ProbSet5_Solutions(2) - Hand in answers to the 4 problems...

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Unformatted text preview: Hand in answers to the 4 problems marked with a * on Thursday, October 8, 2009. ANSWER KEY Q1. *Two different conformations of a protein are separated in energy by 15 kJ mol-1 . (i) At what temperature will the ratio of their populations be equal to 1:2? (ii) What will be their relative populations at room temperature (300K)? (iii) What energy difference between the two levels would yield a relative population of 1:2 at room temperature? Answer: U = 15 kJ mol-1 .Note that the units are kJ mol-1 , so use R instead of k in the Boltzmann Equation. i. N 2 N 1 = exp( U RT ) = 1 2 (condition given by the question) Take the logarithm of both sides to give: ln 1 2 = 0.693 = U RT = 15000 RT (not that the expression for R involves J not kJ, so energy is expressed in J mol-1 here) Therefore: RT = 15000 0.693 = 21645 At this point you can calculate T: T = 21645 8.314 = 2603 K ii. Recall that at room temperature, RT 2.5 kJmol-1 . For this temperature, N 2 N 1 = e 15 2.5 = e 6 = 0.0025 iii. N 2 N 1 = 0.5 = exp( U 2.5 ) Take the logarithm of both sides to get:-0.693 = U 2.5 Therefore: U = 1.73 kJ mol-1 Q2. A calorimeter and a heat bath are shown in the diagram below. The system is deFned in two different ways, as indicated in (i) and (ii). The calorimeter contains a solution of protein molecules. A solution containing drug molecules is added and energy is released when the drug binds to the protein. or (i) and (ii) below circle whether A, B or C represents the correct situation with respect to heat UC Berkeley. MCB 100A/Chem 130A Problem Set 5 Fall 2010 1 of 9 transfer. If none of the three situations is applicable, write down the correct description of heat transfer. Answer: (i) A: dqsys < 0 dqsurr > 0 (ii) B: dqsys > 0 dqsurr = 0 Q3. Which of the following properties are extensive: a. Pressureb. Temperature c. Volume d. Density e. Molarity f. Energy g. Number of moles h. Mass i. Amount of heat released Answer: Extensive properties: c, f, g, h, i Q4. Consider 5 L of nitrogen gas, held in a heat bath at 298 K. Assume ideal gas behavior. The gas expands under a constant external pressure of 1 atm until its volume is 24.5 L. Calculate the work done by the gas. How many minutes would a 4 watt light bulb (a refrigerator light) stay lit if the work done by the gas was used with 100% efFciency to light the light bulb? Hint: Watt is the standard unit UC Berkeley. MCB 100A/Chem 130A Problem Set 5 Fall 2010 transfer. If none of the three situations is applicable, write down the correct description of heat transfer. Answer: (i) A: dqsys < 0 dqsurr > 0 (ii) B: dqsys > 0 dqsurr = 0 Q3. Which of the following properties are extensive: a. Pressureb. Temperature c. Volume d. Density e. Molarity f. Energy g. Number of moles h. Mass i. Amount of heat released Answer: Extensive properties: c, f, g, h, i Q4. Consider 5 L of nitrogen gas, held in a heat bath at 298 K. Assume ideal gas behavior. The gas expands under a constant external pressure of 1 atm until its behavior....
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ProbSet5_Solutions(2) - Hand in answers to the 4 problems...

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