Atomic Structure, Moles, and Energy

Atomic Structure and Properties

• The periodic table consists of alkali metals, alkaline earth metals, transition metals, halogens, and noble gases.
• Mass number equals the number of protons plus the number of neutrons (P + N).
• Isotopes are atoms of an element that have different numbers of neutrons.
• Average atomic mass is calculated from the weighted average of isotope masses and relative abundance (frequency).

Moles

• The ideal gas law is represented as PV = nRT.
• Avogadro's number is 6.022 * 10^23.
• At Standard Temperature and Pressure (STP), which is 1 atm and 273K, the volume is 22.4 L/mol.
• Molarity (M) is expressed as moles/L.
• Percent composition is determined by dividing the mass of each element/compound by the total molar mass of the substance.
• An empirical formula is the simplest ratio, while the molecular formula is the actual formula for a substance.

Energy

• Electron potential energy increases with distance from the nucleus.
• Electron energy is quantized, existing only at specific energy levels at specific intervals, not in between.
• Coulomb's law is F = kq1q2/(r^2), where F is the electrostatic force.
• Atoms absorb energy in the form of electromagnetic radiation as electrons jump to higher energy levels; when electrons drop to lower levels (closer to the nucleus), atoms give off energy.

Photoelectron Spectroscopy

• Energy is measured in electronvolts (eV).
• Incoming radiation energy equals the binding energy plus the kinetic energy of the ejected electron.
• Electrons that are further from the nucleus require less energy to eject and, consequently, move faster.
• Each section of peaks in the photoelectron spectrum represents a different energy level (1, 2, 3, etc.).
• Subshells within each energy level are represented by the peaks (1s, 2s, 2p, etc.) and represent where an electron can likely be found orbiting the nucleus.
• s(2) is the first subshell, and p(6) is the second subshell.
• The height of peaks determines the number of electrons in the subshell (e.g., the peak of the p subshell in energy level 2 is 3x that of the s subshell).

Electron Configuration

• Electron configuration, such as spdf, is a shorthand notation that often uses the noble gas configuration as a starting point.
• The Aufbau principle states that electrons fill the lowest energy subshells available first.
• The Pauli exclusion principle restricts that no more than 2 electrons in the same orbital can have the same spin.
• Hund's rule states that electrons occupy empty subshells first.
• Most other transition metal charges vary, but a number of transition metals only have one charge, including: Zn +2, Ag +1, Al +3, Cd +2.

Periodic Trends

• Electrons are more attracted if they are closer to the nucleus or if there are more protons.
• Electrons are repelled by other electrons; if there are electrons between the valence electrons and the nucleus, the valence electrons will be less attracted (shielding).
• Completed shells and subshells are very stable, and atoms will add/subtract valence electrons to complete their shell.
• Atomic radius increases down and to the left of the periodic table.
• Ionization energy and electronegativity increase up and to the right of the periodic table.
• Ionization energy is the energy required to remove an electron from an atom.
• Electronegativity is how strongly the nucleus of an atom attracts electrons of other atoms in a bond.
• Electron affinity is the energy change that occurs when an electron is added to an atom in the gas state, typically exothermic, meaning energy is released.

Molecular and Ionic Compound Structure and Properties

• Atoms are more stable with full valence shells.
• Ionic bonds involve a cation giving up electrons completely.
• Electrostatic attractions in a lattice structure (Metals and nonmetals (salts))
• According to Coulomb's law, a greater charge leads to greater bond/lattice energy and a higher melting point.
• If both ions have equal charges, the smaller radius will have greater coulombic attraction.
• Ionic solids do not have electrons that move around the lattice.
• Ionic solids are poor conductors of electricity.
• Ionic liquids conduct electricity because ions are free to move around, but electrons are still localized around particular atoms.

Metallic Bonds

• Sea of electrons model: positively charged core is stationary, while valence electrons are very mobile.
• Metals bond to form alloys; interstitial alloys are formed with metals of different radii, while substitutional alloys are formed with metals of similar radii.

