CHEM 1400 Study Guide PDF Fall 2022

CHEM 1400 Study Guide By Amanda Weiner Unit 1: Atoms Core Understandings What you should be able to do: Unit 2: Electrons and Orbitals Core Understandings What you should be able to do: Unit 3: Bonding, Molecular Shape, and Macroscopic Properties Core Under...

CHEM 1400 Study Guide By Amanda Weiner Unit 1: Atoms Core Understandings What you should be able to do: Unit 2: Electrons and Orbitals Core Understandings What you should be able to do: Unit 3: Bonding, Molecular Shape, and Macroscopic Properties Core Understandings What you should be able to do: Unit 4: Stoichiometry Core Understandings What you should be able to do: Unit 5: Systems Thinking Core Understandings What you should be able to do: Unit 6: Chemical Reactions Core Understandings What you should be able to do: Unit 7: Kinetics and Equilibrium - How Far / How Fast Core Understandings What you should be able to do: 1 Unit 1: Atoms Core Understandings ➔ Matter is made of atoms which are the smallest distinguishable part of an element. ➔ Atoms are composed of subatomic particles (protons, neutrons, and electrons), and the number and arrangement of these particles defines the properties and reactivity of the atom. ➔ Although subatomic particles are too small to see by eye, their existence was proposed based on experimental observations. ➔ We use models (mental and physical) to represent different chemical entities; We use different models for different purposes. ➔ Theories (such as atomic theory) change over time according to the evidence available. ➔ The periodic table organizes elements according to their characteristic properties, and it can be used to predict how elements will combine into more complex molecules. ➔ Attraction and repulsion between charged particles (electromagnetic forces) explain the structure of atoms and the forces between atoms that cause them to form molecules. ➔ Energy dictates how atoms and molecules rearrange, combine, and interact. ➔ The states, properties, and reactions of matter depend on the types, interactions, and motions of atoms within it. Therefore, bulk matter can be understood by looking at the atomic level. What you should be able to do: 1. Make an argument (claim, evidence, reasoning) for the existence of: a. Atoms Through advanced imaging technology (electron microscopy), scientists are able to see atoms. b. Electrons We know that electrons exist because of the cathode-ray tube experiment performed by Thomson. In his experiment, Thomson applied high energy to different materials to cause a stream of particles to be expelled. He placed a negatively and a positively charged plate on opposite sides of the tube and observed that the particles emitted always bent away from the negatively charged plate. To conclude that all atoms must have these particles, he repeated his experiment multiple times with different metals and no matter what, the particles were always emitted and always bent away from the negative charge. This led him to the conclusion that all matter must contain these tiny (they were easy to bend and therefore lightweight), negatively charged particles. c. The existence of small, massive, and positively charged nucleus Rutherford discovered the existence of a small, positively charged nucleus through his gold foil experiment. In this experiment, Rutherford shot alpha particles at a thin piece of gold foil surrounded by a detector. Based on Thomson’s plum pudding model of the atom, Rutherford expected almost all of the alpha particles to pass through the gold foil to the detector. However, Rutherford observed alpha particles that were deflected at angles, some coming straight back to the detector, though most went straight through. Rutherford 2  reasoned that the alpha particles must be hitting (or going very close to) something dense and positively charged to experience such deflections. Since so many alpha particles still went through the gold foil, Rutherford also concluded that atoms are mostly empty space, and the concentrated mass of positive charge must be very small. 2. Draw diagrams/pictures of the various models of the atom as they changed over time. Dalton Thomson Rutherford Bohr (Quantum model) Quantum Mechanical Model (Electron Orbital) pz 3. Use the models to explain how and why the model of the atom changed over time as new evidence arose. Dalton viewed atoms as small, indivisible units that behaved similar to billiard balls. Thomson devised an experiment in which he was able to emit charged particles from different materials in a cathode-ray tube. He observed that these tiny particles always bent away from the positively charged plate, no matter the orientation of the charged plates or the material that they came from. Since atoms are neutrally charged, he figured these negative particles must exist in a positive body. Rutherford performed his gold foil experiment which led him to the conclusion that atoms are mostly empty space and that they have dense, positively charged nuclei. He fired alpha particles at a sheet of gold and, based on Thomson’s “plum pudding” model of the atom, expected them to pass right through. However, Rutherford observed that while most particles did pass right through, some of them were returned back towards the particle emitter. This led him to the conclusion that atoms were mostly empty space, but had a massive, positively charged nucleus. Bohr developed his model based on experimental data for the atomic emission spectra of hydrogen. He knew that electron energies existed in discrete levels. His model of the 3  atom showed orbitals of discrete energies, however, these orbital levels were only accurate for atoms or ions with one electron (e.g. H, He⁺, Li²⁺). In the mid-1920s, three physicists (Heisenberg, de Broglie, and Schrödinger) developed the wave (quantum) mechanical model of the atom. This model describes electrons as existing in orbitals (NOT circular/Bohr orbitals) defined by a specific wave function. This model also includes the Heisenberg uncertainty principle: we cannot know the exact position and velocity of electrons. 