3.4. Problems
 A quantity of 0.35 mole of an ideal gas initially at 15.6°C is
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expanded from 1.2 L to 7.4 L. Calculate the values of w, q, ΔU, ΔS,
and ΔG if the process is carried out (a) isothermally and reversibly,
and (b) isothermally and irreversibly against an external pressure of
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1.0 atm.
 Certain bacteria in the soil obtain the necessary energy for growth
by oxidizing nitrite to nitrate:
2NO2− (aq) + O2 (g) → 2NO3− (aq)
Given that the standard Gibbs energies of formation of NO2− and
NO3− are 234.6 kJ mol−1 and 2110.5 kJ mol−1, respectively,
calculate the amount of Gibbs energy released when 1 mole of
NO2− is oxidized to 1 mole of NO3−.
128
General Questions
1. What all is true for an adiabatic process
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a) dQ=0
b) dW=−nCvdT
c) TVy−1=constant
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d) all the above three
2. The state of an ideal gas is changed isothermally from position 1 to
position 2 is shown above. What is the change in the internal energy of
the gas during this process? Similar to one curve of carnot
(A) ΔU = W
(B) ΔU = Q
(C) ΔU > 0
(D) ΔU = 0
(E) ΔU < 0
129
3. An ideal gas is taken from state 1 to state 2 and then to state 3. If
the process 1-2 is adiabatic and 2-3 is isothermal, what is a true
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statement about the change in temperature and heat transferred
during 1-2?
(A) ΔT > 0, Q > 0
(B) ΔT < 0, Q = 0
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(C) ΔT = 0, Q = 0
(D) ΔT > 0, Q < 0
(E) ΔT = 0, Q < 0
4. An ideal heat engine operates between two temperatures 600 K and
900 K. What is the efficiency of the engine?
(A) 50%
(B) 80%
(C) 100%
(D) 10%
(E) 33%
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5. Which of the following statement is correct for an ideal gas?
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a) h=u+pv
b) h=u+RT
c) h=f(T)
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d) all of the mentioned
6. Air in a cylinder is suddenly compressed by a piston which is
then maintained at the same position. After some time, the
___________
a) Pressure will increase
b) Pressure remains the same
c) Pressure will decrease
d) Pressure may increase or decrease
6. A gas does work during adiabatic expansion. The source of
mechanical energy so produced is the internal energy of the
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gas itself.
a) True
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b) False
8. In an adiabatic process, the quantity which remains constant
is ___________
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a) Volume
b) Pressure
c) Temperature
d) Total heat of the system
9. The efficiency of a Carnot engine operating with reservoir
temperatures kept at 100 °C and -23°C will be ___________
a) (100+23)/100
b) (100-23)/100
c) (373+250)/373
d) (373-250)/373
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10. A Carnot engine, whose sink is at 300 K, has an efficiency of
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40%. By how much should the temperature of source be
increased, to increase the efficiency by 50% of original efficiency?
a) 380 K
b) 275 K
d) 250 K
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c) 325 K
11. During an adiabatic expansion the increase in volume
is associated with
A.
Decrease in pressure
and decrease in
temperature
C.
Increase in pressure
and increase in
temperature
B.
D.
Increase in pressure
and decrease in
temperature
Decrease in pressure
and increase in
temperature
12. In an adiabatic change the system
133
Takes heat from the
B.
surroundings
surrounding
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A.
Gives heat to the
Partly takes heat and
Exchanges no heat
C.
D.
with the surroundings
partly leaves to the
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surroundings
Heat taken from
surroundings is
exactly equal to heat
E.
rejected to
surroundings
13. Work done by an expanding gas under adiabatic condition results in
No change in
A.
Temperature
B.
temperature
134
increase
Temperature
Temperature
C.
D.
decreases first
decrease
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and then increase
Temperature
increase first and
E.
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then decrease
14. An amount of heat given to a gas under isothermal conditions will be
A.
For a temperature rise
B.
For doing external work
For doing external work
For increasing the internal
C.
and also for a temperature
D.
energy of the gas
rise
E.
None of the above
135
15. In an adiabatic compression the decrease in volume is associated
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with
Decrease in temperature
A.
Decrease in temperature
B.
and increase in pressure
and decrease in pressure
Increase in temperature and
D.
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C.
Increase in temperature and
decrease in temperature
increase in pressure
16. A frictionless heat engine can be 100% efficient only if its exhaust
temperature is
Equal to its input
A.
Less than its input
B.
temperature
C.
0?C
E.
?100?C
temperature
D.
136
0?K
17. During
an adiabatic process the square of the pressure of a gas is
proportional to the fifth power of its absolute temperature. The ratio of
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specific heat Cp / Cv for that gas is
a. 3/5
b. 4/3
c. 5/3
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d. 3/2
18. Which one of the following statements is true about a gas
undergoing isothermal change
a. The temperature of the gas is constant
b. The pressure of the gas remains constant
c. the volume of the gas remains constant
d. The gas is completely insulated from the surrounding’s
19. Which one of the following formulas is correct
I.