Molecular Covalent Bonds

• Two atoms share electrons so both atoms achieve complete outer shells.
• These bonds occur between 2 nonmetals.
• Molecular covalent bonds create molecules, in which 2 or more atoms are covalently bonded together.
• A single bond has 1 sigma bond (order 1), the longest length bond, with the least energy.
• A double bond has 1 sigma and 1 pi bond (order 2), an intermediate length bond, with an intermediate energy.
• A triple bond has 1 sigma and 2 pi bonds (order 3), the shortest length bond, with the greatest energy.
• A bond forms when potential energy is at a minimal level.
  • If atoms are too close, potential energy increases due to repulsive forces, while if atoms are too far, potential energy is near 0 because attractive forces are very weak.
  • Minimal potential energy occurs when repulsive and attractive forces are balanced.
• Network covalent bonds form a lattice of covalent bonds and are poor conductors with high melting and boiling points.

Conductivity

• Conductivity of different substances in different phases:
  • Ionic: No (Solid), Yes (Aqueous), Yes (Liquid), No (Gas)
  • Molecular covalent: No for all phases
  • Network covalent: No (Solid), N/A (Aqueous), No (Liquid), No (Gas)
  • Metallic: Yes (Solid), N/A (Aqueous), Yes (Liquid), No (Gas)

Lewis Dot Structures

• Resonance is used for bond order calculations, by averaging together all possible orders of a specific bond.
• Boron is stable with 6 electrons and does not need a full octet.
• Atoms of elements from n=3 or greater (those with a d subshell) can have expanded octets with [8,12] valence electrons on the center atom, and noble gases can form bonds by filling empty d orbitals with electrons.
• Formal charge is calculated as the number of valence electrons minus assigned electrons (1 e- for each line "shared" bond); neutral molecules have a formal charge of 0.

Molecular Geometry (VSEPR)

• Double and triple bonds have more repulsive strength than single bonds, so they occupy more space.
• Lone electron pairs have more repulsive strength than bonding pairs, so molecules with lone pairs will have slightly reduced angles between terminal atoms.
• Hybridization depends on how many atoms are attached (sp, sp2, sp3, sp3d, etc.).

Intermolecular Forces and Properties

• Covalent bonds where electrons are unequally shared create polar covalent bonds.
• Dipoles are caused by polar covalent bonds and are a pair of opposite electric charges separated by some distance, like partial charges on atoms in a polar covalent bond.
• If 2 identical atoms bond (ex. Cl-Cl) the electrons are equally shared, creating a nonpolar covalent bond with no dipole.
• Bonds can be polar, as can molecules, depending on the molecular geometry (and polarity of bonds - secondary).
• In polar molecules, more electronegative atoms will gain a negative partial charge.
  • The central atom will usually be positive, with the exception of hydrogen (terminal), which is usually positive since it has less electronegativity.

Intermolecular Forces

• Intermolecular forces are the forces between molecules in a covalently bonded substance that need to be broken apart for covalent substances to change phases.
• Changing phase: ionic substances break bonds between individual ions; covalent substances keep bonds inside a molecule in place but break bonds between molecules.
• Dipole-dipole forces have polar molecules where the positive end of one molecule is attracted to the negative end of another molecule.
  • Greater polarity leads to greater dipole-dipole attraction and a larger dipole moment, resulting in higher melting/boiling points, though they are relatively weak overall, so these substances melt and boil at low temperatures.
  • Hydrogen bonds are a special type of dipole-dipole attraction where the positively charged hydrogen end of a molecule is attracted to the negatively charged end of another molecule containing an extremely electronegative element (F, O, N)
  • These are much stronger than normal dipole-dipole forces since a hydrogen atom “sharing”/giving up its lone e- to a bond is left with no shielding, resulting in higher melting/boiling points than substances held together only by other types of IMF (intermolecular force)
• London dispersion forces occur in all molecules and are very weak attractions due to the random motion of electrons on atoms within molecules (instantaneous polarity). Molecules with more e- experience greater LDF (more random motion). A higher molar mass usually means greater LDF (as mass increases, e- increases for the molecule to remain electrically neutral).
• Ionic substances are generally solid at room temperature; melting them requires lattice bonds to be broken, which is a necessary energy determined by coulombic attraction.
• Covalent substances (liquids at room temp) boil when intermolecular forces are broken; for molecules of similar size, from strongest to weakest: hydrogen bonds, permanent dipoles, LDF (temporary dipoles - greater for larger molecules). Melting/boiling points of covalent substances are LOWER than for ionic substances.

