bonds of polar reactants, thereby lengthening and weaking the, permitting the reaction to occur faster. Unsure proportional Adding a catalyst increases reaction rate because it lowers the activation energy of a reaction. Strong (aka, the rate of reaction) rate constant k of a reaction As the magnitude of the exponent gets smaller, it actually moves from a more negative value toward zero (because of the negative sign of the exponent in the equation. Thus, mathematically, as T increases, the rate constant k also increases. This should also make sense conceptually: increasing the temperature will increase reaction rate because the particles' kinetic energy is increased, allowing them to surpass the necessary activation energy. HOWEVER, especially in biological systems, if the temperature is TOO high, a catalyst may denature–and consequently the reaction rate will fall dramatically. Variable X Variable Y Relationship Gas–Liquid Equilibrium pressure condensation proportional General Chemistry Gas–Liquid Equilibrium temperature of a gas condensation inverse General Chemistry Gas–Liquid Equilibrium temperature of a liquid vapor pressure of the evaporated particles proportional The pressure that a gas exerts over a liquid at equilibrium is the vapor pressure of the liquid. Vapor pressure increases as temperature increases because more molecules have sufficient kinetic energy to escape into the gas phase. The temperature at which the vapor pressure of the liquid equals the ambient pressure is called the boiling point, and this is explains why liquid boils at high temperatures or at low pressures. Unsure General Chemistry Liquid–Solid Equilibrium temperature of a solid energy of microstates proportional The availability of energy microstates increases as the temperature of a solid increases. In basic terms, this means that the molecules have greater freedom of movement, and energy disperses. If the atoms or molecules in the solid phase absorb enough energy, the threedimensional structure of the solid will break down, and the atoms will escape into the liquid phase; this transition is called fusion or melting. Unsure Strong Strong Subject Topic General Chemistry Explanation / Example / Application In a covered or closed container, liquid molecules that evaporate into the gas phase are trapped above the solution. These liquid molecules thus exert a countering pressure, which forces some of the gas particles back into the liquid phase; this process is caleld condensation. Condensation is faciliated by lower temperature or higher pressure. General Chemistry Standard Heat of Combustion size of alkane reactant in a combustion reaction number of combustion products proportional Combustion often involves the reaction of a hydrocarbon with oxygen to produce carbon dioxide and water. Longer hydrocarbon chains yield greater amounts of combustion products and release more heat in the process–that is, the reaction is more exothermic. In other words, the larger the alkane reactant, the more numerous the combustion products. For example, the combustion of n-pentane would have a greater exothermic standard of combustion than ethane, propane, or n-butane. General Chemistry Entropy energy distributed into a system at a given temperature entropy ΔS of the system proportional Entropy is a measure of the degree to which energy has een spread out throughout a system or between its surroundings. When energy is distributed INTO a system at a given temperature, its entropy increases. When energy is distributed OUT of a system at a given temperature, its entropy decreases. Understanding Unsure Unsure Based on the equation for Standard Gibbs free energy from the equilibruim constant: ΔGº = –RT ln Keq General Chemistry Free Energy ΔG, Keq, and Q Keq spontaneity of a (forward) reaction proportional General Chemistry Atmospheric Pressure height above earth mercurcy height in a barometer column inverse General Chemistry Atmospheric Pressure depth underwater mercurcy height in a barometer column proportional General Chemistry Ideal Gas Law number of moles n of a gas Volume V that the gas occupies proportional General Chemistry Ideal Gas Law Volume V that a gas occupies Pressure P of the gas inverse General Chemistry Ideal Gas Law Temperature T Volume V that a gas occupies proportional General Chemistry Ideal Gas Law Temperature T proportional General Chemistry Ideal Gas Law (in Kelvin) Pressure P Ideal Gas Law variables (in Kelvin) variables in: Boyle's Law Charles' Law Gay-Lussac's Law Avogadro's Principle Mathematically, the greater the value of Keq, the more positive the value of its natural logarithm. The more positive the natural logarithm, the more negative the standard free energy change. The more negative the standard free energy change, the more spontaneous the reaction. In other words, ↑ Keq = ↑ ln Keq = ↓ ΔGº = ↑ spontaneity of a reaction. A reading on a barometer can be obtained by measuring the height of the mercurcy column (in mm), which will be directly proportional to the incident (usually atmospheric) pressure being applied to the mercury. At the top of a mountain, atmospheric pressure is lower, causing the column to fall because mercury flows out of the column under its own weight. Under water, hydrostatic pressure is exerted on the barometer in addition to atmospheric pressure, causing the column to rise because more mercury is forced into the column. Unsure Weak Strong shown by Avogadro's Principle and the Ideal Gas Law: Strong (n1) / (V1) = constant = (n2) / (V2) shown by Boyle's Law and the Ideal Gas Law: Strong (P1)(V1) = constant = (P2)(V2) shown by Charles' Law and the Ideal Gas Law: Strong (V1) / (T1) = constant = (V2) / (T2) shown by Gay-Lussac's Law and the Ideal Gas Law: Strong (P1) / (T1) = constant = (P2) / (T2) ideal gas law: PV = nRT combined gas law: (P1V1) / T1 = (P2V2) / T2 notice how the Ideal Gas Law, PV = nRT , is basically just algebraic paraphrase of all of the equations shown above (Boyle's Law, Charles' Law, Gay-Lussac's Law, and Avogadro's Principle) all combined into ONE simplified equation. The relationships in the PV = nRT equation essentially explain in each of those individual scientist's discoveries, where R is a constant (≈0.08 L⋅atm / K⋅mol). Hence, the ideal gas law was discovered after Boyle's Law, Charles' Law, and Dalton's Law had already been well-established. Unsure Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding according to Henry's Law: [gas in solution]1 / P1 = [gas in solution]2 / P2 = kH , where kH is Henry's constant (whose value depends on the identity of the gas) General Chemistry Henry's Law partial pressure of a gas solubility (concentration) of the gas proportional Solubility (concentration) and pressure are directly related. In biology, this is a critically important relationship for gas and nutrient exchange. If the atmospheric pressure changes, as it does from sea level to high altitude, then the partial pressure of oxygen in the atmosphere also changes (as explained by Dalton's Law), and the amount of gas exchanged is altered accordingly; if the parital pressure of a particular gas is elevated (such as when delivering hyperbaric oxygen), the amount of gas dissolved in the blood is also elevated. Unsure According to the Kinetic Molecular Theory of gases, General Chemistry Kinetic Molecular Theory temperature of a gas particle (in kelvins) General Chemistry Maxwell– Boltzmann Distribution Curve temperature of a molecule (in kelvins) Kinetic Energy = (1/2)mv^2 = (3/2)(kB)(T) kinetic energy of the gas particle proportional where kB is the Botlzmann constant (1.38e–23 J/K). From the equation, we can see that the average kinetic energy of a gas particle is proportional to the absolute temperature of the gas (in kelvins), and it is the same for ALL gases at a given temperature, irrespective of the chemical identity or atomic mass. Strong (also essentially the same explanation as above, since Kinetic Energy and speed are directly proporitonal) speed of the molecule As shown in a Maxwell–Boltzmann distribution curve and the equation for Root-MeanSquare Speed (urms): proportional Strong molecules at higher temperatures move at faster speeds. http://www.entropy-book.com/wp-content/uploads/2013/10/Fig.