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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, C_{p,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 ^{o}C and is 44.01
kJ/mol

at 25 ^{o}C. Assuming both
heat capacities are constant, calculate DC_{p,m} for the
process

H_{2}O(l) =
H_{2}O(g) {- 44.5 J/mol-K}

in this temperature range.

3 - Under what circumstances would
(C_{p}/T)dT + (P/T)dV be an exact differential for an ideal
gas? Show your work. {(dC_{p}/dV) = 0, where
“d” represents a “partial” sign.}

4 - We're going to heat 2.00 moles of an
ideal gas ( C_{v,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 C_{v,m }= 3R + 0.0050T. {7352 J}

5 - The critical temperature and pressure of
CO_{2} are 73.8 bar and 304.2 K, respectively.

What is the molar volume of
CO_{2} at 150 bar and 380 K? {0.133 L/mol}

6 - Consider the reaction, at 25
^{o}C.

Br_{2} (g) +
Cl_{2}(g) = 2 BrCl(g) DH^{o}= -1.50 kJ

a) If the bond enthalpy of
Br_{2} is 192 kJ/mol, and the bond enthalpy of
Cl_{2 }is

243 kJ/mol, calculate the bond enthalpy of the Br-Cl bond. {218 kJ/mol}

b) Assuming DC_{p} = 0 for the
reaction above, calculate DH^{o
}at 37 ^{o}C. { - 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 =
x^{2}dx + y^{2}dy.

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 C_{2}H_{5}OH(l) at 298
K,

DU_{combustion} = -
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
CO_{2} having C_{p,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
C_{v,m}. What was the predicted value of C_{v,m}(vib) from
classical mechanics? {6.3 J/K, 4R}

11 - Let's denature some myoglobin, Mb, at
25 ^{o}C. For the reaction

Mb(coiled) = Mb(denatured),

DS^{o} (rxn) = 400
J/mol-K, and K_{eq} = 0.0041

a) Calculate DH^{o} for the
reaction, at 25 ^{o}C. {138.5 kJ/mol}

b) Calculate K_{eq} at 37
^{o}C, assuming DC_{p} = 0.
{0.0036}

c) Calculate DH^{o} for the reaction
at 37 ^{o}C, using DC_{p} = 7900
J/mol-K.{233kJ/mol}

12 - The critical constants of
CO_{2} are T_{c} = 304.2 K,
P_{c} = 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
CO_{2} at these conditions. {415 g/L}

13 - Consider the differential:
x^{2}y dx + y^{2}x 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
C_{57}H_{104}O_{6} (s) + 80
O_{2} (g) =57 CO_{2}(g) + 52
H_{2}O(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 CO_{2}(g) and
H_{2}O(l) are -394 kJ/mol and -286 kJ/mol
respectively,

a) Calculate the molar enthalpy of formation
of C_{57}H_{104}O_{6}(s). {-3862
kJ/mol}

b) Calculate the change in internal energy
of the metabolism reaction above at 25 ^{o}C.{-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 C_{p,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
PCl_{3}(g) + Cl_{2} (g) =
PCl_{5}(g). DH^{o} = -87.9
kJ/mol

DS^{o} = -170.3
J/mol-K

a) Calculate the equilibrium constant at
25^{ o}C. {3.2x106}

b) Use Le Chatelier's Principle to predict
if the equilibrium constant would be larger or smaller at 50
^{o}C. {smaller}

c) Use thermodynamics to make the same
prediction. Don't calculate the new K_{eq}.

{K2/K1 = exp(-5.03)}

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Solutions, Problem Set 5