Page 139 - Essentials of physical chemistry

The Second and Third Laws of Thermodynamics 101

2 2
(10) 7. Given a ¼ 3.610 atm L =mol and b ¼ 0,0429 L=mol for the van der Waals equation of CO 2 ,
calculate the pressure P in atm of 5 mol of CO 2 in a 5 L container at 708C.
(P ¼ 25.81 atm)
(10) 8. Show that (C P C V ) ¼ R for an ideal gas.
(See chapter notes)

Physical chemistry 303 Summer 2009 D. Shillady, Professor
(Points) Midterm examination (Attempt all problems) 120 min

(15) 1. Using h visc ¼ (1=2)n*m vl ¼ 2:08 10 4 poise at 258C and 1 atm pressure for O 2 , compute
d, l, Z 1 , and Z 11 . (Atomic weight for O ¼ 15.9994 g=mol) (d ¼ 3.573 10 8 cm,
3
9
1
l ¼ 716 10 8 cm, Z 1 ¼ 6.203 10 s , Z 11 ¼ 7.634 10 28 binary=cm s)
(15) 2. Using the Boltzmann distribution, set up the distribution function for the speed of a gas
molecule in any direction; derive formulas for v, v rms , and the most probable speed a.
(See chapter notes)
(10) 3. Calculate v for He (atomic weight 4.002503) gas molecules at 258C in mph.
(2809.22 mph)
(10) 4. Show (C P C V ) ¼ R for an ideal gas. (See chapter notes)
0
0
(10) 5. Compute DH 298 for the reaction 3(HC CH ! C 6 H 6(l) given the data DH comb
0
(HC CH) ¼ 1301:1 kJ=mol and DH comb (C 6 H 6 ) ¼ 3267:6 kJ=mol.
(DH 0 ¼ 635:7 kJ)
298
(15) 6. Find P c , V c , and T c for a van der Waals gas and show the law of corresponding states.
(See chapter notes)
(15) 7. Calculate the temperature of air compressed adiabatically in a one-cylinder diesel
3
3
engine from 1050 cm at 228C and 1 atm pressure to 50 cm . Given C V ¼ (5=2)R, compute
moles air, Q, W, DH, and DU for this compression.
(Q ¼ 0, W ¼ DU, DU ¼ 151.78 cal ¼ 636. 0 J, DH ¼ 212:5 cal ¼ 889:1, n ¼ 0.0434)
(10) 8. Calculate the entropy of fusion (DS fus ) of a compound at 08C given that its DH fus is 39 kJ=mol
at 1568C (mp) and the molar C P values are 28.0 J=8C for the liquid and 20.0 J=8C for the
solid. (DS fus ¼ 87:263 J= K at 08C)

DS took 80 min

PROBLEMS

5.1 Estimate the absolute entropy of 1-deutero-naphthalene at 18K using S ¼ k B ln W.
5.2 Calculate the efficiency of a internal combustion heat engine operating with a heat source at
10008C and discarding exhaust heat at 7008C.
5.3 Calculate the entropy of mixing for a mixture of n-heptane and n-octane versus mole fraction
and sketch a graph showing DS mix for mole fractions of n-heptane as 0.01, 0.25, 0.4, 0.5, 0.6,
0.75, and 0.99 on the same graph using a different scale on the Y-axis plot
DG mix ¼ DH mix T DS mix assuming DH mix ¼ 0 and T ¼ 258C. Scale DS mix 100.
5.4 Derive all eight of the basic thermodynamic equations starting from the first law, the definition
of H and dS ¼ dq rev =T. Derive the four Maxwell relationships using the idea of reversing the
order of differentiation.
1
5.5 Calculate DS 298 for the reaction H 2 (g) þ O 2 (g) ! H 2 O (liq) at 298.158K using the data in
2
Table 5.1. Then use that value to correct the value of DS 298 to DS 1000 at 10008K using the
polynomials in Table 4.4.