4. Explain how a scientific theory differs from everyday use. In everyday language, a “theory” is a guess about the way something works. (In science, this would be considered a “hypothesis.”) In scientific language, a “theory” is “a well- substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment” (American Association for the Advancement of Science). (Oregonstate.edu) 5. Compare the tenets of the various atomic theories that stayed the same over time and those that changed. Refer to numbers 2 and 3 6. Develop a scientific question, a scientific explanation, and use evidence and data to make an argument. (Refer to experiments discussed in #3) 7. Construct an atomic level explanation for why two isolated atoms would attract each other as they approach, and why they would repel if they get too close together. Each atom contains a positive nucleus and negatively charged electrons. An isolated atom’s positive nucleus would be attracted to the electrons of the other isolated atom, and the atom’s electrons would be attracted to the other’s positive nucleus. However, when the atoms get too close, the like charges from both of their electrons and from both of their nuclei would cause them to repel each other. 8. Show and explain how data can be used to represent the Law of Definite Proportions or Law of Multiple Proportions. The law of definite proportions = a given compound always contains exactly the same proportion of elements by mass (Zumdahl, Zumdahl). Sulfuric acid, H2SO4, is always composed of 2 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms. HSO42- is called hydrogen sulfate; losing one hydrogen atom (altering the proportions) changes the identity of the compound. The law of multiple proportions = when two elements form a series of compounds, the ratios of the masses of the second element that combine with 1 gram of the first element can always be reduced to small whole numbers (Zumdahl, Zumdahl). ○ Example from Zumdahl, Zumdahl: Mass of Nitrogen that Combines with 1 gram of Oxygen Compound A 1.750 g 4  Compound B 0.8750 g Compound C 0.4375 g The ratios of nitrogen that combine with the 1 g of oxygen should be able to be reduced to small whole numbers: 𝐴 1.750 2 𝐵 0.8750 2 𝐴 1.750 4 = = = = = = 𝐵 0.8750 1 𝐶 0.4375 1 𝐶 0.4375 1 All of these ratios can be reduced to whole numbers, therefore, they depict the law of multiple proportions. Compound A: NO4 Compound B: NO2 Compound C: NO4- 5 Unit 2: Electrons and Orbitals Core Understandings ➔ Electromagnetic radiation has both wave and particle properties. ➔ Electrons in atoms have quantized energy levels. ➔ Electrons (and all forms of matter) have both wave and particle properties. ➔ Periodic trends result from the quantized arrangement of electrons in atoms. ➔ Most periodic trends can be explained using the idea of effective nuclear charge. ➔ Atomic theories have changed over time as new experimental evidence arises. What you should be able to do: 1. Use the relationship between the frequency and wavelength and velocity of a wave to calculate any one (frequency, wavelength, or velocity) given the other two. 𝜆 = 𝑐/𝜈 ○ Relates the wavelength to the frequency of the wave and the speed of light. Speed of light (c): 3.00 × 108m/s ○ Units: [m, nm] = [m/s]/[Hz, s-1] Think that the units between frequency and speed of light should cancel out to leave only meters (or nanometers). 𝜆 = ℎ/𝑚𝑣 ○ Relates the wavelength to Planck’s constant and momentum (product of mass and velocity) Planck’s constant (h):6.626 × 10−34 𝐽 ⋅ 𝑠 ○ Units: [m] = [J⋅s] / [kg][m/s] 2. Draw and compare two waves of different frequency, wavelength, or amplitude. 3. Make an argument (claim, evidence, reasoning) about why we can consider electromagnetic radiation as a wave. Claim: Electromagnetic radiation behaves as a wave. Evidence: (from the double-slit experiment, watch here) When light is passed through two-slits, an interference, or diffraction, pattern is produced. 6  Reasoning: If light behaved only as a particle, the photons should pass through the two slits to show two slits of light on the detector. However, this is not what is observed. Rather, a series of dark and light bands is produced. This diffraction/interference pattern is produced by constructive and destructive interference among the waves. Constructive interference occurs between two waves in the same phase; they “add” to each other to intensify the light (creating the light stripes). Destructive interference occurs between waves in opposite phases; they cancel each other out, creating the dark stripes. (image and explanation here) 4. Make an argument (claim, evidence, reasoning) about why we can consider electromagnetic radiation as a particle. Claim: Electromagnetic radiation behaves as a particle. Evidence: (from Einstein’s photoelectric effect) No electrons are emitted from a specific metal below a certain frequency threshold; this was observed regardless of the intensity of the light. When the frequency of the light was above the frequency threshold, the amount of electrons emitted increased with the intensity of the light. Also when the frequency was above the threshold, increasing it increased the kinetic energy with which the electrons were emitted. Reasoning: Based on these observations, Einstein rationalized that electromagnetic radiation must be quantized, in little packets called photons, and the threshold frequency represents the minimum amount of energy needed to remove an electron; the “extra” energy given to the electron manifests as kinetic energy. (Zumdahl, Zumdahl) 5. Explain how (and why) different atoms emit different wavelengths of light. Atoms emit wavelengths when they go from an excited state to a less excited state. When the electrons move down to another discrete energy level, the excess energy is released as a photon of light. The wavelength of light (the color) is dependent on the change in electron energy; they are inversely proportional to each other. 7 6. Compare and contrast atomic emission and absorption spectra and how they arise. (image source) Emission spectra depict the wavelengths of light emitted by an atom when its electrons move to a lower energy level. This is why an emission spectrum looks black with individual colored lines. An absorption spectrum is the opposite; black lines on a rainbow background. Each black line represents the wavelength of light that has the right energy to bring an electron to a more excited energy level. 7. Make an argument for why spectra are direct evidence for the existence of quantized energy levels in an atom. When light is passed through a prism, a continuous spectrum (all the colors of the rainbow) is observed. The linear emission spectra of atoms show different lines corresponding to the specific wavelengths of light emitted by the atom. The fact that the spectra show individual lines show that the radiation emitted is not continuous. Rather, the energy is quantized; it is emitted in discrete packets of energy. 