-3-graph-hot-cold-correct.jpg As shown in a Maxwell–Boltzmann distribution curve and the equation for Root-MeanSquare Speed (urms): General Chemistry Maxwell– Boltzmann Distribution Curve molar mass of a molecule speed of the molecule inverse the larger a molecule is, the slower they move. For example, a Helium gas particle (which has a molar mass of 4 g/mol) will move faster than Xenon gas particle (which has a molar mass of 131.3 g/mol) because Helium is lighter in weight. Strong http://www.entropy-book.com/wp-content/uploads/2013/10/Fig.-3-graph-hot-cold-correct.jpg As shown by Graham's Law of Diffusion and Effusion: r1 / r2 = √(M2 / M1) General Chemistry Graham's Law of Diffusion & Effusion General Chemistry From this equation, we can see that, mathematically, a gas that has a molar mass 4 times that of another gas will travel half as fast as the lighter gas. Conceptually, because all gas particles have the same average kinetic energy at the same temperature (KE = (1/2)mv^2), it must be true that particles with greater mass travel at a slower average speed. Since diffusion and effusion both deal with the movement of molecules, then larger molecules with larger molar masses will diffuse/effuse more slowly than smaller molecules with lighter molar masses. In other words, heavier molecule = slower speed = slower rate of diffusion/effusion. molar mass of a molecule rate of diffusion/effusion of that molecule inverse Characteristics of an Ideal Gas intermolecular interactions ideal gas behavior inverse By definition, an Ideal Gas is a gas that does NOT participate in any intermolecular interactions. Strong General Chemistry Characteristics of an Ideal Gas pressure exerted by a sample of gas ideal gas behavior inverse As the pressure of a gas increases, the particles are pushed closer and closer together. The closer they are, the more they participate in intermolecular forces. By definition, an Ideal Gas is a gas that does NOT participate in any intermolecular interactions. For example, oyxgen behaves more ideally when its partial pressure is 1 atm rather than at 50 atm. Strong General Chemistry Characteristics of an Ideal Gas temperature of a gas ideal gas behavior proportional As the temperature of a gas is decreased, the average speed of the gas molecules decreases and the attractive intermolecular forces become increasingly significant. By definition, an Ideal Gas is a gas that does NOT participate in any intermolecular interactions. For example, oxygen gas behaves more ideally at 500ºK than at 200ºK. Strong General Chemistry Characteristics of an Ideal Gas volume a container containing a sample of gas proportional Decreasing the volume of a sample of gas makes it behave less ideally because the individual gas particles are in closer proximity in a smaller volume. Thus, this makes them more likely to engage in intermolecular interactions. However, by definition, an Ideal Gas is a gas that does NOT participate in any intermolecular reactions. For example, oxygen behaves more ideally when inside a 50 L container than a 50 mL container. Strong ideal gas behavior Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding General Chemistry Solutions dissolution ΔS of the SOLUTE proportional Entropy ican be thought of as the measure of molecular disorder, or the number of energy microstates available to a system at a given temperature. Therefore, at constant temperature and pressure, entropy of a solute always increases upon dissolution. For example, when NaCl dissolves into water, the rigidly ordered arrangement of the Na and Cl ions is broken up and freed from their lattice arrangment to have a greater degree of freedom to move around in different ways in the solution (aka their energy is more distributed and their entropy increases). General Chemistry Solutions dissolution ΔS of the SOLVENT inverse (following up from the NaCl example from above) Unlike the solute during dissolution, the solvent (such as water) becomes more restricted in its movement because it is now interacting with the ions. Thus the number of energy microstates available to water (that is, the water molecules' ability to move around in different ways) is reduced, so the entropy of water decreases. Unsure proportional In the end, the increase in the entropy experienced by the dissolved solute (NaCl) is greater than the decrease in entropy experienced by the water, so the overall entropy change is positive–energy is, overall, dispersed by the dissoluation of NaCl in water. In this particular example, because of the relatively low endothermicity and relatively large positive change in entropy, this explains why NaCl spontaneously dissolves in liquid water. Unsure Unsure General Chemistry Solutions dissolution ΔS of the overall system General Chemistry Solutions concentration of solute added to a solvent density of the solution proportional As aqueous soltuions become more concentrated with solute, their densities become significantly different from that of pure water; most water-solutble solutes have molar masses signifcantly greater than that of water, so the density of the solution increases as the concentration increases. This phenomenon is related to boiling point elevation and freezing point depression. Strong General Chemistry Solubility Product Constants temperature solubility product Ksp for non-gas solutes proportional Solubility product constants, like ALL other equilibrium constants (Keq, Ka, Kb, and Kw), are temperature DEPENDENT. Generally speaking, the solubility product constant increases with increasing temperatures for non-gas solutes and decreases for gas solutes. Strong General Chemistry Solubility Product Constants pressure solubility product Ksp for gas solutes proportional Higher pressures favor dissolution of gas solutes, and therefore the Ksp will be larger for gases at higher pressures than at lower ones. For example, as you dive deeper into the ocean where the pressure is higher, the more nitrogen gas that will be dissovled into your blood because nitrogen gas is the main inert gas in the air we breathe. If you rise too quickly to the surface, nitrogen gas bubbles will form in your bloodstream and can damage your tissue, which is very painful and potentially fatal if not properly treated. General Chemistry Solubility Product Constants ion product (IP) solubility product Ksp General Chemistry Solubility Product Constants General Chemistry concentration of a solution with a constituent ion of the The Common Ion salt being dissolved (aka, the Effect concentration of common ions) formation of complex ions If IP < Ksp: If IP = Ksp: If Ksp < IP: unsaturated saturated supersaturated solubility of a salt (containing the same metal) in solution proportional solubility of the salt inverse when IP < Ksp, the solution is unsaturated, and the solute will continue to dissolve when IP = Ksp, the solution is saturated, and the solution is at equilibrium (ΔG = 0) when IP > Ksp, the solution is supersaturated, and precipitation will occur The formation of complex ions increases the solubility of a salt in solution. Because a complex ion contains multiple polar bonds between the ligands and the central metal ion (based on the definition of a complex ion), it should be able to engage in a very large amount of dipole-dipole interactions. This stabilizes the dissolution of the complex ion. The end result is that such complexes tend to have VERY high Ksp values, termed "Kf" to represent the formation or stability constant of the complex in solution. The very high Kf value of the complex ion is significantly larger than the Ksp of the salt providing the metal ion to the complex, which partially explains why the initial dissolution of the salt is the rate-limiting step of complex ion formation. As an amount of metal ion is being used up to form the complex ion itself, the dissociation reaction of the salt shifts to the right, providing more metal for complex ion formation. The solubility of a salt is considerably reduced when it is dissolved in a solution that already contains one of