(T2/T1) Y-1 = (V1/V2)
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(T2/T1) = (V1/V2)1-Y
III.
(P2/P1) Y = (V1/V2)Y
IV.
(P2/P1) = (V1/V2)
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II.
20. Suppose we have 3 moles of an ideal polyatomic gas initially with a
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volume of 2 m3, and a temperature of 273 K. This gas is compressed
isothermally to 1/2 its initial volume. How much heat must be added to
the system during this compression?
21. Joule Thomson describe gas
I.
Expansion
II.
Contraction
III.
Sudden expansion
IV.
Volume increase
138
22. Joule Thomson effect is based upon
I.
Sudden expansion of gases
Sudden compression of gases
III.
Cooling of gases
IV.
Heating of gases
The values of ΔfHo(298 K) for SO2(g) and SO3(g) are –296.8 and
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23.
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II.
–395.7 kJ mol–1. What is the value of ΔrHo(298 K) per mole of
SO2 for the following reaction?
2SO2(g) + O2(g) → 2SO3(g)
 -692.5 Kj/M
 -98.9
 692.5
 98.5
139
If a reaction
is carried out
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at constant
pressure,
which of the
following
correct?
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statements is
The reaction is likely to be exothermic.
The heat change is equal to the change in temperature.
The heat change is equal to the enthalpy change.
The reaction is likely to be endothermic.
If the standard enthalpies of formation of HBr(g)
and Br2(g) are –36 and +31 kJ mol–1 (at 298 K)
respectively, what is ΔrHo(298 K) for the following
reaction?
H2(g) + Br2(g) → 2HBr(g)
+103 kJ mol–1
–67 kJ mol–1
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+67 kJ mol–1
–103 kJ mol–1
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The standard enthalpy of formation of NH3(g) at
298 K is –46 kJ mol–1. Which of the following
values is correct for the standard enthalpy change
for the following reaction? The answer is given per
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mole of reaction.
2NH3(g) → N2(g) + 3H2(g)
The complete combustion of cyclohexane occurs
according to the following equation:
C6H12(g) + 9O2(g) → 6CO2(g) + 6H2O(l)
141
–92 kJ mol–1
+92 kJ mol–1
–46 kJ mol–1
+46 kJ mol–1
For this process, ΔcHo(298 K) = –3953 kJ mol–1.
If values of ΔfHo(298 K) for CO2(g) and H2O(l)
the value of ΔfHo(C6H12, g, 298 K)?
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are –394 and –286 kJ mol–1, respectively. What is
+127 kJ mol–1
–8033 kJ mol–1
–127 kJ mol–1
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–156 kJ mol–1
26 calculate
Heat of enthalpy for the hydrolysis of Urea to give carbon
dioxide and ammonia in aqeous solution from the following data
H2NCONH2 +
H 2O
============== CO2 + 2NH3
1. C(graphite) + 2H2 + ½ O2 + N2 ========== H2NCONH2
-317.77 KJ mol-1
2.
H2 + ½ O2 =========================== H20
-285.85 KJ mol-1
142
3.
C(graphite) + ½ O2 =================== CO2
-413.8 KJ mol-1
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4. N2 + 3H2 ==========================2NH3
-161.42 KJ mol-1
28.32
II.
-28.32
III.
219.23
IV.
219.23
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I.
27. Entropy principle is the quantitative statement of the second law of
thermodynamics.
I.
True
II.
False
28. Which of the following is NOT a state variable?
A) Work
B) B) Internal energy
143
C) C) Entropy
D) D) Temperature
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E) E) Pressure
29. In a reversible reversible, entropy of the universe
Increases
II.
Decreases
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I.
III.
Remains constant
IV.
Equal zero
30. In an irreversible reversible, entropy of the universe
I.
Decreases
II.
Increases
III.
Sometimes increases and sometimes decreases
IV.
Remains constant
31. The efficiency of the carnot cycle may be increased by
144
I.
Increasing the lowest temperature
Decreasing the highest temperature
III.
Increasing the highest temperature
IV.
Decreasing the lowest temperature
32. What
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II.
is a necessary condition for a reaction to be spontaneous at all
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temperatures?
a. �H < �G
b. �G and H should be positive
c. �H = �G = 0
d. �G and �H should be negative
33. The
accompanying diagram represents a reversible carnot cycle for
an ideal gas, The net work is 60 j, and it operates between 500 and 200 k
The heat absorbed at 500k is
I.
II.
100 J
40
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o.o25
IV.
0.01
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III.
