Chemistry 271, Section 21xx Your Name: Prof. Jason Kahn University of Maryland, College Park Your SID #: General Chemistry and Energetics Your Section # or time: Exam II (100 points total) April 6, 2011 You have 52 minutes for this exam. Exams written in pencil or erasable ink will not be re-graded under any circumstances. Explanations should be concise and clear. I have given you more space than you should need. There is extra space on the last page if you need it. You will need a calculator for this exam. No other study aids or materials are permitted. Generous partial credit will be given, i.e., if you don’t know, guess. Useful Equations: Ka = [H+][A–]/[HA] pH = – log([H+]) Kb = [HA][HO–]/[A–] Kw = [H+][HO–] pH = pKa + log [A–]/[HA] ∆G° = – RTlnKeq R = 0.08206 L·atm/mole K 0 °C = 273.15 K lnKeq = –∆H°/(RT) + ∆S°/R ∆S – q/T ≥ 0 R = 8.314 J/mole K = 1.987 cal/mole K S = kBlnW ∆G = ∆H – T∆S E = Σ ni εi W = N!/(∏ ni!) ni/n0 = exp[–(εi–ε0)/kT] N = Σ ni R = NAkB kB = 1.38 x 10–23 J/K t′ = t –vx/c2 Chemical standard state: 1 M solutes, pure liquids, 1 atm gases Biochemical standard state: pH 7, all species in the ionic form found at pH 7 nano: 10–9 pico: 10–12 zepto: 10–21 Honor Pledge: At the end of the examination time, please write out the following sentence and sign it, or talk to me about it: “I pledge on my honor that I have not given or received any unauthorized assistance on this examination.” (+1 pt)Chemistry 271, Section 21xx Exam II, 4/6/2011 2/7 Score for the page 1. (24 pts) Multiple choice: Circle the single best answer for each question (a; 4 pts) An ensemble in statistical thermodynamics is: (1) A description of the position and velocity of each particle in a system. (2) A set of microstates that all share the same set of observables P, T, n, etc. (3) The set of all of the possible microstates that have a given value of total E. (4) A set of imaginary replicates of the system. (b; 4 pts) The idea of the Predominant Configuration is that: (1) The configuration with the lowest energy is the one we observe. (2) The vast majority of microstates correspond to the same set of macroscopic observables. (3) The individual microstates with the largest entropy are most likely to be observed. (4) All of the above. (c; 4 pts) When a gas in a thermally insulated piston expands against a non-zero external pressure that is less than the internal pressure (1) q = 0, w = 0 , and ∆E = 0 (2) q < 0, w > 0 , and ∆E = 0 (3) q = 0, w < 0 , and ∆E < 0 (4) None of the above. (d; 4 pts) Endothermicity per se makes reactions tend to be unfavorable (non-spontaneous) because (1) It accompanies bond formation, and the universe prefers bond breaking. (2) It always decreases the total entropy of the universe. (3) It requires heat to flow uphill. (4) It decreases the entropy of the surroundings. (e; 4 pts) ∆S = qrev/T for the entropy change of a reservoir (1) Means that exothermicity buys less entropy when heat is rejected to a hot reservoir. (2) Lets us convert the second law of thermodynamics into a statement that concerns only the system. (3) Is incorrect. (4) (1) and (2) (f; 4 pts) The entropy of a pure substance is (1) always positive (2) always an increasing function of temperature (3) always more when it is a liquid than a solid (4) All of the aboveChemistry 271, Section 21xx Exam II, 4/6/2011 3/7 Score for the page 2. (21 pts) Microstates (a; 9 pts) In terms of combinations of sets of microstates, explain why S is defined as a logarithm of W (times a constant kB). Why not just define S = kB W, or W2, or some other function of W? (b; 12 pts) Consider a solution of sodium chloride in liquid water. To completely describe a microstate of the system, what would one have to specify? Give an example of a configuration of the solution that has the same total energy as the predominant configuration but includes many fewer microstates.Chemistry 271, Section 21xx Exam II, 4/6/2011 4/7 Score for the page 3. (28 pts) Thermodynamics and Statistical Mechanics The chart on the left below shows one possible distribution of 21 quanta of energy among 17 molecules, similar to our discussion of microstates in class and to a past exam, sigh. (a; 6 pts) Write down and evaluate a numerical expression for the number of microstates W for the configuration shown on the left above. (b; 6 pts) Now, we transfer two quanta of energy from the highest-energy molecule to the lowest, as indicated by the arrows in the chart. Draw the new configuration in the chart on the right. Write down and evaluate the expression for W for this new configuration. Table of factorials: 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 17 3.55687E+14 18 6.40237E+15 21 5.10909E+19 39 2.03979E+46Chemistry 271, Section 21xx Exam II, 4/6/2011 5/7 Score for the page (c; 6 pts) Let’s do a real example. The molar entropy of liquid water at 298 K is 69.9 J/mol K. Write a numerical expression for W for a mole of water. (This is one reason to use logs!) How many microstates can a mole of water sample in a year (31 million seconds) if it goes through one microstate per picosecond? How many can it sample in the age of the universe (15 billion years)? (d; 10 pts) Sketch a van’t Hoff plot for the temperature dependence of the equilibrium constant for an endothermic disordering reaction. Indicate the region of the graph that represents a spontaneous reaction. In this context, quantitatively what do we mean by “spontaneous?”Chemistry 271, Section 21xx Exam II, 4/6/2011 6/7 Score for the page 4. (27 pts) Calculation of Free Energy and Keq (Adapted from Atkins) The reaction of boron oxide with HF is encountered in the etching/removal of borosilicate glass and the synthesis of the useful but corrosive Lewis acid BF3. B2O3 (s) + 6 HF (g) ⇌ 2 BF3 (g) + 3 H2O (g) (a; 10 pts) Use the data in the table to calculate ∆H°(rxn) and ∆S°(rxn) at 25°C for the reaction. (b; 5 pts) Calculate the free energy change ∆G°(rxn) and the equilibrium constant for this reaction at 150 °C, assuming that ∆H°(rxn) and ∆S°(rxn) are constant with temperature. Compound ∆H°f (kJ/mole) S° (J/mole K) B2O3 (s) –1272.8 54.0 HF (g) –271.1 173.8 BF3 (g) –1137.0 254.1 H2O (g) –241.8 188.8Chemistry 271, Section 21xx Exam II, 4/6/2011 7/7 Score for the page (c; 2 pts) Write