Bonding/Phases

• Substances with weak IMF (LDF) tend to be gases at room temp (N2); substances with strong IMF (hydrogen bonds) tend to be liquids at room temp (H2O)
• Ionic substances do not experience IMF - since ionic bonds are stronger than IMF, ionic substances are usually solids at room temp

Vapor Pressure

• Molecules in a liquid are in constant motion; if they hit the surface of the liquid with enough kinetic energy, they can escape the intermolecular forces holding them to other molecules and transition into the gas phase
• Vaporization (NOT boiling) occurs even without outside added energy.
• Temperature and vapor pressure are directly proportional, and at the same temperature, vapor pressure is dependent on strength of IMF (stronger IMF, lower vapor pressure)

Solution Separation

• Solutes and solvents - like dissolves like.
• Paper chromatography places a piece of filter paper with substance on the bottom into water.
  • More polar components of substance travel further up the filter paper with the polar water and distance substance travels up the paper measured by retention/retardation factor Rf = (distance traveled by solute - substance being separated)/(distance traveled by solvent front - water) then Stronger attraction - larger Rf.
• In column chromatography, a column is packed with a stationary substance then a separable solution (analyte) is injected, adhering to stationary phase then another solution (eluent - liquid/gas) is injected into column - more attracted analyte molecules will move through faster and leave column first.
• Distillation takes advantage of different boiling points of substances by boiling a mixture at an intermediate point.
• Vapor is collected, cooled, and condensed back to a liquid separate of leftover liquid.

Kinetic Molecular Theory

• Kinetic energy of a single gas molecule: KE = ½ mv^2.
• Average kinetic energy of a gas depends on the temperature (directly proportional), not the identity of the gas (different gases will have same KE at same temp).
• Ideal gases have insignificant volume of molecules, no forces of attraction between molecules, and are in constant motion without losing KE.
  • Deviations occur at low temperatures or high pressures (gas molecules are packed too tightly together), in which case the Volume of gas molecules becomes significant (less free space for molecules to move around than predicted), and in which gas molecules attract one another and stick together (real pressure is smaller than predicted pressure).
• Maxwell-boltzman diagrams exhibit that higher temperature leads to greater KE and a greater range of velocity, and smaller masses have greater velocities to achieve the same KE.
• Effusion is the rate at which a gas escapes from a container through microscopic holes caused by high to low pressure, greater speed, greater temp, greater rate of effusion, so that if at same temp, gas with lower molar mass will effuse first.

Equations

• Ideal gas equation: PV = nRT and R=0.0821.
• Combined gas law: P1V1/T1 = P2V2/T2.
• Dalton's law: P(total) = Pa + Pb + Pc + ....
• Partial pressure: Pa = P(total)*(moles of gas A)/(total moles of gas)
• Density: D = m/V, so From ideal gas law: Molar mass = DRT/P
• E=hv,
  • E = energy change; h = Planck's constant 6.626*10^-34; v = frequency
• C = lambda * v,
  • C = speed of light 2.998*10^8; v = frequency; lambda = wavelength.
• Beer's law: A = abc
  • A = absorbance; a = molar absorptivity (constant depending on solution); b = path length of light through solution (constant); c = concentration of solution.
  • Colorimetry - direct relationship between concentration and absorbance.