its constituent salts as compared to its solubility in a pure solvent. This reduction in molar solubility is called the Common Ion Effect, which is really just Le Châlier's Principle in action. For example, if a salt such as NaBr is dissolved into water already containing Na+ ions (from some other salt, perhaps NaCl), the solution will dissolve less NaBr than would an equal amount of pure water. Because the solution already contains one of the constituent ions from the products side of the dissiociation of NaBr, the system will shift toward the left side, reforming solid NaBr. As a result, the molar solubility of the solid is reduced, and less of the solid dissolves in the solution (although Ksp remains constant because.... Ksp... is dependent... only on... temperature) Weak Strong Unsure Strong As demonstrated by Raoult's Law: PA = XA PºA General Chemistry Raoult's Law concentration of (volatile) solute added to a solvent vapor pressure of the solvent (in ideal solutions) inverse where PA is the vapor pressure of solvent A when solutes are present, XA is the mole fraction of the solvent A in the solution, and PºA is the vapor pressure of solvent A in its pure state. As more solute is added to the solvent, the mole fraction of solvent is decreased, causing the vapor pressure of the solvent to decrease proportionately. Raoult's Law explains the phenomenon of Vapor Pressure Depression. Strong Subject General Chemistry Topic Raoult's Law General Chemistry Raoult's Law General Chemistry Raoult's Law General Chemistry Raoult's Law Variable X Variable Y concentration of (volatile) solute added to a solvent boiling point of the solvent Relationship freezing point of the solvent proportional Strong inverse The presence of solute particles in a solution interferes with the formation of the lattice arrangement of solvent molecules associated with the solid state. Thus, a greater amount of energy must be removed from the solution (resulting in a lower temperature) in order for the solution to solidify. For example, pure water freezes at 0ºC, but for every mole of solute dissovled in 1 kg of water, the freezing point is lowered by 1.86ºC. This effect is the explanation for why we salt icy roads in the winter. Strong inverse Examining Raoult's Law on a molecular level, the presence of the solute molecules can block the evaporation of solvent molecules also. Strong NONE The condensation rate of a solvent is unaffected by the presence of solute particles in solution. Unsure (in ideal solutions) concentration of (volatile) solute added to a solvent evaporation rate of solvent concentration of (volatile) solute added to a solvent condensation rate of the solvent Understanding Recall that the boiling point is the temperature at which vapor pressure of the liquid equals ambient (incident) pressure. Thus, vapor pressure depression goes hand in hand with Boiling Point Elevation; the lowering of a solution's vapor pressure would mean that a higher temperature is required to match atmospheric pressure, thereby raising the boiling point. For example, salt water boils at a higher temperature than pure water due to the concentration of solute (NaCl) added to the water. (in ideal solutions) concentration of (volatile) solute added to a solvent Explanation / Example / Application (in ideal solutions) As shown by the equations for Boiling Point Elevation and Freezing Point Depression: ΔTb = i Kb m General Chemistry van't Hoff factor number of particles into which a compound dissociaties in a solution (aka, the van' Hoff factor) boiling point elevation freezing point depression melting point depression proportional and ΔTf = i Kf m where ΔTb is the increase in boiling point and ΔTf is freezing point depression. The variable i is the van't Hoff factor, which corresponds to the number of particles into which a compound dissociates in solution. For example, i = 2 for NaCl because each formula unit of NaCl dissociates into two particles–a sodium ion and a chloride ion–when it dissolves. Covalent molecules such as glucose do not readily dissociate in water and thus have i values of 1. The larger the value of i, the larger the boiling point elevation or the larger the freezing point depression. Strong As shown by the equation for Osmotic Pressure: General Chemistry Osmotic Pressure molarity of a solution temperature the van't Hoff factor osmotic pressure proportional Like ALL equilibrium constants, the value for K is dependent ONLY on temperature. The equilibrium constant Kw is no different. Isolated changes in concentration, pressure, volume, etc will NOT affect Kw. However, at different temperatures, the value for Kw changes proportionally. At temperatures above 298 K, Kw will increase; this is a direct result of the endothermic nature of the autoionization reaction. Strong inverse Given the fact that pH + pOH = 14, as pH increases, pOH decreases by the same amount. Strong [H3O+] inverse Strong pOH [OH-] inverse A p scale is defined as the negative logarithm of the number of items. Therefore, mathematically, low pH indicates a relative excess of hydrogen ions, and the solution is acidic; high pH (or low pOH) indicates a relative excess of hydroxide ions, and the solution is basic. Ka acidity (dissociation) "strength" proportional The strongest acids, such as HCl, have high Ka's (and low Kb's) Strong Kb basicity (dissociation) "strength" proportional The strongest bases, such as NaOH, have high Kb's (and low Ka's) Strong pKa acidity (dissociation) "strength" inverse The strongest acids, such as HCl, have low pKa's (and high pKb's) Strong pKb basicity (dissociation) "strength" inverse The strongest bases, such as NaOH, have low pKb's (and high pKa's) Strong Acid–Base Chemistry temperature Kw proportional General Chemistry Acid–Base Chemistry pH pOH General Chemistry Acid–Base Chemistry pH General Chemistry Acid–Base Chemistry General Chemistry Acid–Base Chemistry General Chemistry Acid–Base Chemistry General Chemistry Acid–Base Chemistry General Chemistry Acid–Base Chemistry Acid–Base Chemistry Unsure where Π is the osmotic pressure, i is the van't Hoff factor, M is the molarity of the solution, R is the ideal gas constant, and T is the temperature. General Chemistry General Chemistry Π = iMRT electronegative elements positioned near an acidic proton acidity (dissociation) "strength" proportional One important theme for acid strength is the Effect of Induction. Electronegative elements positioned near an acidic proton increase acid strength by pulling electron density out of the bond holding the acidic proton. This weakens proton bonding and facilitates dissociation. Thus, acids that have electronegative elements nearer to acidic hydrogens are stronger than those that do not. http://schoolbag.info/chemistry/mcat_2/mcat_2.files/image580.jpg Strong Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding The buffering capacity is defined as the ability to which a system can resist changes in pH. According to the Henderson–Hasselbalch equation: General Chemistry Acid–Base Chemistry the concentrations of the conjugate pair [A-] and [HA] while maintaining the same ratio of [A-]/[HA] pH = pKa + log[A-]/[HA] buffering capacity proportional Clearly, changing the ratio of the conjugate base to the acid will lead to a change in pH of the buffer solution. But what about changing the concentrations while maintaining a constant ratio? What would happen if the concentrations of both the acid and the conjugate base were doubled? While the pH would not change since the ratio of [A-]/[HA] is the same, the buffering capacity would in fact double. In other words, the addition of a small amount of acid or base to this system will now cause even less deviation in pH. Unsure One way to describe electrochemical cells includes the electromotive force (emf), which corresponds to the voltage or electrical potential difference of the cell. if the emf is +, the cell is able to release energy (–ΔG), which means it is spontaneous if the emf is –, the cell must absorb energy (+ΔG), which means it is nonspontaneous It is important to note that ΔGº and Eºcell will ALWAYS have opposite signs. Strong proportional