8. Describe how the wave properties of the electron are taken into account in the current model of the atom. After de Broglie showed that particles can exhibit wavelike behavior, Schrödinger applied this idea to electrons. Since electrons can only exist at specific energies, he thought of them like standing waves. He developed his equation, Ĥ𝜓 = 𝐸𝜓(simplified), in which 𝜓is a wave function. Solving Schrödinger’s equation yields multiple solutions (as wave functions). The specific wave functions for an atom are also its atomic orbitals (where the electron is likely to be 90% of the time). “The quantum mechanical model of the atom”, from Khan Academy 8 9. Draw and recognize pictures of s, p, and d orbitals. 10. Describe an atomic orbital and what it represents. An atomic orbital is a wave function solution to the Schrödinger equation. Each orbital is a region of probability in which an electron in that orbital may be found. 11. Identify core and valence electrons for elements. A (neutral) atom has the same number of total electrons as it has protons. Not including the transition metals, the easiest way to determine valence electrons for an element is to count which group it is in. The other electrons are all core electrons. Example with phosphorus: Phosphorus has atomic number 15 and is in period 5A. Therefore, based on the previous ruling, it has five valence electrons and ten core electrons. Example with calcium: Calcium has atomic number 20 and is in period 2A. Therefore, calcium has two valence electrons and eighteen core electrons. 9 12. Describe how the model of the atom changed from Dalton to Thomson, Rutherford, Bohr to Schrodinger, explaining why each model changed and pointing out the problems with the previous model. Refer to Unit 1, numbers 2 and 3 13. Choose an atomic model to explain a phenomenon (ex., atomic line spectra) and explain why you chose it. Bohr’s model of hydrogen, Khan Academy 14. Describe how ionization energies support the idea of quantized energy levels in atoms. Ionization energy is the energy required to remove an electron from an atom. It requires a specific (minimum) amount of energy to remove an electron from an atom; it must be enough energy to overcome the attractive force between the positively charged nucleus and the electron. Any amount of energy less than the minimum will not be enough to remove the electron. 15. Predict trends in ionization energies based on placement in the periodic table. As you continue across a period, ionization energy gets greater. ○ Across a period, atoms increase in their number of protons. With more protons, these atoms can keep a tighter hold on their electrons. As you go down a group, ionization energy decreases. ○ As you go down a group, the atoms get larger because they have more electron orbitals. Because of this, the attraction between the nucleus and the valence electrons is weak; the layers of electron orbitals “shield” the valence electrons, making them easier to remove. 16. Explain the concept of effective nuclear charge and how it affects the size of atomic and ionic radii. Effective nuclear charge is the net charge experienced by an electron. It is estimated by the element’s atomic number minus the number of shielding electrons. As you go across a period from left to right, the radii of the atoms decreases. Even though there are more electrons, they are pulled in tighter by the also increasing number of protons in the nucleus. 17. Predict the relative sizes of isoelectronic atoms and ions. Isoelectronic atoms are those that have the same number of electrons. An isoelectronic series (all have 10 electrons) in order of decreasing radii: O 2-, F-, Na+, Mg2+, Al3+. The atoms with a higher positive charge are pulling in their electrons much tighter because there is a higher attractive force between the nucleus and electrons. 10 Unit 3: Bonding, Molecular Shape, and Macroscopic Properties Core Understandings ➔ Macroscopic properties of a substance can be explained by interactions at the molecular level. ➔ A number of different models are used to explain bonding (e.g. valence bond, molecular orbital), and different models are invoked to explain different phenomena. ➔ To explain bonding we need to consider both electrostatic ideas and quantum mechanical ideas. ➔ 3D molecular structures, combined with knowing the relative electronegativity of atoms within a molecule can be used to infer the type and strength of intermolecular forces between molecules, and hence the macroscopic properties. ➔ Interactions of atoms with other atoms (and molecules with other molecules) can be explained and predicted using the concept of forces and energy. What you should be able to do: 1. Predict and explain the changes in the potential energy, the kinetic energy, and the total energy as two isolated atoms approach each other. As two atoms approach each other, their potential energy decreases. Since the total energy of the system must remain the same, the kinetic energy increases as they approach each other. 2. Draw an energy diagram showing potential energy as a function of internuclear distance. Y → (potential energy axis) positive potential energy represents repulsive forces; negative potential energy represents attractive forces X → (internuclear distance axis) shows the distance between the nuclei of two atoms A → this point is where the two atoms have the lowest potential energy -- the maximum attractive force; if the atoms are able, this is the distance at which they will bond. The depth of this “well” indicates the strength of the bond: the deeper the well, the stronger the bond (stronger attractive force!) When the internuclear distance is at or near zero, the atoms are experiencing nucleus- nucleus repulsion. At the distance of the minimum potential energy, the atoms are 11  experiencing nucleus-electron attraction. As the internuclear distance increases, the atoms experience electron-electron repulsion. 3. Contrast the energy change that occurs when two pairs of atoms combine (for example, what is different about the energy change for two He atoms versus two H atoms). The well is deeper for the hydrogen interaction than for the helium interaction. This indicates that the hydrogen-hydrogen interaction is stronger than the helium-helium interaction. The location of the minimum potential energy of the helium interaction is at a greater internuclear distance than that of hydrogen. This is because helium is a larger atom than hydrogen. 