Chemical Reactions

• Synthesis: everything combines to form one compound.
• Decomposition: one compound + heat is split into multiple elements/compounds.
• Acid-base reaction: Acid + base -> water + salt.
• Oxidation-reduction (redox) reaction: changes the oxidation state of some species
• Combustion: substance with H and C + O2 -> CO2 + H2O.
• Precipitation: aqueous solutions -> insoluble salt (+ more aq sometimes).
  • Can be written as net ionic; those free ions not in net ionic are spectator ions.

Solubility Rules

• Alkali metal cations or ammonium (NH4+) cations are ALWAYS soluble.
• Compounds with a nitrate (NO3-) anion are ALWAYS soluble.

Common Polyatomic Ions

• Acetate: C2H3O2-
• Ammonium: NH4+
• Carbonate: CO32-
• Chlorate: ClO3-
• Chlorite: ClO2-
• Chromate: CrO42-
• Cyanide: CN-
• Dichromate: Cr2O72-
• Bicarbonate: HCO3-
• Bisulfate: HSO4-
• Bisulfite: HSO3-
• Hydroxide: OH-
• Hypochlorite: ClO-
• Nitrate: NO3-
• Nitrite: NO2-
• Oxalate: C2O42-
• Perchlorate: ClO4-
• Permanganate: MnO4-
• Phosphate: PO43-
• Sulfate: SO42-
• Sulfite: SO32-

Calculations

• Percent error: 100 * abs(experimental - expected)/(expected).
• Combustion analysis uses the law of conservation of mass (if x g of CO2 is produced, find g of C which will be starting amount).
• Gravimetric analysis is used when asked to determine the identity of a certain compound. -Find g of component produced, then use mass percent (g found / total sample mass) Compare to mass percent of options (molar mass of component / molar mass of entire compound)

Oxidation States

• Neutral atoms not bonded to other atoms have an oxidation state of 0
• Monoatomic ions have an oxidation state equal to the charge on that ion (ex. Zn2+ will be +2)
• Oxygen is -2 (EXCEPTION: in hydrogen peroxide, H2O2, O is -1)
• Hydrogen is +1 with nonmetals, -1 with metals
• In absence of oxygen, most electronegative element in a compound will take an oxidation state equal to its usual charge (ex. F is -1 in CF4)
• IF none of the above rules apply, determine the oxidation state by adding up all elements' oxidation states to 0/charge on ion C, N, S, P frequently vary oxidation states (low electronegativity)

Redox Reactions

• Write full reaction as 2 half reactions (oxidation and reduction; OIL RIG)
  • Add H2O to compensate for oxygen on one side
  • Add H+ to compensate for H from H2O on other side
  • Balance 2 half reactions to have the same number of electrons and add them together to produce one complete reaction
    • ACIDIC: stop here
    • BASIC: Add OH- to both sides - enough for all H+ on one side to be converted to H2O; then cancel out H2O so it only remains on one side

Acids and Bases

• Color change signals the end of a titration (can be redox or acid/base)
• Acids are capable of donating protons (H+); bases are capable of donating electrons
• Species with the H+ ion are acids, same species but without H+ is a base - conjugate acid/base pairs
• Water can act as an acid or base - amphoteric

Kinetics

• Rate = k [A]^x [B]^y [C]^z
• Can calculate x, y, z via a table from (concentration factor)^x = (rate factor)
• K is only dependent on temperature (always increases with T)
• Keq = K1 (rate constant of forward reaction) / K2 (rate constant of reverse reaction)

