Page 167 - Essentials of physical chemistry

Gibbs’ Free Energy and Equilibria 129

PROBLEMS

6.1 Calculate the moles of H 2 ,D 2 , and HD for the equilibrium in Example 1 at 08C and again at
508C and predict whether the yield of HD is increased or decreased at higher temperatures.
6.2 Calculate DS vap for ethanol using the vapor pressures of 24.2 mmHg at 108C and 541.1 mmHg
at 708C. Report the values you find for DH vap and the normal boiling point.
6.3 Calculate the boiling point of benzene using the data in Table 6.2 and the vapor pressure at 208C.
6.4 Calculate DH 0 for CCl 4 using two well spaced temperatures from Table 6.1 or 6.2 and then
vap
find the ‘‘normal boiling point’’ (at 1 atm pressure) of CCl 4 .
6.5 Calculate the pressure on a single ice skate blade 10 in. long by (0.125 in.) wide supporting the
weight of an adult male skater weighing 180 lb. Give the answer in atm, bar, psi and pascals.
6.6 Calculate the vapor pressure of I 2 crystals using the DH 0 value due to the temperature of
sub
988F from the breath of a forensic investigator.
6.7 Calculate C P C V for CS 2 at 208C.
6.8 Suppose you are employed by a laboratory that has synthesized and patented a new liquid
detergent called ‘‘Brand X’’ and they want to know its partial molal volume in water, so they
can calculate how much to mix with water to achieve a given bottle volume at a given
concentration of the detergent. By performing a number of total volume measurements you
obtain points related to the moles of the detergent and fit a polynomial to the data using a
computer program. Your supervisor wants to know the partial molal volume formulas as a
function of ‘‘m’’ moles of detergent from the polynomial you have fitted to the total volume
3
2
data which is V tot (cm ) ¼ 1002:83 þ 12:4635m þ 0:9834m where ‘‘m’’ is the moles of the
detergent. Calculate V H 2 O and V detergent for this solution.
TVa 2
6.9 Derive the expression (C P C V ) ¼ . If this question occurred on an examination, how
b
long would it take for you to do the derivation: 5 min, 3 min? This exercise is an excellent
review of the manipulation of partial derivatives.
6.10 Given the value of DH 0 ¼þ17:06 kcal and DG 0 ¼þ9:72 kcal for the equilibrium
298 298
2NOCl (g) ƒ 2NO (g) þ Cl 2(g) , estimate the temperature at which K P ¼ 0.500 assuming the
ƒ!
values of DH and DG remain constant.

TESTING, GRADING, AND LEARNING?
Here we provide another actual midterm examination from the intense Summer P. Chem. course at
VCU in 2008. If students are told they are responsible for derivations like the van der Waals critical
point and the Carnot cycle they will have a chance to learn them, but it is unlikely students will ‘‘learn’’
such derivations without fair warning. Since students can learn massive amounts of encyclopedic
information in organic chemistry and biochemistry, there is no reason not to expect them to learn key
multistep derivations. Learning these key derivations improves the level of the math skill in the class.

Physical chemistry 303 Midterm, Summer 2008 D. Shillady, Professor
(Points) (120 min. Attempt all problems.)

P q rev
(15) 1. Show that ¼ 0 for a Carnot cycle; derive the efficiency formula.
T
(Answer in Chapter 4, how fast can you do the derivation?)
(10) 2. Calculate the laminar bulk flow rate in gallons=min for blood with h ¼ 0.015 poise through
an aorta 5 in. long and (1=4 in.) inner diameter due to a pressure difference of (120–60)
mmHg. Multiply by a ‘‘duty factor’’ of 0.05 to compensate for pulsation.
[(V=t) ¼ 1.3285 gallons=min]
(15) 3. Find P c , V c , and T c for a van der Waals gas and show the law of corresponding states.
(Answer in Chapter 1, how fast can you do the derivation?)