Chemistry 271, Section 22xx 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) November 1, 2010 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 = klnW ∆G = ∆H – T∆S E = Σ ni εi W = N!/(∏ ni!) ni/n0 = exp[–(εi–ε0)/kT] N = Σ ni 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 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.”Chemistry 271, Section 22xx Exam II, 11/1/2010 2/7 Score for the page 1. (24 pts) Multiple choice: Circle the single best answer for each question (a; 4 pts) A configuration 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) All of the possible microstates that have a given value of total E. (4) All of the possible microstates that could describe a system at any value of E. (b; 4 pts) The Boltzmann distribution describes: (1) The distribution of energy among particles in the microstates of the predominant configuration. (2) The distribution of microstates among different ensembles. (3) The distribution of coin flips for small numbers of coins. (4) The distribution of entropy among different microstates. (c; 4 pts) Boltzmann defined entropy as S = kBlnW because (1) It’s a postulate – it doesn’t need to be justified. (2) Using a logarithm is the only way to make entropy an extensive state function that increases as W increases. (3) The value of “kB” could be chosen to make the numerical values of S fall into an arbitrary and convenient range. (4) All of the above. (d; 4 pts) Exothermicity per se makes reactions tend to be favorable because (1) It accompanies bond breaking (2) It decreases the total energy of the universe (3) It increases the entropy of the surroundings (4) None of the above (e; 4 pts) Protein folding from a random coil to a native tertiary structure occurs with (1) Positive ∆H° and negative ∆S° (2) Positive ∆H° and positive ∆S° (3) Negative ∆H° and positive ∆S° (4) Negative ∆H° and negative ∆S° (f; 4 pts) The temperature at which W = 1 for a system and therefore S = 0 is (1) Unknowable (2) Absolute zero (3) 100 °C (4) InfiniteChemistry 271, Section 22xx Exam II, 11/1/2010 3/7 Score for the page 2. (20 pts) Short-answer questions (a; 12 pts) Briefly describe the ergodic hypothesis and why it is hard to test in practice. (b; 8 pts) List one biotechnology technique that requires nucleic acid hybridization, and briefly and qualitatively describe why/how nucleic acid thermodynamics can be applied to the design of the oligonucleotides used.Chemistry 271, Section 22xx Exam II, 11/1/2010 4/7 Score for the page 3. (31 pts) Thermodynamics (a; 12 pts) Sketch a van’t Hoff plot for the temperature dependence of the equilibrium constant for an endothermic ordering reaction A+B -> C. If there is a region of the graph corresponding to the reaction being spontaneous, indicate where it is. If there is no such region, explain why not.Chemistry 271, Section 22xx Exam II, 11/1/2010 5/7 Score for the page The chart on the left below shows one possible distribution of 48 quanta of energy among 24 molecules, similar to our discussion of microstates in class. (b; 3 pts) Write down but do not evaluate a numerical expression for the number of microstates W for the configuration shown on the left above. W =N !n0!( )n1!( )n2!( )= (c; 6 pts) Now, consider transferring one quantum of energy from one of the molecules with 7 quanta to one of the ones with 4, as indicated by the arrows in the chart on the left above. This will yield molecules with 5 and 6 quanta. Write down the expression for W for this new configuration. By what factor did W increase upon this small redistribution of energy? You do not need to evaluate W to figure this out.Chemistry 271, Section 22xx Exam II, 11/1/2010 6/7 Score for the page (d; 5 pts) If we continue to redistribute energy among the particles, we will reach the equilibrium state described by the Boltzmann distribution. By drawing circles in the chart on the right above, add in a reasonable guess for the energy levels of the 13 remaining molecules according to Boltzmann,. (e; 5 pts) Clearly W would be maximized if every ni were equal to 1 or 0. Why doesn’t every isolated system just evolve to maximum entropy by placing every molecule on its own unique level? Write down the equation from the front page that expresses this constraint. 4. (25 pts) Applied thermodynamics: RNA folding The folding of a single-stranded RNA into a stem-loop is simpler than hybridization of two separate strands to make a duplex. Consider the equilibrium UN(folded) ⇌ S(tem) L(oop) below. For the reaction as written, ∆H° = –52000 J/mol and ∆S° = –150 J/mol K (made up but reasonable numbers). (a; 3 pts) Calculate the free energy change ∆G° at 37 °C. (b; 6 pts) Write down the equilibrium constant expression and calculate its value at 37 °C.Chemistry 271, Section 22xx Exam II, 11/1/2010 7/7 Score for the page (c; 6 pts) Calculate the percentage of the RNA in the SL form at 37 °C. (d; 2 pts) The melting temperature Tm is the temperature at which 50 % of the RNA is in the SL form and 50 % is in the UN form. What is the equilibrium constant for UN ⇌ SL at the Tm? (Note that this is not the same Keq as for formation of duplex from