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Questions found on previous First Hour Exams; the answers are in curly brackets.
D stands for delta; for example, DH represents delta H.
1 - For a certain gas, Cp,m = 29.1 K/mol-K.
a) Could the gas be helium? Explain. {Nope!}
b) Two moles of the gas are expanded adiabatically from 300K, 1.00 Liters to
200 K, 10.0 Liters.
i) Calculate w for the process. {- 5280 J}
ii) Calculate DH for the process. {- 7438 J}
iii) Calculate DS for the process. { 14.7 J/K}
iv) Is the process reversible, irreversible, or impossible? Show why. {irrev.}
2 - The molar heat of vaporization of water is 40.67 kJ/mol at 100 oC and is 44.01 kJ/mol
at 25 oC. Assuming both heat capacities are constant, calculate DCp,m for the process
H2O(l) = H2O(g) {- 44.5 J/mol-K}
in this temperature range.
3 - Under what circumstances would (Cp/T)dT + (P/T)dV be an exact differential for an ideal gas? Show your work. {(dCp/dV) = 0, where “d” represents a “partial” sign.}
4 - We're going to heat 2.00 moles of an ideal gas ( Cv,m= 3R) by an adiabatic compression. If we start at 300K, 1.00 atm, and end at 400K,
a) calculate the final pressure if the process were reversible. (Do this later; it could take time.) {3.16 atm}
b) In fact, the final pressure is 3.00 atm. Calculate DU, DH, and w. {49900J, 6850 J, {49900J}
c) Is the process reversible, irreversible, or impossible? {irrev.}
Explain.
d) Just to see if you can do it, calculate DH if Cv,m = 3R + 0.0050T. {7352 J}
5 - The critical temperature and pressure of CO2 are 73.8 bar and 304.2 K, respectively.
What is the molar volume of CO2 at 150 bar and 380 K? {0.133 L/mol}
6 - Consider the reaction, at 25 oC.
Br2 (g) + Cl2(g) = 2 BrCl(g) DHo= -1.50 kJ
a) If the bond enthalpy of Br2 is 192 kJ/mol, and the bond enthalpy of Cl2 is
243 kJ/mol, calculate the bond enthalpy of the Br-Cl bond. {218 kJ/mol}
b) Assuming DCp = 0 for the reaction above, calculate DHo at 37 oC. { - 1.50 kJ}
c) Bromine is a liquid at room temperature and has a heat of vaporization of
30.91 kJ/mole. Calculate the molar heat of formation of BrCl(g) at 298 K. {-32.41 kJ/mol}
7 - Consider the differential: dz = x2dx + y2dy.
a) Is the differential exact? Show your work. {yep!}
b) So what? What does your answer in a) tell us about Dz? {exact differential}
c) Give an example of a quantity whose differential's exactness is like the one above. {U, H, V}
8 - a) Under what circumstances is the heat change, Q, given by Q = CDT, where C is the heat capacity? Why? {Const. V or P}
b) Give examples of two processes for which Q isn’t equal to CDT; one must be isothermal, and the other non-isothermal.
9 - A bomb calorimeter experiment gives, for the combustion of C2H5OH(l) at 298 K,
DUcombustion = - 1366 kJ/mol. Calculate the molar enthalpy of combustion of ethane.{-1368
(I, of course, will sell you the equation for the combustion reaction if necessary.) kJ/mol}
10 - Let's expand 2.00 moles of CO2 having Cp,m = 37.1 J/mol-K. We'll start at Standard Temperature and Pressure (STP), and assume the gas behaves ideally. The external temperature is 298 K.
a) Let's heat the gas isochorically, to 400K. Calculate q, w, DE, DH, DS, and DS universe . {7310 J, 0, 7310 J, 9420 J, 22.0 J/K, -2.53 J/K}
b) Was the process reversible, irreversible, or impossible? Justify your answer. {imposs.}
c) Calculate the vibrational contribution to Cv,m. What was the predicted value of Cv,m(vib) from classical mechanics? {6.3 J/K, 4R}
11 - Let's denature some myoglobin, Mb, at 25 oC. For the reaction
Mb(coiled) = Mb(denatured),
DSo (rxn) = 400 J/mol-K, and Keq = 0.0041
a) Calculate DHo for the reaction, at 25 oC. {138.5 kJ/mol}
b) Calculate Keq at 37 oC, assuming DCp = 0. {0.0036}
c) Calculate DHo for the reaction at 37 oC, using DCp = 7900 J/mol-K.{233kJ/mol}
12 - The critical constants of CO2 are Tc = 304.2 K, Pc = 71.9 bar.
a) Calculate the molar volume at 400 K, 200 bar, {0.166 L/mol}
i) assuming ideal behavior. {0.106 L/mol}
ii) using the compressibility factor graph.
b) Calculate the density of CO2 at these conditions. {415 g/L}
13 - Consider the differential: x2y dx + y2x dy. {exact}
a) Show if the differential is exact or inexact.
b) So what? What is the significance of the result in a)?
14 - The reaction that occurs when a typical fat, glyceryl trioleate, is metabolized in the body is C57H104O6 (s) + 80 O2 (g) =57 CO2(g) + 52 H2O(l)
At constant pressure, 37.8 kJ of heat are evolved when 1.00 gram of this fat
(MW = 885.4 g/mol) is metabolized. If the standard molar enthalpies of formation of CO2(g) and H2O(l) are -394 kJ/mol and -286 kJ/mol respectively,
a) Calculate the molar enthalpy of formation of C57H104O6(s). {-3862 kJ/mol}
b) Calculate the change in internal energy of the metabolism reaction above at 25 oC.{-33410 kJ/mol}
15 - 4.01 moles of a gas of unknown identity is going to be compressed from 10.0 L, 10.0 bar, 300 K. The molar heat capacity of the gas is Cp,m = 29.1 J/mol-K.
a) The gas is compressed by a constant external pressure of 30.0 bar to a volume of 5.00 L, and a temperature of 350 K. Calculate DU, q, w, DS, and DH, and express all answers in SI units.
{4170 J, -10810 J, 15000J, -10.3 J/k, 5385 J}
b) Was the process in a) possible? Use the second law to show why. {Sure, if T(external) is about 300 K.}
16 - a) Show that dG = - SdT + VdP
b) (dG/dP)T = ? {V}
c) (dS/dP)T= ? {-(dV/dT)P}
17 - Consider the reaction PCl3(g) + Cl2 (g) = PCl5(g). DHo = -87.9 kJ/mol
DSo = -170.3 J/mol-K
a) Calculate the equilibrium constant at 25 oC. {3.2x106}
b) Use Le Chatelier's Principle to predict if the equilibrium constant would be larger or smaller at 50 oC. {smaller}
c) Use thermodynamics to make the same prediction. Don't calculate the new Keq.
{K2/K1 = exp(-5.03)}
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Solutions, Problem Set 5