All batteries are influenced by temperature changes. For instance, in lead–acid batteries in cars, like most galvanic cells, tend to fail the most often in cold weather. Strong chemical change induced in an electrolytic (+ΔG) cell proporitonal Michael Faraday's laws state that the liberation of gas and deposition of elements on electrodes is directly proportional to the number of moles of electrons being transferred during the oxidation–reduction reaction. Here, normality or game equivalent weights is used. These observations are proxy measurements of the amount of current flowing in a circuit. Strong E red tendency of a species to gain electrons and be reduced proportional The species in a reaction that will be oxidized or reduced can be determined from the reduction potential of each species, defined as the tendency of a species to gain electrons and to be reduced. Each species has its own intrinsic reduction potential; the more positive the potential, the greater the tendency to be reduced. Strong E red tendency of a species to lose electrons and be oxidized inverse Since reduction potential is defined as the tendency to be reduced, a less positive Eºred means a greater tendency for oxidation to occur because oxidation and reduction are opposite processes. Strong emf General Chemistry Electrochemistry ΔGº General Chemistry Electrochemistry temperature effectiveness of batteries General Chemistry Electrochemistry number of electrons exchanged during a redox reaction General Chemistry Electrochemistry reduction potential, General Chemistry Electrochemistry reduction potential, General Chemistry Electromotive Force and Thermodynamics Eºcell inverse Based on the equation relating Gibbs Free Energy and Electromotive Force: number of moles of electrons exchanged during a redox reaciton ΔGº ΔGº = –n F Eºcell inverse Strong the negative sign on the right side of the equation shows that a redox reaction that transfers more moles of electrons is more spontaneous (more negative ΔGº) than a redox reaciton that transfers less moles of electrons. By combining different equations for Gibbs Free Energy: ΔGº = –n F Eºcell and ΔGº = –RT ln Keq to get: –n F Eºcell = RT ln Keq Mathematically, when the equilibrium constant Keq is less than 1 (meaning that the equilibrium state favors the reactants), the Eºcell will be negative because the natural logarithm of any number between 0 and 1 is negative. These properties are characteristic of Electrolytic cells, which house nonspontaneous redox reactions. Instead, if Keq is greater than 1 (meaning that the equilbrium state favors the products), the Eºcell will be positive because the natural logithm of any number greater than 1 is positive; these properties are characteristic of Galvanic cells, which house spontanoues redox reactions. And when Keq is equal to 1, then ln(1) is 0, so Eºcell is 0. General Chemistry Electromotive Force and Thermodynamics Keq Eºcell if Keq < 1, Eºcell is negative if Keq > 1, Eºcell is positive if Keq = 1, Eºcell is 0. General Chemistry Electrochemistry number of ions present in solution (total # of cations + anions after dissociation) electrical conductivity (electrolyte strength) proportional In comparing MgCl2 and HNO3, since MgCl2 dissociates into 3 ions total in solution (one Mg2+ and two Cl- ions), and HNO3 dissociates into 2 ions total (one H+ and one NO3- ion), MgCl2 is said to have a higher electrical conductivity and is a better electrolyte. Strong General Chemistry Electrochemistry # of free (nonbonded) electrons electrical conductivity proportional Materials such as graphite are good electrical conductors because its structure consists of carbons that are covalently bonded to 3 other atoms (recall that cabon is tetrahedral), leaving a "sea" of free electrons that can conduct electricity. In contrast, diamond is a poor conductor because each of its carbon atoms are bound to 4 other atoms, leaving no free electrons. Strong Unsure Subject Topic General Chemistry Spectroscopy General Chemistry Spectroscopy Variable X Variable Y Relationship visible region of the electromagnetic specrum ROY G BV wavelength λ frequency ƒ and energy E wavelength decreases from left to right frequency & energy increases from left to right wavelength absorption of a sunscreen ability of the sunscreen to block UV light proportional Explanation / Example / Application Red 700 Orange 600 Yellow 575 Green 500 Blue 450 Violet 400 Understanding (approximate wavelengths absorbed) Strong ↑ wavelength (~700 nm) ↓ frequency and energy ↓ wavelength (~400 nm) ↑ frequency and energy in a wavelength vs. absorption plot, the area under the curve represents the amount of UV light a sunscreen can absorb. For a given sunscreen, more area under the curve = more effective sunscreen Strong Organic Chemistry Organic Chemistry Spectroscopy Organic Chemistry Spectroscopy Organic Chemistry Organic Reactions strength of bond vibration frequency proportional due to combining the concept that bonds are like springs with Hooke's Law mass of atoms in a bond vibration frequency inverse due to combining the concept that bonds are like springs with Hooke's Law basicity leaving group inverse weaker bases = better leaving groups because they can stablize extra electrons. Unsure Strong (single < double < triple) https://www.youtube.com/watch?v=ETdNsO7mKXM https://www.youtube.com/watch?v=ETdNsO7mKXM Weak Weak Organic Chemistry Organic Reactions presence of ElectronWithdrawing Groups acidity proportional Based on the Effect of Induction, the presence of an EWG (and especially the closer its proximimity to the acidic hydrogen), results in increased acidity because the EWG stabilizes the conjugate base of that compound via resonance. In contrast, the presence of an EDG decreases acidity because it destabilizes the compound. Organic Chemistry Organic Reactions ring strain reactivity proportional 4-membered ring structures (like Beta Lactams in penicillin) are more reactive than 6-ring structures due to ring strain. Strong Organic Chemistry Ultraviolet (UV) Spectroscopy wavenumber frequency proportional Wavenumber (defined as 1/λ) is inversely proportional to wavelength, and directly proportional to frequency (c/λ). Strong proportional In UV spectroscopy, UV spectra are obtained by passing UV light through a sample that is usually dissolved in an inert, nonabsorbing solvent, and then recording the absorbance. The absorbance is then plotted against wavelength. The absorbance is caused by electronic transitions between orbitals. The biggest piece of information we get from this technique is the wavelength of the maximum absorbance, which tells us the extent of conjugation within conjugated systems: the more conjugated the compound, the lower the energy of the transition and the greater the wavelength of absorbance. Unsure inverse By definition, wavenumber = 1 / λ. Based on the explanation above that increased conjugation results in increased wavelength absorbance, then this means that increased conjugation will result in a lower wavenumber. Unsure Organic Chemistry Ultraviolet (UV) Spectroscopy extent of conjugation within a compound wavelength of maximum absorbance in UV spectroscopy Organic Chemistry Ultraviolet (UV) Spectroscopy extent of conjugation within a compound wavenumber of maximum absorbance in UV spectroscopy Organic Chemistry Ultraviolet (UV) Spectroscopy difference in energy between LUMO and HOMO absorption wavelength inverse UV spectroscopy works because moleucles with π-electrons or nonbonding electrons can be excited by UV light to higher-energy antibonding orbitals. Molecules with a lower energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are more easily excited and can absorb longer wavelengths (lower frequencies) with lower energy. Unsure In other words, HOMO stands for highest occupied molecular orbital; LUMO stands for lowest unoccupied molecular orbital. In UV spectroscopy, electrons are excited from the HOMO to the LUMO. The smaller difference in energy between the two, the longer the wavelengths that can be absorbed by the molecule in UV spectroscopy. Organic Chemistry H–NMR Spectroscopy number of chemically