4. Explain the forces and energy changes that take place when a bond is formed. Two atoms move together because of the attraction between one atom’s electron cloud and the other’s positively charged nucleus (and vice versa), increasing their kinetic energy. As the atoms move closer together, they start experiencing repulsive forces. At the bond length (or distance of minimum potential energy), the attractive forces between the atoms are stronger than the repulsive forces. 5. Explain why isolated atoms don’t have macroscopic properties like melting points, boiling points, while macroscopic materials do. Melting points and boiling points come from the intermolecular forces that act upon molecules. Isolated atoms are not interacting via intermolecular forces and therefore cannot have a melting or boiling point. 12 6. Predict, draw models (pictures), and explain why macroscopic properties such as relative melting points and boiling points for different compounds depend on the kind of bonding (intermolecular interactions) that exist in molecules. Comparison between ethane and ethanol: Ethanol has a higher boiling point (and melting point) than ethane because it has stronger intermolecular forces. Ethane molecules are only able to interact with each other via London dispersion forces, which are very weak. Ethanol molecules can interact with each other via LDFs, hydrogen bonding, and dipole-dipole interactions. It requires less energy to break up the LDFs among ethane molecules than it does to break up dipole-dipole interactions and hydrogen bonding among ethanol molecules. 7. Predict/rank relative melting and boiling points of given compounds. Compare the boiling points of ethyl methyl ether, butanol, butane, and ethanol: Butane has the lowest boiling point because it can only interact via LDFs. Ethyl methyl ether has the second lowest boiling point because even though it can interact via LDFs, dipole-dipole interactions, and hydrogen bonding, it is only able to be a hydrogen bond acceptor. Both butanol and ethanol can interact via dipole-dipole, LDFs, and hydrogen bonding (acceptors and donors). Why butanol has a higher boiling point than ethanol is due to its larger size; butanol has more surface area with which it can interact with other butanol molecules. 13 8. Compare and contrast the valence bond model and molecular orbital. Identify the similarities and differences. Molecular Orbital Model Valence Bond Model Atomic orbitals combine to form an equal Atomic orbitals overlap to form a bond number of molecular orbitals (standard or hybridized) Each orbital can contain up to two Each bond is made up of two electrons electrons Electrons are localized in the bond Electrons are de-localized The greater the overlap, the stronger the Electrons in bonding orbitals stabilize the bond system Electrons in anti-bonding orbitals make it less stable 9. Use Lewis structures and VSEPR to deduce electron pair geometry and molecular shape of molecules. Phet simulation: Molecule Shapes Source 14 10. Use Lewis structures to deduce the hybridization of the atoms in a molecule. Count the number of electron groups around each atom. Khan Academy: Hybridization and Hybrid Orbitals (chapter) 11. Use molecular structure and polarity to predict the types of intermolecular forces present in molecules, including London dispersion forces, dipole-dipole interactions, and hydrogen bonding. LDFs Dipole-dipole (polar molecule) Hydrogen bond acceptor LDFs Dipole-dipole (polar molecule) Hydrogen bond acceptor Hydrogen bond donor LDFs 15 Unit 4: Stoichiometry Core Understandings ➔ Changes in matter can be represented by chemical equations, which contain symbolic, numeric, and atomistic representations of the reaction that occurs. ➔ Chemical reactions conserve the number and type of atoms present, but result in a different arrangement of atoms (for example, breaking into different types of molecules). ➔ Chemical reactions involve making and breaking chemical bonds. ➔ The mole allows us to convert from the molecular to macroscopic level. What you should be able to do: 1. Draw a molecular level picture showing how atoms rearrange during a chemical reaction (try using Lewis structures). 2. Identify the bonds broken and bonds made during a chemical reaction. (Refer to #1) 3. Balance a chemical reaction. Writing and Balancing the Equation for a Chemical Reaction (Problem-Solving Strategy from Zumdahl, pg. 223): 1. Determine what reaction is occurring. What are the reactants, products, and the physical states involved? 2. Write the unbalanced equation that summarizes the reaction described in step 1. 3. Balance the equation by inspection, starting with the most complicated molecule(s). Determine what coefficients are necessary so that the same number of each type of atom appears on both reactant and product sides. Do not change the identities (formulas) of any of the reactants or products. 16 4. Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. One carbon, two hydrogens, and two oxygens on reactants side, with a total mass of 46.03 grams. Products side has two hydrogens, one carbon, and two oxygens, also with a mass of 46.03 grams. 5. Use mole-mass conversions to calculate how many moles of a substance are in a given mass (and vice versa). Calculating Masses of Reactants and Products in Chemical Reactions (Problem-Solving Strategy from Zumdahl, pg 227): 1. Balance the equation for the reaction. 2. Convert the known mass of the reactant or product to moles of that substance. 3. Use the balanced equation to set up the appropriate mole ratios. 4. Use the appropriate mole ratios to calculate the number of moles of the desired reactant or product. 5. Convert from moles back to grams if required by the problem. 17  Sample Problem (Zumdahl): Chapter 5, #69 Ascorbic acid, or vitamin C (C6H8O6), is an essential vitamin. It cannot be stored by the body and must be present in the diet. What is the molar mass of ascorbic acid? Vitamin C tablets are taken as a dietary supplement. If a typical tablet contains 500.0 mg vitamin C, what amount (moles) and what number of molecules of vitamin C does it contain? 