34) Which one of the following processes produces a decrease in the
entropy of the system?
A) boiling water to form steam
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B) dissolution of solid KCl in water
C) mixing of two gases into one container
D) freezing water to form ice
E) melting ice to form water
35) When a system is at equilibrium, __________.
A) the reverse process is spontaneous but the forward process is not
B) the forward and the reverse processes are both spontaneous
C) the forward process is spontaneous but the reverse process is not
D) the process is not spontaneous in either direction
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E) both forward and reverse processes have stopped
36) The first law of thermodynamics can be given as __________.
A) ΔE = q + w
B)
H
rxn
=
 nH
f
(products) -
 mH
f
(reactants)
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C) for any spontaneous process, the entropy of the universe increases
D) the entropy of a pure crystalline substance at absolute zero is zero
E) ΔS = qrev/T at constant temperature
37.
I.
For Isothermal process dS=
q
II.
qrev/T
III.
q+w
IV.
q/0
38. Which one of the following is always positive when a spontaneous
process occurs
147
II.
ΔSsystem
ΔSsurroundings
III.
ΔSuniverse
IV.
ΔHuniverse
ΔHsurroundings
39. Which one of the following thermodynamic quantities is not a
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V.
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I.
state function?
(a) Gibbs free energy
(b) Enthalpy
(c) entropy
(d) internal energy
(e) work
40. The Ho for the following reaction at 298 K is -36.4 kJ.
1/2 H2(g) + 1/2 Br2(l)
148
HBr(g)
Calculate Eo at 298 K. The universal gas constant, R, is 8.314
J/mol K.
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(a) -35.2 kJ
(b) +35.2 kJ
(c) -36.4 kJ
(d) -37.6 kJ
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(e) +37.6 kJ
Ho for the reaction:
Na2O(s) + SO3(g)
given the following information:
41. Calculate
(1) Na(s) + H2O(l)
NaOH(s) + 1/2 H2(g)
(2) Na2SO4(g) + H2O(l)
(3) 2Na2O(s) + 2H2(g)
Na2SO4(g)
Ho
-146 kJ
2NaOH(s) + SO3(g) +418 kJ
4Na(s) + 2H2O(l)
(a) +255 kJ
(b) -435 kJ
(c) -581 kJ
(d) +531 kJ
(e) -452 kJ
149
+259 kJ
42. Calculate Horxn for the following reaction at 25.0 oC:
Hfo (kJ/mol) -1118
-110.5
(a) -263 kJ
(b) 54 kJ
-272
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(c) 19 kJ
3FeO(s) + CO2(g)
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Fe3O4(s) + CO(g)
-393.5
(d) -50 kJ
(e) 109 kJ
43. The
entropy will usually increase when
I. a molecule is broken into two or more smaller molecules.
II. a reaction occurs that results in an increase in the number of
moles of gas.
III. a solid change to a liquid.
IV. a liquid change to a gas.
(a) I only
(b) II only
150
(c) III only
(d) IV only
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(e) I, II, III, and IV
44. Calculate Go for the reaction given the following information:
2SO2(g) + O2(g)
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Gfo for SO2(g) = -300.4 kJ/mol
2SO3(g)
Gfo for SO3(g) = -370.4 kJ/mol
(a) -70.0 kJ
(b) +70.0 kJ
(c) -670.8 kJ
(d) -140.0 kJ
(e) +140.0 kJ
45. For the following reaction at 25oC, Ho = +115 kJ and So =
+125 J/K. Calculate Go for the reaction at 25o.
SBr4(g)
S(g) + 2Br2(l)
(a) +152 kJ
151
(b) -56.7 kJ
(c) +77.8 kJ
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(d) +37.1 kJ
(e) -86.2 kJ
46. The
heat of vaporization of freon, CCl2F2, is 17.2 kJ/mol at
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25oC. What is the change of entropy for one mole of liquid freon
when it vaporizes at 25oC? (Hint: The vaporization process is at
equilibrium and what is true for G at equilibrium?)
(a) 57.7 J/K
(b) 0.688 J/K
(c) 5.13 x 103 kJ/K
(d) 3.16 J/K
(e) 239 J/K
47. Estimate the boiling point of Br2(l) ( H = 30.9 kJ; S = 93.0
J/K).
Br2(l)
152
Br2(g)
(a) 85oC
(b) 373oC
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(c) 177oC
(d) 59oC
(e) 44oC
C, Ho = +30 kJ; So = +50 J/K.
48. For the reaction, A + B
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Therefore the reaction is:
(a) Spontaneous at all temperatures.
(b) Nonspontaneous at all temperatures.
(c) Spontaneous at temperatures less than 600 K.
(d) Spontaneous at temperatures greater than 600 K.
(e) Spontaneous only at 25oC.