Equations Relating to Kinetics

• K calculated by dividing any rate in table by the concentrations to their respective powers
• Units for rate are M/s, units for concentration are M -> calculate units for k from there
• If A + 2B + C -> D; rate of formation of D = rate of disappearance of A and C = 0.5* rate of disappearance of B
• Zero-order -Rate = k -Concentration vs time has slope -k
• First-order -Rate = k[A] -In[A] vs time has slope -k -In[A]t = -kt + In[A]0
• Second-order -Rate = k[A]^2 -1/[A] vs time has slope k -1/[A]t = kt + 1/[A]0
• Half-life -First order reactions only have a constant half life -t1/2 = In(2)/k = 0.693/k
• Chemical reactions occur because reactants are constantly moving and colliding with one another When reactants collide with sufficient energy (activation energy Ea), a reaction occurs
  • Gaseous/aqueous: increased concentration increases rate of reaction (more likely to collide) Stirring increases reaction rate for heterogeneous mixtures (causing heterogeneous mixture to move around increases collisions; insignificant once the mixture becomes homogeneous due to the number of collisions happening due to inherent motion of aq molecules) Greater temp increases reaction rate (greater fraction of reactant molecules has sufficient energy to exceed activation energy barrier - vertical line on Maxwell-Boltzmann with multiple temps) Reactions only occur if reactants collide with correct orientation to break the right bonds

Reaction Energy Profile

reactions that are produced in a mechanism but are also fully consumed and do not appear in the balanced equation are intermediates Adding up all mechanism steps and canceling out different species leads to the balanced reaction

• Elementary steps with 2 reactants (even if they are the same) are bimolecular; elementary steps with 1 reactant are unimolecular
• Speed is determined by slow step (rate determining step) Consistency is determined by slow step and those leading up to it -Make rate for slow step (ex. If X + B -> Y, rate = k[X][B]) -Substitute in rate for X from above equilibrium reaction -Compare to actual reaction's rate equation -Slow step has highest activation energy
• Catalysts Catalysts increase rate of chemical reaction without being consumed in the process Catalysts do not appear in balanced equation In a reaction mechanism, catalysts enter first, then exit

Catalysis

catalysis (reaction with a catalyst) Surface catalysis - reaction intermediate is formed enzyme catalysis - catalyst binds to reactants to reduce activation energy Acid-base catalysis - reactants lose/gain protons to change reaction rate

Thermodynamics

• Temperature/heat is the average amount of kinetic energy due to molecular motion in a given substance Heat is the energy flow between 2 different substances at different temperatures first law of thermodynamics: energy can be neither created nor destroyed when bonds are formed, energy is released; when bonds are broken, energy is absorbed
• Exothermic - energy transferred from system to surroundings (delta H is negative) More energy is released when the product bonds form than is necessary to break reactant bonds endothermic - energy transferred from surroundings into system (delta H is positive) More energy is required to break reactant bonds than is released when bonds in products form [Image] energy diagrams
• Endothermic Reaction (activation energy larger than exothermic reaction)
• Exothermic Reaction (activation energy less than endothermic reaction) [End Image]

Enthalpy

• enthalpy of formation Change in energy when one mole of a compound is formed from its component pure elements under standard conditions (25C/298K)
• Delta Hf = delta Hf for products - delta Hf for reactants Multiply delta Hf for each product/reactant by the coefficient if delta Hf is negative, energy is released when the compound is formed, so the product is more stable (exothermic) if delta Hf is positive, energy is absorbed when the compound is formed, so the product is less stable than its constituent elements (endothermic) Heat of formation is 0 when the pure element is in its standard state (ex. H2(g) or F2(g))

Bond Energy

• delta H (J) = bond energies of reactants - bond energies of products Multiply bond energies for each bond by the coefficient

Hess's Law

• Finding delta H for the overall reaction from knowing delta H for the steps of the reaction Flipping the equation flips the sign of delta H
• Multiplying/dividing the equation by a coefficient multiplies/divides delta H by that coefficient Adding/subtracting equations adds/subtracts their delta H values the breaking of solute bonds - energy required is equal to the lattice energy (positive delta H since bonds are being broken; hydration energy = step 2 + step 3 energies; Enthalpy of solution = step 1 + 2 + 3 energies

Enthalpy of Solution

• Enthalpy of solution in ionic substances dissolving in water: first breaking of solute bonds - energy required is equal to the lattice energy (positive delta H since bonds are being broken), then Separation of solvent molecules - water molecules must spread out to make room for the solute ions (requires energy to weaken the IMF between water molecules - positive delta H); 3: Creation new attractions - free floating ions are attracted to the dipoles of water molecules (energy is released - negative delta H) hydration energy = step 2 + step 3 energies; Enthalpy of solution = step 1 + 2 + 3 energies