6. Determine the limiting reagent when given the masses of two or more reactants, and calculate the amount of product produced. Sample Problem (Zumdahl): Chapter 5, #117 Ammonia is produced from the reaction of nitrogen and hydrogen according to the following balanced equation: N2 (g) + 3H2 (g) → 2NH3 (g) a. What is the maximum mass of ammonia that can be produced from a mixture of 1.00 x 103 g N2 and 5.00 x 102 g H2? Since N2 is only able to form 1.22 x 103 grams of ammonia, it is the limiting reactant. b. What mass of which starting material would remain unreacted? Start by solving for the amount of H2 that was reacted, using the amount of the limiting reactant. Then subtract the amount that was reacted from the initial amount of H2. 7. Calculate percent yield for a reaction, when given the experimental yield. The formula for percent yield of a reaction is: 18  𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 % 𝑦𝑖𝑒𝑙𝑑 = × 100 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 Sample Problem (Zumdahl): Chapter 5, #123 The reaction of ethane gas (C2H6) which chlorine gas produces C2H5Cl as its main product (along with HCl). In addition, the reaction invariably produces a variety of other minor products, including C2H4Cl2, C2H3Cl3, and others. Naturally, the production of these minor products reduces the yield of the main product. Calculate the percent yield of C2H5Cl if the reaction of 300.0 g of ethane with 650.0 g of chlorine produced 490.0 g of C2H5Cl. 19 Unit 5: Systems Thinking Pages 1-3 of Extra Practice Doc Core Understandings ➔ Macroscopic properties such as temperature and pressure can be explained by the behavior and properties of atoms and molecules at the molecular level. ➔ Temperature is a measure of the kinetic energy of a system; two different substances at the same temperature will have the same kinetic energy, regardless of the identity of the substance. ➔ Interactions of atoms with other atoms (and molecules with other molecules) can be explained and predicted using the concept of forces and energy. ➔ Quantifying energy changes associated with chemical reactions provides an explanation for which reactions occur and the extent to which they occur. ➔ Chemical processes and whether or not energy is stored or released can be understood in terms of the rearrangements of atoms into new molecules, with consequent changes in the sum of all bond energies. Such energy changes can be measured by measuring the temperature changes associated with reactions. ➔ Phase changes involve changes in enthalpy and entropy that can be predicted by thinking about the changes in intermolecular interactions. Phase changes occur at a constant temperature. ➔ Entropy describes the number of arrangements (position and/or energy levels) available to a system existing in a given state. ➔ The direction of change is determined by an increase in the total entropy change of the universe, ΔSuniverse, or the Gibbs energy change of the system (at constant T and P), ΔGsystem. What you should be able to do: 1. Explain the difference/relationship between temperature, thermal energy, and kinetic energy. Temperature → the average kinetic energy of the molecules in a substance Thermal energy → the kinetic energy of moving particles of matter Khan Academy article: Heat and temperature 2. Explain the connection between macroscopic properties such as temperature or pressure, and molecular level behavior such as speed of molecules and number of collisions. Increasing the temperature of the system increases the kinetic energy of the molecules, therefore, they will move at a higher velocity. Pressure is caused by the collisions of molecules into their container. As temperature increases, the molecules move faster, colliding with the container more often and with greater force (increases system pressure). 3. Explain why particles in gases move at a range of different velocities at a given temperature. Draw Boltzmann distributions of particles at different temperatures, 20  or for particles of different molecular weights. Drawings should accurately represent the shape of the distribution (broader and less high for species moving faster). At higher temperatures, some particles have more kinetic energy and, therefore, move at greater velocities. When the temperature is higher, a greater fraction of the molecules can move at these high velocities. 4. Explain why heat capacity of a substance is affected by the molecular-level structure, and predict relative heat capacities for different substances. Heat capacity is dependent on (1) the amount of substance, (2) molecular structure, and (3) intermolecular interactions. Molecules are able to “store” heat in their bonds in the form of vibrations, rotations, and bending. The more places a molecule has to “store” energy, the greater its heat capacity will be. If the molecule only has a few places to store the energy, the remaining heat energy will go towards raising the velocity of the molecule and therefore the temperature of the system. 5. Draw heating or cooling curves showing how the temperature changes when thermal energy is added to a substance (including a phase change). Explain why the temperature changes when thermal energy is added. Explain why temperature doesn’t change when the substance is undergoing a phase change. Drawings should accurately represent enthalpy of phase changes and differences in heat capacity between different phases. A → Adding heat to the system increases the temperature of the system. B → At 100℃ (bp of H2O), the temperature does not increase right away. The heat energy being added is going into bond vibrations and rotations of H2O. C → After a while, the H2O bonds cannot “hold” more heat energy, so it goes toward increasing the KE of the molecules and breaking up intermolecular forces; this increases the temperature of the system (temp is the measure of average KE). Also, this line is steeper than A because H2O vapor has a lower specific heat than liquid H2O (it takes less energy to increase the temperature/KE of system). 21 6. Explain the difference between state and path functions and give examples. State functions = properties/values that are not dependent on the method of synthesizing the compound ○ Ex., density, enthalpy, internal energy Path functions = properties/values that rely on the path taken to get there Example from Zumdahl (pg. 285): Imagine a plane flying from Chicago to Denver. The change in elevation is always 4606 feet no matter how you get there (i.e., state function). However, the distance traveled to get from Chicago to Denver is dependent on how you get there (i.e., path function). 