equivalent protons in a compound height (or area under the curve) of the peak produced by the protons in an H–NMR Spectrum (also known as integration) proportional In H–NMR, each unique group of protons has its own peak. The integration (area under the curve) of this peak is proportional to the number of protons contained under hte peak. Strong Variable X Variable Y H–NMR Spectroscopy number of electronegative atoms close in proximity to a proton (H atom) deshielding of the proton distance Downfield (to the left) in an H–NMR spectrum H–NMR Spectroscopy number of electron shielding of the proton DONATING groups close in distance Upfield (to the proximity to a proton (H atom) right) in an H–NMR spectrum Subject Topic Organic Chemistry Organic Chemistry Relationship Explanation / Example / Application Understanding proportional When electronegative atoms are attached near a hydrogen (the proton), these atoms pull electron density away from the surrounding atoms, thus deshielding the proton from a magnetic field. The more the proton's electron density is pulled away, the less it can "shield" itself from the applied magnetic field, resulting in a reading further downfield (to the left) in an H–NMR spectrum. Strong proportional With the same reasoning as above, we know that if we had an electron-donating group, such as a silicon atom, it would help shield the H nuclei and give it a position further upfield (to the right. Strong In chromatography, IF the mobile phase being used is nonpolar, then more nonpolar compounds will elute first and migrate the farther distance. Think about it as "like dissolves like". Because a NONPOLAR compound is "like" the NONPOLAR mobile phase, it will migrate toward that similar mobile phase. Organic Chemistry Separations & Purifications which compound elutes first similarity to the mobile phase proportional Oppositely, if a polar compound is more similar to the polar stationary phase being used, it will therefore NOT elute/migrate a far distance.. because it likes to stay close to a phase that is "like" them. (aka stayin' in yo own comfort zone and choosing to be near what's similar to you) Weak For example, if silica gel, often used as a polar stationary phase, is being used with benzene, then this means that nonpolar compounds will elute first and travel farthest. The the more polar compound, the later it will elute and also the closer it will stay to the stationary phase. Rf is calculated as (the distance the compound migrates) / (distance to the solvent front). Polar compounds DO NOT migrate far (since the stationary phase, such as silica gel, is ALSO very polar), therefore this mathematically results in a LOW Rf. Organic Chemistry Thin Layer Chromatography polarity of compound X (with a polar stationary phase) Rf value inverse Nonpolar compounds travel farthest up the card (towards the nonpolar solvent front such as hexane), which this mathematically results in a HIGH Rf. Weak (e.g. a compound with an Rf of 0.20 is more polar than a compound with an Rf of 0.75) https://www.youtube.com/watch?v=_DEScXFyI8s&list=PLbKSbFnKYVY0lrUz8bb--eIGvVOf8YMcl&index=5 Physics Physics Physics Forces and Acceleration Forces and Acceleration height h above the earth mass of two objects acceleration due to gravity g gravitational forces between them inverse proportional Acceleration due to gravity, g, DECREASES as the height of the object above Earth INCREASES. And vice versa, acceleration increases the closer one gets to the Earth's center of mass. Near the Earth's surface, g = 10 m/s^2. (e.g. acceleration due to gravity is less up in mount everest than it is at sea level) Gravity is an attractice force that is felt by ALL forms of matter. Although all objects exert a measurable gravitational force on each other, gravitational forces usually do not have much significance on a small scale because other forces tend to be much larger in magnitude. Only on the planetary level do gravitational forces really take on a significant value. (e.g. there does exist a small (but measurable) force between you and your textbook, but it is insignificant compared to the force between you and Earth) Based on the equation for gravitational Forces F = (G) (m1) (m2) / (r^2) , we can see that the magnitude of gravitational Force is directly realted to the masses of the objects; If m1 is tripled, then F will triple. The farther two objects are from each other, the less gravitational force is seen acting on them. (e.g. the Sun and the Earth have a stronger gravitional force betwen each other than the Sun and Pluto) Physics Forces and Acceleration the distance between two objects' center of mass gravitational forces between them inverse (exponentially, by a power of 2) Strong Strong Based on the equation for gravitational Forces F = (G) (m1) (m2) / (r^2) , we can see that the magnitude of gravitational Force is inversly related to the square of the distance; if r is halved, then F will quadruple. (note the similarity of this gravitational Force relationship and the relationship between distance between two charges and the electrostatic Force) Strong Subject Topic Physics Kinematics Variable X Variable Y the displacement that spring forced needed to keep a is compressed/stretched from spring compressed/stretched its equilibrium position Relationship Explanation / Example / Application Understanding based on the equation for Hooke's Law: proportional F=–kx Strong Physics Kinematics area of contact frictional forces f proportional Strong based on the Kinetic Energy Equation: K = (1/2)mv^2 Physics Kinetic Energy speed of an object kinetic energy proportional (exponentially, by a power of 2) we see that the kinetic energy is a function of the square of the speed. If the speed doubles, then the kinetic energy will quadruple (assuming mass is constant). Also note that the kinetic energy is related to speed, not velocity. An object has the same kinetic energy REGARDLESS of the direction of its velocity vector. Strong based on the gravitational Potential Energy Equation: Physics Potential Energy mass of an object height of an object from the datum U = mgh (graviational) potential energy proportional we see that potential energy U has a direct relationship with all three of the variables. Changing any one of them by some factor will result in a change in the potential energy by the same factor. For example, tripling the mass of an object (or tripling the height) will increase the gravitational potential energy U by a factor of 3. based on the Work–Energy theorem Equation: Strong Wnet = ΔK Physics Work–Energy Theorem net work done by all the forces acting on an object change in kinetic energy of that object proportional This relationship is important to understand, as it allows you to calculate work without knowing the magnitude of the forces acting on an object or the displacement through which the forces act. If you calculate the change in kinetic energy experienced by an object, then–by definition– the net work done on or by an object is the same. For example, pressing the brake pedal in your car puts the work–energy theorem into practice. The brake pads exert frictional forces against the rotors, which are attached to the wheels. These frictional forces do work against the wheels, causing them to decelerate and bringing the car to a halt. The net work done by all these forces is directly equal to the change in kinetic energy "1/2mv^2" of the car. Strong based on one of the equations of mechanical Work: W=F d Physics Mechanical Advantage distance through which a amount of force required to force must be applied in order accomplish that amount of to do a given amount of work work Physics Mechanical Advantage amount of force required to move an object the same displacement length of an inclined plane inverse inverse Using simple machines to provide mechanical advantage (reducing the force needed to accomplish a given amount of work) does have a cost associated with it; the distance through which the smaller force must be applied in order to do the work must be increased. This is illustrated in inclined planes. For example, pushing a 100 N block up an incline over