Phase Changes

• Solid to gas is sublimation, gas to solid is deposition When vapor pressure equals the surrounding atmospheric pressure, the liquid boils - lower atmospheric pressure (high elevation) means a lower boiling point enthalpy of fusion: energy to melt a solid.
• Enthalpy of Vaporization is when energy has vaporizes to turn a liquid into a has. Has condenses when a substance condenses. IMF is stronger for a liquid than a gas, and for a solid than a liquid, and the stronger IMF is more stable, therefore going from a gas to a liquid or a liquid to a solid releases energy (exothermic) as heat is added to a substance, the temperature of the substance can increase OR it can change phases, but not both at once when a substance is changing phases, the temperature of the substance remains constant

Calorimetry

• Specific heat is the amount of heat required to raise the temperature of one gram of a substance by one degree C/K; a substance with Large specific heat can absorb much heat without a significant temperature change and Low specific heat can quickly changes temperature.
• Heat added J or cal q = mcΔT and and q1 = q2 for mixtures
• calorimetry: measurement of heat changes during chemical reactions (find J from q, find mol from stoich, divide the two to find delta H(J/MOL))

Equilibrium

• reaction is at equilibrium when all concentrations stop changing , reaction does not stop - rate of forward and reverse reactions become equal. All concentrations do NOT sum to initial concentration of reactants, so that in reaction 2A -> B, concentration of A will decrease 2x as much as concentration of B increases Equilibrium Expression

Equations and Constants

• FOR the reaction aA + bB -> cC + dD: Keq = ([C]^c * [D]^d) / ([A]^a + [B]^b), so that [A], etc. are molar concentrations/partial pressures at equilibrium, products IN numerator, reactants in denominator. coefficients in balanced equation become exponents in equilibrium expression only gaseous and aqueous species are included in the expression Keq has no units K>1 favors forward reaction; K<1 favors reverse reaction different equilibrium constants: Kc FOR molar concentrations Kp FOR partial pressures Ksp is solubility product (no denominator because reactants are solids) Ka is acid dissociation constant FOR weak acids Kb is base dissociation constant FOR weak bases Kw describes the ionization of water (Kw = 1*10^-14) different equilibrium manipulation constants:Keq FOR a flipped reaction is the reciprocal of Keq FOR initial reaction Keq FOR a reaction multiplied by a coefficient is the initial Keq TO the power of the coefficient
• Le Chatelier's principle states is shifting is the reaction to be at equillibrium. Increasing pressure increasing concentration of reactants shifts reaction TO favor products (forward) and vice versa

Thermodynamics and Solutions

Increasing temperature IN an endothermic reaction shifts the reaction TO favor products (forward); increasing temperature IN an exothermic reaction shifts the reaction TO favor reactants (reverse) Treat "heat" AS a reactant (endothermic) OR product (exothermic) TO see shifts like with concentration change diluting aqueous equilibriums shifts the reaction TO favor the side with more aqueous species; removing water (evaporation) shifts the reaction TO favor the side with less aqueous species shifts caused by concentration/pressure are temporary shifts and DO not change

Reactant Quotient

• Q CAN be calculated AT any point with current concentrations/pressures; Keq CAN only be calculated with equilibrium values, SO that FOR the reaction aA + bB -> cC + dD: Q = ([C]^c * [D]^d) / ([A]^a + [B]^b) [A], etc. ARE initial molar concentrations OR partial pressures if QK EQUILIBRIUM

Electrolye Solubility

A salt is considered soluble "IF more than 1g CAN be dissolved. Soluble salts ARE assumed. Most solids BECOME more soluble. Soluble products FOR the reaction. the FORmulas for Reactant Quotient.

Solubility Product

A salt considered soluble. Soluble salts with solid or liquid.

Common Ion Effect

is ions IS present

Acids and Bases