49. Which statement is incorrect?
a. At constant pressure, H = E + P V
b. Gibbs free energy is a state function.
c. For an endothermic process, H is negative.
153
d. If the work done by the system is greater than the heat
50. Which statement is false?
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absorbed by the system, E is negative.
(a) The thermodynamic quantity most easily measured in a "coffee
cup" calorimeter is H.
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(b) No work is done in a reaction occurring in a bomb calorimeter.
(c) H is sometimes exactly equal to E.
(d) H is often nearly equal to E.
(e) H is equal to E for the reaction:
2H2(g) + O2(g)
51. For
2H2O(g)
the process H2O (l)====== H2O (g) at 100 C and 1 atm.
The correct choice is
I.
Ssys>0 and Ssurr>0
II.
Ssys>0 and Ssurr<0
III.
Ssys<0 and Ssurr<0
154
Ssys<0 and Ssurr>0
IV.
(at equilibrium S univer=0 Ssys + Ssurr=0 , Ssys>0 and
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Ssurr<0
52. The entropies of a mixture of ideal gases is the sum of
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entropies of constituents evaluated at
I.
II.
Temperature and pressure of a mixture
Temperature of the mixture and mole fraction of the
constituents
III.
Temperature and volume of a mixture
IV.
Temperature and volume of a mixture
53. Which
I.
statement is incorrect for the increase of the Entropy
liquids or solutions are formed from solids,
155
gases are formed from solids or liquids,
III.
the number of gas molecules increase,
IV.
the temperature is decreased.
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II.
54. What is the increase in entropy when 3.00kg of ice
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at 0∘C melt to form water at 0∘C
I.
1.84*1000 J/K
II.
3.67*1000
III.
1.84*100000000
IV.
3.76*100000000
55. In an adiabatic process, no transfer of heat takes place
between system and surroundings. Choose the correct option for
free expansion of an ideal gas under adiabatic condition from the
following.
(i)
q = 0, ∆T ≠ 0, w = 0
156
q ≠ 0, ∆T = 0, w = 0
(iii)
q = 0, ∆T = 0, w = 0
(iv)
(iv) q = 0, ∆T < 0, w ≠ 0
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(ii)
56. The entropy change can be calculated by using the
expression ∆S = rev q T . When water freezes in a glass beaker,
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choose the correct statement amongst the following :
∆S (system) decreases but ∆S (surroundings) remains the
(i)
same.
(ii)
∆S (system) increases but ∆S (surroundings) decreases.
(iii) ∆S (system) decreases but ∆S (surroundings) increases.
(iv) ∆S (system) decreases and ∆S (surroundings) also
decreases.
57. Which of the following is not correct?
(i)
∆G is zero for a reversible reaction
157
(ii)
∆G is positive for a spontaneous reaction
(iii) ∆G is negative for a spontaneous reaction
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(iv) (∆G is positive for a non-spontaneous reaction
58. The standard molar entropy of H2O (l ) is 70 J K–1 mol–1. Will the
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standard molar entropy of H2O(s) be more, or less than 70 J K–1 mol–1?
59. Expansion of a gas in vacuum is called free expansion. Calculate the
work done and the change in internal energy when 1 litre of ideal gas
expands isothermally into vacuum until its total volume is 5 litre?
60. If S is + Ve and H is -Ve value then
I.
The reaction is spontaneous at all temperature
II.
The reaction is nonspontaneous at all temperature
III.
The reaction is spontaneous at high temperature
IV.
The reaction is spontaneous at low temperature
158
61. G is net energy available to do useful work and is thus a
measure of “free energy”. If a reaction has positive enthalpy
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change and positive entropy change, under what condition will the
reaction be spontaneous?
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62. The Clapeyron equation is:
I.
dP/dT = H/TV
II.
dT/dP = H/TV
III.
dP/dT = S/V
IV.
dP/dT = S/TV
63. The vapor pressure of 1-propanol is 0.013 atm (10 torr) at 14.7
°C. Calculate the vapor pressure at 52.8 °C.
Given: Heat of vaporization of 1-propanol = 47.2 kJ/mol
159
64. The vapor pressure of water is 1.0 atm at 373 K, and the enthalpy of
vaporization is 40.7 kJ mol-1. Estimate the vapor pressure at temperature
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363 and 383 K respectively.
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90
65. Determine ΔHvap for a compound that has a measured vapor pressure
of 24.3 torr at 273 K and 135 torr at 325 K.
66. A certain liquid has a vapor pressure of 6.91 mmHg at 0 °C. If this
liquid has a normal boiling point of 105 °C, what is the liquid's heat of
vaporization in kJ/mol?
67. The molar enthalpy of vaporization of hexane (C6H14) is 28.9
kJ/mol, and its normal boiling point is 68.73 °C. What is the vapor
pressure of hexane at 25.00 °C?
160