7. For chemical reactions and phase changes, identify the direction of thermal energy change, the sign of q or ΔH, and the sign of ΔS. Chemical Reaction ΔH ΔS H2O (l) → H2O (g) + + Ag+ (aq) + Cl- (aq) → AgCl (s) - - 2 SO2 (g) + O2 (g) → 2 SO3 (g) - - CH4 (g) + 2 O2 (g) → CO2 (g) + 2 H2O (g) - - 8. Explain the meaning of entropy in terms of microstates and macrostates. Khan Academy: Entropy: Embrace the chaos Entropy is a measure of disorder. Microstates refers to the positional configurations/arrangements of atoms and energy. The macrostate is what is visible to humans. The more microstates for a particular macrostate, the greater the entropy of the system. Activity 27 9. Explain the second law of thermodynamics in terms of the system and surroundings. (From Zumdahl) The second law of thermodynamics = “In any spontaneous process there is always an increase in the entropy of the universe” (pg. 645). The entropy of the universe: ΔSuniverse = ΔSsystem + ΔSsurroundings When ΔSuniv is positive, the process is spontaneous as written. If ΔSuniv is negative, the process is spontaneous in the reverse direction. When ΔSsys is the same magnitude as ΔSsurr , ΔSuniv = 0 ; at equilibrium. 10. Explain why we usually use ΔGsystem instead of ΔSuniverse to predict whether a process is thermodynamically favorable. ΔSuniverse is difficult to calculate. Also, why would we calculate it when we really only care about the thermodynamic favorability of our system? Calculating ΔGsystem is much easier: ○ ΔGsystem = Gfinal - Ginitial 22  ○ ΔGsystem = ΔHsystem - TΔSsystem 11. Calculate ΔHº, ΔSº, and ΔGº for chemical reactions. (Pages 1-6 of extra practice pages) 12. Predict whether a reaction will become more or less favorable as temperature increases or decreases. ΔH ΔS ΔG (low temp) ΔG (high temp) Spontaneity + + + - Spontaneous at high temps + - + + Never spontaneous - + - - Spontaneous at all temps - - - + Spontaneous at low temps 23 Unit 6: Chemical Reactions Pages 4-6 of Extra Practice Document Core Understandings ➔ The polarity and H-bonding capabilities of H2O contribute to how it solvates substances. ➔ Relative solubility of substances can be predicted by considering intermolecular interactions between the solute and solvent. ➔ Changes in matter can be represented by chemical equations, which contain symbolic, numeric, and atomistic representations of the reaction that occurs. ➔ Chemical reactions conserve the number and type of atoms present, but result in a different arrangement of atoms. ➔ Chemical reactions involve making and breaking chemical bonds. ➔ Chemical reactions can be classified by how the valence electrons behave during the course of the reaction. ➔ Energy changes in reactions arise from the changes in bond energies as bonds in reactants are broken and new bonds are formed. What you should be able to do: 1. Understand and explain the terms: solute, solvent, solution, hydration, molarity, concentration, dilute, concentrated. (From Zumdahl) Solute → “a substance dissolved in a liquid to form a solution” Solvent → “the dissolving medium in a solution” Hydration → “the interaction between solute particles and water molecules” Molarity (M) → “moles of solute per volume of solution in liters” Concentration → generally, the molarity of a solution Dilute → adding water to a solution so that it reaches a desired molarity/concentration Concentrated → a solution with a large number of solute particles 2. Perform calculations using molarity (M) and volume of solution, to convert to mass of solute, and determine the volume of a dilute or concentrated solutions. 𝑚𝑜𝑙𝑠 𝑠𝑜𝑙𝑢𝑡𝑒 𝑀= 𝐿 𝑠𝑜𝑙′𝑛 Sample Problem (Zumdahl): Chapter 6, #35 What mass of NaOH is contained in 250.0 mL of a 0.400 M sodium hydroxide solution? 24  Sample Problem (Zumdahl): Chapter 6, #43 A standard solution is prepared for the analysis of fluoxymesterone (C20H29FO3), an anabolic steroid. A stock solution is first prepared by dissolving 10.0 mg of fluoxymesterone in enough water to give a total volume of 500.0 mL. A 100.0-µL aliquot (portion) of this solution is diluted to a final volume of 100.0 mL. Calculate the concentration of the final solution in terms of molarity. 3. Draw molecular level diagrams showing how solute and solvent interact, including, for example, how water molecules solvate ionic compounds. The partially negative oxygen atoms are attracted to the cations. The partially positive hydrogen atoms are attracted to the anions. (Zumdahl) 4. Predict the relative solubility of compounds in H2O by considering intermolecular interactions between the solute and solvent. Ionic compounds are soluble in H2O Most polar compounds are soluble in H2O Has to do with attraction of ions for water molecules 5. Draw a molecular level picture showing how atoms rearrange during a chemical reaction (try using a Lewis structure to do this). (Refer to Unit 4, #1) 25 6. Identify the bonds broken and bonds made during a chemical reaction and use this information to calculate energy change. Compound ΔHf (kJ/mol) NaOH (aq) -470 H2O (l) -286 HCl (aq) -92 NaCl (aq) -407 7. Identify the molecular structural features that lead to acidic and basic properties in a molecule, and explain why these features are important. Acids have a hydrogen bonded to an electronegative atom (usually an oxygen or halogen) Factors that influence strength of an acid: ○ Ability to delocalize (through resonance) ○ Ability to stabilize negative charge (with electronegative atoms or electron withdrawing groups) The proximity of these groups also matters Bases often have a lone pair that is capable of “attacking” a proton from another molecule (i.e., an atom capable of accepting an H+) 8. Know common strong acids, common strong bases, and common polyatomic ions. 26 9. Predict and explain relative strengths of a range of related acids (and bases) using arguments of size, resonance, electronegativity, electron withdrawing groups, and electron donating groups. Size: Larger ions are able to stabilize a charge more effectively; makes for stronger acids/bases. An increase in the atomic radius of the atom providing the proton (or electron pair) correlates to a decrease in basicity (an increase in acidity). Resonance: Having more resonance structures makes for a stronger acid because it allows for the electrons to be