a distance of 20 m to a height of 10 m requires half as much force than trying to raise the block vertically 10 m. This is because the incline distributes the workload over a greater distance to perform the same amount of work. Strong (as explained above) When a device provides mechanical advantage, it decreases the input force required to generate a particular output force. Generally, this is accomplished at the expense of increased distance over which the force must act. Strong based on the equation for mechanical efficiency: Physics Mechanical Advantage effort in a pulley system effort distance to maintain the same work output inverse efficiency = (load)(load distance) / (effort)(effort distance) As the effort (required force) decreases in a pulley system, the effort distance increases to generate the samea mount of work. based on the equations for thermal expansion and volumetric expansion: ΔL = αLΔT Physics Thermal Expansion temperature change in a solid's length change in a liquid's volume proportional and Strong ΔV = βVΔT Rising temperatures cause an increase in length (for solids) and volume (for liquids), and vice versa: falling temperatures cause a decrease in length/volume. Thermal expansion is often seen in hardwood; it is also the reason why bridges are built with gaps in between its segments in order to maintain its structural integrity during changing temperatures throughout a year. Volumetric expansion is seen in mercury: this is why the mercury in thermometers rise up the column as temperature rises. It is because the volume of the liquid expands. Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding based on the equation for internal energy: ΔU = ± Q ± W Physics First Law of Thermodynamics amount of heat ADDED to a system internal energy of the system ∆U proportional The first law of thermodynamics tells us that an INCREASE in the total internal energy of a system is caused by either (1) transfering heat into the system or (2) performing work on the system. An example of this is heating up a pot of water increases the internal energy of that pot of water. Unsure based on the equation for internal energy: ΔU = ± Q ± W Physics First Law of Thermodynamics amount of work done ON a system internal energy of the system ∆U proportional The first law of thermodynamics tells us that an INCREASE in the total internal energy of a system is caused by either (1) transfering heat into the system or (2) performing work on the system. An example of this is compressing a spring will increase the internal energy of the spring. Unsure based on the equation for internal energy: ΔU = ± Q ± W Physics First Law of Thermodynamics amount of heat LOST from a system internal energy of the system ∆U inverse The first law of thermodynamics tells us that the total internal energy of a system will DECREASE when either (3) heat is lost/dissipated from the system or (4) work is being performed by the system. An example of this is car tires "burning rubber" results in a loss of heat due to frictional forces. Thus, the internal energy of the tires is "lost" (however this heat is gained by the surrounding road and air). Unsure based on the equation for internal energy: ΔU = ± Q ± W Physics First Law of Thermodynamics Physics Pressure amount of work done BY a system internal energy of the system ∆U inverse altitude atmospheric pressure inverse (aka height from the Earth's surface) The first law of thermodynamics tells us that the total internal energy of a system will DECREASE when either (3) heat is lost/dissipated from the system or (4) work is being performed by the system. An example of this is when a Pogo stick bounces off of the driveway surface, it is doing work on the surface (aka its surrounding). Consequently, the internal energy of the Pogo stick is lost. As altitude increases, atmospheric pressure decreases: residents of Denver (5280 feet above sea level) experience atmostpheric pressure equal to 632 mmHg (0.83 atm) travelers making their way through Death Valley (282 feet below sea level) experience atmospheric pressure equal to 767 mmHg (1.01 atm) Unsure Strong demonstrated by Archimedes' Principle: Fbouy = (ρfluid) (g) (Vsubmerged) Physics Physics Physics Hydrostatics Fluid Dynamics Fluid Dynamics density of fluid ρ surrounding an object viscosity η of a fluid proximinity to the center of a closed pipe Buoyant Force acting on said object viscous drag linear speed of fluid proportional proportional proportional By taking a closer look at Archimedes' Principle and Newton's 3rd Law, we see that the buoyant force acting on an object is equal in magnitude to the weight of the fluid it displaces (e.g. if two identical objects of equal mass were placed in either water or mercury, the bouyant force acting on the object submerged in mercury would be greater because mercury is MORE dense than water; the same principle applies for dense air vs. less dense air. A skydiver in dense air would experience more buoyant force than he would if he was in thin air) Strong Thick fluids like whole blood and honey have higher viscosity and thus objects move through these fluids with significantly more viscous drag than they would in fluids with low viscosity, like air or water. Strong Laminar flow is the movement of a fluid characterized by the smooth and orderly flow lines of a fluid that flow parallel to each other. However, the layers will not necessarily have the same linear speed; the layer closest to the wall of a pipe flows more slowly than the more interior layers of fluid because of the friction-like forces against the wall that oppose the movement of fluid. demonstrated by Poiseuille's Law: Strong Q = (πr^4P) / (8ηL) Physics Fluid Dynamics radius r of a closed pipe pressure P exerted by the fluid (deals with real fluids, such as blood) inverse (exponentially, by a power of 4) (assuming flow rate Q is constant) A very slight change in the radius of a pipe has a very significant effect on the pressure gradient. Applied to the human body, decreasing the radius of a blood vessel by some factor (aka vasoconstriction) causes an increase in pressure by the same factor to the fourth power! This illustrates why blood pressure is dramatically increased during increased sympathetic activity; it is because of the blood vessels constricting and decreasing their radius resulting in a dramatic increase in blood pressure. Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding demonstrated by Poiseullie's Law: Q = (πr^4ΔP) / (8ηL) fluid flow rate Q Physics Fluid Dynamics fluid viscocity η (deals with real fluids, such as blood) inverse When comparing two fluids with different viscosities, the fluid with the higher viscosity will have a slower fluid flow rate (also referred to flux). In other words, viscosity causes more internal friction of a fluid, which consequently prevents it from flowing as easily. (e.g. honey has a higher viscosity than water. Thus, a closed pipe with flowing honey has less volume of fluid passing a point per unit time in a closed pipe containing pure water) demonstrated via the Continuity Equation: Strong A1 V 1 = A 2 V 2 Physics Fluid Dynamics cross-sectional area A of a tube linear speed v of a fluid (deals with ideal fluids only) inverse in order to avoid a common confusion, it is important to note that fluid linear speed v and fluid flow rate Q refer to two DIFFERENT things: fluid speed v deals with the linear speed; it is the measure of displacement of a fluid per unit time; it can change depending on the cross-sectional area A Flow rate Q however is a measure of the volume of a fluid that passes a point per unit time; Q is always constant for a closed system and does not depend on changes in cross-sectional area A. This is essentially due to the law of conservation of mass. That being said, if we know the flow rate Q is constant at all points of a closed pipe with moving fluid... the continuity equation tells us that fluids move faster through narrow passages and move more slowly through wider passages. Strong demonstrated via Bernoulli's Equation: P + (1/2)ρv^2 + ρgh = constant Physics Fluid Dynamics linear speed v of a fluid internal