Page 217 - Essentials of physical chemistry

More Kinetics and Some Mechanisms 179

of the x-intercept where (1=V) ¼ 0. Compare the value of the new K M value with the K M from
the problem. Submit your graph along with your calculations.

[S] 4.8 mM 1.2 mM 0.6 mM 0.3 mM
1=[S] 0.21 0.83 1.67 3.33
DOD 540 (V i ) 0.060 0.032 0.019 0.011
1=V i 16.7 31.3 52.6 90.9

TESTING, GRADING, AND LEARNING?
Next, we present a final examination from the 2008 Summer course in CHEM 303. The time limit was
3 h including 110 min. for an ACS standardized test and the students knew that the grade on this test
would be their final grade if the score was higher than their average including the score on the final.

Physical chemistry 303 Final examination Summer 2008 D. Shillady, Professor
(points) (Attempt all problems)

1 4
(20) 1. Using h n*m vl ¼ 2:08 10 g=cm s at 258C and 1 atm for O 2 , compute s, l, Z 1 ,
visc ¼
2
28
and Z 11 . (atomic weight O ¼ 15.9994 g=mol, s ¼ 3:57 Å, l ¼ 716 Å, Z 11 ¼ 7.63 10 )
X q rev
(20) 2. Show that ¼ 0 for a Carnot cycle, derive the Carnot efficiency formula.
T
(20) 3. Calculate the temperature of air compressed adiabatically in a one-cylinder diesel engine from
3
3
1040 cm at 258C and 1 atm to 40 cm . Given C V ¼ (5=2)R compute Q, moles of air, W, DU,
and DH for this compression.
(Q ¼ 0, n ¼ 0.0425, T ¼ 10978K, W ¼ DU ¼ 168:8 cal, DH ¼ 236:3 cal, P ¼ 95.71 atm)
ffiffiffiffiffi ffiffiffiffiffi
3
p p
2
3
(20) 4. Derive the expressions for v, v , and v of a gas using the Boltzmann principle.
(20) 5. Given the normal boiling point of CH 3 CH 2 OH is 78.458C and the vapor pressure is 78.5
mmHg at 308C, compute DH vap for CH 3 CH 2 OH and compute the vapor pressure at 708C.
(DH vap ¼ 9924 cal=mol, P ¼ 535.7 mmHg at 708C)
(20) 6. Find P c , V c , and T c for a van der Waals gas and show the law of corresponding states.

qU
(20) 7. Derive the expression for of a van der Waals gas and use it to compute DU for the
qV
T

isothermal compression of 10 mol of Ne gas from 500 to 50 L at 258C ‘‘a’’ ¼ 0.21

qP
2
2
L atm=mol ; use dU ¼ T P (DU ¼ 9:15 cal, note the sign)
qT
V
(20) 8. If A k 1 ! B k 2 ! C with t 1=2 (A) ¼ 3 h and t 1=2 (B) ¼ 8 h, calculate the time when [B]
is a maximum given [A] ¼ 100 and [B] ¼ [C] ¼ 0at t ¼ 0. (Answer: 6.794 h)
(10) 9. 198 Au is radioactive with t 1=2 ¼ 2:70 days. How long will it take for 69% of 250 g to decay?
79
(Answer: 4.563 days)
(20) 10. Derive the formula for DS mix of a binary liquid, assuming DH mix ¼ 0. Show that DG mix is a
minimum and DS mix is a maximum when the mole fractions are 0.5.