delocalized. The delocalization of these electrons makes the molecule more stable. (Usually decreases basicity.) Electronegativity: If a molecule has electronegative atoms, they can help to stabilize the negative charge that occurs when a proton is donated, making for a stronger acid. Electron-withdrawing groups (EWGs): Presence of EWGs reduces the electron density (spread out electrons over a greater area), making a molecule more acidic (can help stabilize negative charge). (Reduces basicity.) Electron-donating groups (EDGs): Puts greater electron density around the atom that is donating the proton or electron pair, making it want to hold on to its proton more or accept another proton. (Increase basicity, reduces acidity). The Influence of Structure on Reactivity (chem.ucla.edu) 10. Predict the products of acid-base reactions, based on the relative strength of the acids and bases. (Refer to #12) 11. Predict the extent of acid-base reactions (more products or more reactants) based on relative acid/base strengths. From looking at the Kas of the compounds, we can see that the hydronium ion is a stronger acid than acetic acid. This means that the hydronium ion is going to “want” to donate its proton more than acetic acid will; there will be more molecules of acetic acid 27  than the hydronium ion. The equilibrium in this reaction is towards the left so there will be more reactants at equilibrium. In this reaction, ethylamine is the base and accepts a proton from water (the acid). The Ka of water is 1.0 x 10-14 and the Ka of ethylammonium ion is 2.1 x 10-11. Ethylammonium has the higher Ka and is therefore the stronger acid. That means that at equilibrium, there will be more reactants than products (equilibrium is towards the left). The Ka of acetic acid is more than the Ka of the ammonium ion and is therefore the stronger acid. Since it “wants” to give up its proton more than NH4+ does, there will be a greater amount of the NH4+ at equilibrium (more products). The equilibrium lies to the right. 12. Calculate pH from given concentrations of strong acids or bases. What is the pH of a 0.056 M solution of HCl? Since HCl is a strong acid, we can assume that it completely dissociates in solution. Therefore, there are the same number of H+ ions in solution as moles of 0.056 of HCl. The pH equation: pH = -log [H+] So, pH = -log [0.056] = 1.25 What is the pH of a 0.065 M solution of KOH? KOH is a strong base so we can assume complete dissociation into K+ ions and OH- ions. Since we have the concentration of OH-, [0.065], we can find the pOH value and use it to solve for the pH: pOH equation: pOH = -log [OH-] So, pOH = -log [0.065] = 1.19 To find pH from pOH, use the following relationship: pH + pOH = 14 So, pH + 1.19 = 14 pH = 12.81 13. Use molarity (mol/L) to calculate amounts of reactants and products for reactions in solution. What mass of Au is in 400.0 L of a 3.30 x 10-4 M solution of Au(CN)2⁻ ? Use the balanced equation: Zn (s) + 2 Au(CN)2- (aq) → Zn(CN)4- (aq) + 2Au (s) 28 - 29 Unit 7: Kinetics and Equilibrium - How Far / How Fast Pages 4-6 of Extra Practice Document Core Understandings ➔ The rates of chemical reactions depend on the concentration of reactants, temperature, structure and orientation of colliding molecules, and the probability that molecules will collide with enough energy to surmount the activation energy barrier. ➔ The rate of a chemical reaction is determined experimentally by measuring the change in concentration of reactants and products. ➔ When the rate of a forward reaction becomes equal to the rate of a reverse reaction, the reaction is said to be “at equilibrium”. At equilibrium, the concentrations of reactants and products are related by an “equilibrium constant”. ➔ The position of equilibrium, but not the equilibrium constant, can be changed by changing concentrations of reactants or products. ➔ Chemical equilibrium is “dynamic”: while the overall concentrations do not change, individual molecules are always changing into other molecules. What you should be able to do: 1. Explain what rate means when discussing a chemical reaction. Khan Academy: Reaction rates and rate laws (videos) The rate of a reaction is determined by the “rate-limiting step.” This is the slowest step of the reaction and its rate is the same as the rate of the overall reaction. 2. Discuss the factors that affect rates of reactions and explain how and why each factor affects the rate by relating chemical reactions to molecular collisions. Temperature → increasing the temperature increases the KE of molecules so they can collide with greater force and have enough energy to initiate the reaction Concentration → the more reactants present, the greater the chance that the molecules will collide in the proper orientation to initiate the reaction Orientation→ molecules must collide with an orientation that promotes breaking and making of bonds Reaction pathway → the more steps in a reaction, generally, the longer it will take Presence of a catalyst → lowers the energy of activation so that more molecules will have the energy required to initiate the reaction 30 3. Draw and label reaction energy profiles (i.e., reaction coordinate diagrams) when given a reaction mechanism, and show the effect of a catalyst. Both of these reactions are elementary reactions, meaning there is only one step and one high- energy intermediate (occur at peaks). The pink pathways show the potential effects of a catalyst. In the first reaction, the catalyst creates an alternate pathway that involves two steps (and two transition states), but it requires less energy. In both reactions, the catalyst lowers the activation energy (Ea) that is required to get the reaction underway. 4. Determine whether a reaction mechanism is consistent with an experimentally determined rate law. Reaction mechanisms must fulfill two requirements: 1. The sum of the elementary steps must give the overall balanced equation for the reaction. 2. The mechanism must agree with the experimentally determined law. Sample Problem (Zumdahl): Ch 11, Ex 11-6 Evaluate whether or not the suggested reaction mechanism fits with the experimentally determined rate law. 5. Calculate the rate of reaction from a table of data or from a graph. Sample Problem (Zumdahl): Ch 11, #33 The reaction I- (aq) + OCl- (aq) → IO- (aq) + Cl- (aq) was studied, and the following data were obtained: 31  [I-]0 (mol/L) [OCl-]0 (mol/L) Initial Rate (mol/L ⋅ s) 0.12 0.18 7.91 × 10-2 0.060 0.18 3.95 × 10-2 0.030 0.090 9.88 × 10-3 0.24 0.090 7.91 × 10-2 Find the rate law and value of the rate constant. 