hydrostatic fluid pressure P inverse A tube that has a fluid traveling at a very high speed has low pressure. Based on the laws of conservation of energy and mass, if dynamic (moving) pressure "(1/2)ρv^2" increases, then static (still) pressure P has to decrease in order to conserve energy... more on this explained below: Strong based on the law of conservation of energy and Bernoulli's Equation: P + (1/2)ρv^2 + ρgh = constant Physics Fluid Dynamics dynamic pressure of a fluid "(1/2)ρv^2" absolute (hyrostatic) pressure of a fluid P inverse In order for energy to be conserved... as the dynamic pressure, (1/2)ρv^2, (aka the pressure of fluid in motion) increases, then... the static pressure, P + ρgh, (aka the pressure of a static fluid) must decrease. **note since ρ, g, and h remain constant, the only variable in the static pressure term that must change is the absolute pressure P... which makes sense: in a closed system, the density of the fluid doesn't just randomly change, neither does gravity on earth, neither does the height of the pipe. Strong demonstrated by the Venturi Effect, which combines the principles of the Continuity Equation and Bernoulli's Equation. Physics Fluid Dynamics cross sectional area A of a pipe internal hydrostatic fluid pressure P (deals with ideal fluids only) proportional if ↑A ↓v then ↑P + (1/2)ρ↓v^2 + ρgh For horizontal flow, there is a direct relationship between cross-sectional area and pressure exerted on the walls of the tube. Physics Fluid Dynamics # of passage ways in parallel total resistance of fluid inverse Strong During exhalation, the total resistance of the encountered airways increases as the air leaves the alveoli to escape out of the nose and mouth. This increase in total resistance is due to the fact that there are fewer airways in parallel with each other as air exits the respiratory system. Strong based on Coulomb's Law: Felectrostatic = (k q1 q2) / r^2 Physics Electrostatics distance between two charges (r) magnitude of the electrostatic force Fe between the two charges inverse (exponentially, by a power of 2) Imagine a positive attracted to a negative charge at a certain distance away. If the two charges are then moved so that they are separated by twice the distance, then the force of attraction between them would change by a factor of (1 / 2^2), or 1/4. In other words, if the distance is doubled, the square of the distance is quadrupled, and the force between the charges is reduced to 1/4 of what it was originally. (note the similarity of this electrostatic Force relationship and the relationship between distance between two masses and the gravitational Force) Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding by dividing Coulomb's Law by the magnitude of the test charge (q), we arrive at the equation for Electric Field: Physics Physics Physics Physics Electrostatics Electrostatics Electrostatics Electrostatics distance between two charges (r) electical Potential Energy U distance between two like charges distance between two opposite charges Electric Field (E) stability of the system electical Potential Energy U electical Potential Energy U inverse (exponentially, by a power of 2) E = k Q / r^2 From this equation, we see that the distance r still has an inverse square relationship to the Electric Field. Therefore, if the distance between a test charge (q) and the source charge (Q) is doubled, then the electric field magnitude will decrease by 1/2^2 (aka, the electric field would be reduced to 1/4 of what it was originally) Strong inverse A low electrical potential energy indicates that the system is become more stable because electrical potential energy is defined as the amount of work required to move a test charge from infinity to a point in space in an electric field surrounding a charge. For example, a change in electrical potential energy from 10 J to 5 J reflects an increase in stability because it is essentially saying that it takes less work in order to keep the test charge in that final position compared to keeping the test charge in the initial position. Strong inverse Due to the fact that like charges experience repulsive forces, if the two repulsive charges are held close together (aka distance between them shortens), then there will be a higher electrical potential energy because more work is required to hold them in this position. Unsure proportional Due to the face that opposite charges experience attractive forces, if the two attractive charges are held close together (aka the distance between them shortens), then not much work is required to let them move toward each other because they are more stable being close to each other.. Hence, the potential energy (work required) is low. Unsure based on the equation for Magnetic Field: Physics Magnetism distance from the current (r) magnitude of the Magnetic Field B B = (μ I) / (2 π r) inverse frequency of applied force Physics Physics Wave Resonance Sound (that is close to the natural frequency of the system) age amplitude of oscilation frequency range of human hearing proportional inverse Magnetic field is stronger closer to a current-carrying wire. For example, when you decrease the distance to a current-carrying wire by half, the magnitude of the magnetic field is greater by double. Strong If a periodically varying force is applied to a system, then the system will be driven at a frequency equal to the frequency of force. This is known as forced oscillation. This can easily be demonstrated by a child on a swing being pushed by a parent. If the parent pushes the child at a frequency nearly equal to the frequency at which the child swings back toward the parent, then the arc of the swinging child will become larger and larger: the amplitude increases because the force frequency is nearly identical to the swing's natural frequency. Strong On the MCAT, know that frequencies between 20 Hz and 20,000 Hz are generally audible to healthy young adults. However, high frequency hearing generally declines with age. This explains why some elderly people can't hear high pitch ringing of cell phones. Strong Based on the equation for the speed of sound: v = √ (B/ρ) Physics Sound stiffness of a medium through which a sound wave travels (aka, how resistant the medium is to compression) speed of sound traveling through the medium proportional B represents the bulk modulus, a measure of the medium's resistance to compression. B INCREASES from gas to liquid to solid, since gas is most compressible and solids are the hardest to compress. Therefore, sound travels fastest through a solid, such as the bones of the ossicles, than it does through gases, such as air. https://www.youtube.com/watch?v=yF4cvbAYjwI&index=130&list=PL1O_shUH1zgVfrG2lDsMWuicLdsxm-Dzz Unsure Based on the equation for the speed of sound: v = √ (B/ρ) Physics Sound density of a medium through which a sound wave travels speed of sound traveling through the medium inverse ρ represents the density of the medium through which sound travels. Therefore, mathematically, we can see that higher ρ results in a lower v. So when comparing the speed of sound through two mediums with the same material, sound travels fastest though solids with low density than solids with high density. An example of this would be wood vs. metal. https://www.youtube.com/watch?v=yF4cvbAYjwI&index=130&list=PL1O_shUH1zgVfrG2lDsMWuicLdsxm-Dzz Physics Sound temperature of air speed of sound traveling proportional Sound travels faster in hot air than in cold air because in hot air is less dense. Based on the equation for the speed of sound, sound travels fastest through a medium if it is less dense. https://www.youtube.com/watch?v=yF4cvbAYjwI&index=130&list=PL1O_shUH1zgVfrG2lDsMWuicLdsxm-Dzz Strong Unsure Subject Topic Variable X Variable Y Sound distance between a moving source of sound (like a train) and the detector (listener) perceived frequency f ' and perceieved pitch Relationship Explanation / Example / Application Understanding Based on the Doppler Effect: Physics inverse As the sound source and detector move closer relative to each other, frequency of the sound detected increases. (e.g. Imagine how when you