32 6. Draw and interpret graphs of how concentration changes with time for reactants and products of a chemical reaction. From the graph only, you can tell that B is the reactant because its concentration decreases to almost nothing. You know that A is the product because there was none of it at the beginning of the reaction, but the concentration grew as the reaction progressed. It can also be noted that the coefficient 2 was given before A because, as can be seen on the graph, the concentration of A increases at a rate double that of B’s decreasing rate. 7. Plot concentration vs. time for reactants and products and use this to predict the reaction order. The following are graphs of the concentrations of a reactant, A, in different orders of reactions. 8. Calculate an equilibrium constant when given concentrations at equilibrium. Sample Problem (Zumdahl): Ch 12, #25 For the reaction 2 NO (g) + 2 H2 (g) ⇆ N2 (g) + 2 H2O (g) it is determined that, at equilibrium at a particular temperature, the concentrations are as follow: [NO (g)] = 8.1 × 10-3 M, [H2 (g)] = 4.1 × 10-5 M, [N2 (g)] = 5.3 × 10-2 M, and [H2O (g)] = 2.9 × 10-3 M. Calculate the value of K for the reaction at this temperature. 2 33 9. Use initial concentrations and equilibrium constants to calculate equilibrium concentrations. Sample Problem (Zumdahl): Ch 12, #51 At a particular, K = 3.75 for the reaction SO2 (g) + NO2 (g) ⇆ SO3 (g) + NO (g) If all four gases had initial concentration of 0.800 M, calculate the equilibrium concentrations of the gases. 10. Use acid dissociation constants (Ka) to calculate pH of weak acid. Use the pH of a weak acid to calculate the Ka. Finding the pH of a weak acid is similar to finding the pH of a strong acid, except you cannot assume that the concentration of H+ ions is the same as the concentration of the acid; it is weak and will not completely dissociate. 34 11. Predict and explain how a position of equilibrium will shift when conditions are changed. Le Châtelier’s principle → if a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change (Zumdahl). Change in concentration: If a reactant or product is added to a reaction system at equilibrium (at constant T and P or constant T and V), the equilibrium position will shift in the direction that lowers the concentration of that component (reactant or product). If a component is removed, the opposite effect occurs (Zumdahl). Change in pressure: Three ways to change pressure: (1) Add or remove a gaseous reactant or product. (2) Add an inert gas (one not involved in the reaction). (3) Change the volume of the container (Zumdahl). ○ (1) is the same as changing the concentration ○ (2) Adding an inert gas will not change the equilibrium position of a system. The equation for K involves the concentrations of the products and reactants involved in the reaction, given in moles per liter. Even if you add another gas to the system, the concentration of the reactants and products won’t change: there is no change in the amounts of reactants/products or a change to the volume of the system. ○ (3) When you change the volume of a system, the amounts of molecules changes in an attempt to keep the concentrations the same. Concentration is moles/liters, so if we increase the volume but keep the moles of molecules the same, the value of the concentration will decrease. So, the reaction’s equilibrium will shift to increase the amount of molecules in the system to reach its initial concentration. For example: N2(g) + 3H2(g) ⇆ 2NH3(g) If the volume of this reaction’s container is decreased, the equilibrium will shift to the left (products) because there are less molecules (two vs four in reactants). Having less moles of compounds will return the concentration to its initial value. Change in temperature: Changing the temperature changes the equilibrium constant (K) of a reaction (changing concentration and pressure only change equilibrium position). Le Châtelier’s principle can be applied if we consider energy as a product or reactant. If energy is a product (exothermic reaction), increasing the temperature (essentially, increasing the “concentration” of a product) will shift the equilibrium constant towards the reactants. For an endothermic reaction, where energy is considered a “reactant,” an increase in temperature will shift the equilibrium constant toward the product side (to the right). 12. Calculate the reaction quotient, Q, and use the relationship between Q and K to predict how a reaction will shift. Solving Equilibrium Problems (Problem-Solving Strategy from Zumdahl, pg 510): 1. Write the balanced equation for the reaction. 2. Write the equilibrium expression. 3. List the initial concentrations. 4. Calculate Q, and determine the direction of the shift to equilibrium. 35  5. Define the change needed to reach equilibrium, and define the equilibrium concentrations by applying the change to the initial concentrations. 6. Substitute the equilibrium concentrations into the equilibrium expression, and solve for the unknown. Check your calculated equilibrium concentrations by making sure they give the correct value of K. Sample Problem (Purdue): 0.035 moles of SO2, 0.500 moles of SO2Cl2, and 0.080 moles of Cl2 are combined in a 5.00 L flask. K = 0.078. What is Q before the reaction begins? Which direction will the reaction proceed in order to establish equilibrium? 0.007 M (0.007 M)(0.016 M) 1.12 x 10⁻³ 13. Explain the concept of dynamic equilibrium, including the idea of reversibility and position of equilibrium. Reactions that are reversible can proceed in either direction (as written or reverse). The reactants will interact to form the products, then the products react with each other to remake the reactants. These reactions occur at the same time. Dynamic equilibrium is the concept that the forward and reverse reactions are always occurring. When a system reaches equilibrium the reaction do not stop; they are proceeding at equivalent rates. The position of equilibrium shifts to correct for increases or decreases in concentrations, volume, and/or pressure. (Refer to #11) MO Theory Revisited Construct MO Diagrams for simple homonuclear and heteronuclear molecules 36  Use MO diagram to predict bond order, diamagnetic/paramagnetic properties, reactivities, conjugation/light absorption. 37