standing still at a subway station... when the train is far from you, the pitch starts off low. As the train gets closer, the pitch of the sound emitted gets higher, aka the frequency is higher) Strong Based on the equation for Intensity and the equation for the surface area of a sphere: I = P / A where A = 4πr^2 Physics Sound distance r that a sound wave has traveled Physics Sound amplitude A of a sound wave intensity I of the sound wave (exponentially, by a power of 2) intensity I of the sound wave (exponentially, by a power of 2) inverse proportional A represents the surface area of a sound wave (which radiates outwardly and is therefore spherical so A = 4πr^2). If r is doubled, then A will increase by a factor of 4, resulting in I decreasing by 1/4. For example, if you are three times as far away from a siren than your friend is, then you will experience 1/9 of the siren's sound intensity than your friend does. This partially explains why sounds get softer as we move farther away from the source (the other reason is that some of the power from the sound source dissipates in the air due to nonconservative forces as it travels farther, a phenomenon called attenuation) Intensity of a sound wave and its intensity are related to each other: intensity is proportional the SQUARE of the amplitude. Therefore, doubling the amplitude produces a sound wave that has four times the intensity (aka, for times the energy transfer per area). Strong Strong Mirrors: same side = +f opposite side = –f Physics Optics mirrors vs. lenses positive or negative sign for focal length f Lenses: same side = –f opposite side = +f If you think about "+" as meaning what you "expect" to happen, lenses and mirrors flip flop signs for f because: for mirrors, you EXPECT the image to be on the SAME side as the object for lenses, you EXPECT the image to be on the OPPOSITE side of the light source think about how you expect a bathroom mirror vs. your eyeglasses to works. Unsure Based on equation for index of refraction: Physics Refraction speed of light v in a given MEDIUM index of refraction n inverse n=c/v The slower a light wave travels through a medium, the higher the index of refraction. Strong demonstrated by Snell's Law: Physics Refraction index of refraction n angle ϴ of refraction (measured from the normal) inverse n1 (sin ϴ1) = n2 (sin ϴ2) as n1 increases, then sinϴ1 decreases, meaning that ϴ1 decreases. demonstrated by Snell's Law: Strong n1 (sin ϴ1) = n2 (sin ϴ2) Physics Refraction index of refraction n of a medium through which light travels (aka the density of the medium) bending of the light ray TOWARDS the normal proportional When light enters a medium with a HIGHER index of refraction n (aka, mediums with more density usually have a higher n), the light ray bends TOWARD the normal. This is shown mathematically because if n2 > n1, then ϴ2 < ϴ1. Conversely, if the light travels into a medium where the index of refraction is SMALLER, the light will bend AWAY from the normal. (e.g. when a light ray travels from air to a more dense medium such as glass or water... the light ray will bend toward the normal in the glass or water... because air has a n = 1.0003 and glass/water has a n > 1. Strong Subject Topic Variable X Variable Y Relationship Explanation / Example / Application Understanding related to the equation to locate Dark Fringes (minima) in a slit-lense setup: (a) (sinϴ) = (n) (λ) Physics Diffraction width of slit a in a slit-lens system length y of the central maximum (aka, the central, brightest spot) projected on a screen as a light ray passes through the slit opening inverse As a, the width of the slit, decreases, then sinϴ must increase because nλ is constant for a given fringe. If sinϴ increases, this means ϴ necessarily increases, implying that the fringes are spreading further apart. This is also seen conceptually: When light passes through a narrow opening, the light waves spread out; as the slit narrows, the light waves spread out even more. When lens is placed between the narrow slit and the screen, a pattern consisting of alternating bright and dark fringes can be observed on the screen. As the slit becomes narrower, the central maximum (the brightest and most central fringe) becomes wider. https://www.khanacademy.org/test-prep/mcat/physical-processes/light-and-electromagnetic-radiationquestions/v/youngs-double-slit-problem-solving Physics The Photoelectric Effect intensity of light beam that hits a metal (aka the number of photons per unit time that hits the metal) the number of electrons per unit time liberated from the metal proportional (aka the magnitude of current produced) Strong Based on a phenomenon called the Photoelectric Effect, when a light of a sufficiently high frequency (typically blue to UV light) is incident on a metal, the metal atoms will emit electrons. Provided that the light beam's frequency is above the threshold frequency of the metal, the light beams of greater intensity produce a greater number number of electrons per unit time liberated form the metal (aka producing greater current). Strong Based on the equation for the Energy of a Photon: Physics Physics The Photoelectric Effect Nuclear Binding Energy frequency ƒ of a light beam magnitude of nuclear binding energy released when nucleons bind together the energy E of each photon in the light beam stability of the nucleus E = hƒ proportional proportional As the frequency of the light ƒ increases, then the energy of the photon of light E also increases (becuase h is a constant known as Planck's constant = 6.626e–34). This relationships explain why on the electromagnetic spectrum, waves with higher frequency (and thus shorter wavelength) correlate with higher energy. Strong Nuclei with greater nuclear binding energies are more stable than the unbonded nucleons. When the nucleons come together to form a nucleus (fusion), energy is released, and the magnitude of this energy is proportional to the stability of the newly formed nucleus. Strong Physics Nuclear Binding Energy size of the nuclei stability of the nucleus normal bell-curve In general, intermediate-sized nuclei are more stable than very small nuclei or very large nuclei. Because the binding energy per nucleon is greatest for intermediate-sized atoms (that is, intermediate-sized atoms are most stable), when small atoms combine or large atoms split, a great amount of energy is released. Unsure Demonstrated by the Rate of Nuclear Decay Equation and Exponential Decay Equation/Curves: Physics Exponential Decay the RATE at which a radioactive nuclei decays in a sample (Δn / Δt) the number of radioactive nuclei n that REMAINS (aka the number that has not yet decayed) Δn / Δt = – λ n proportional and N(t) = N0 e^ –λt The rate at which radioactive nuclei decay, Δn / Δt, is proportional to the number that remain, "– n". In other words, the rate of exponential decay slows down when there is less sample remaining. This relationship is also illustrated in a typical exponential decay curve http://schoolbag. info/physics/physics_math/physics_math.files/image653.jpg ; notice how at points on the curve where the slope (aka the rate of change) is the steeper, the percentage of sample remaining is higher. Strong Behavioral Sciences Based on Weber's Law: ∆I / I = k Psychology Psychology Sensation Sexuality magnitude of a stimulus Rating on Kinsey Scale just-noticeable difference (JND) degree of homosexuality proportional proportional It states that the just-noticeable difference for a stimulus is proportional to the magnitude of the stimulus, and this proportion is constant over most of the range of possible stimulii For example, if the just-noticeable difference (JND) of a 10 kg weight is 1 kg, then the JND of a 50 kg weight would be 5 kg. Unsure the Kinsey Scale scores sexuality from a scale of 0-6, with 0 being completely HETERO-sexual and 6 being completely HOMO-sexual. A Kinsey Scale score of 3 would equate to bisexuality. (Ex: man claims to have had sexual relationships with mostly other men, although he occasionally has been attracted to women at times. Therefore, this man would likely score a 4 or 5 on the Kinsey Scale) Strong