Page 219 - Physical Chemistry

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The derivation is very short. (b) Use the equation derived in (a) Solving a quartic equation can be avoided in this part of the
and the approximation that H° and S° are independent of T problem.) (b) 0.200 mol of N , 0.300 mol of H , and 0.100 mol
2
2
to derive Eq. (6.39). of NH .
3
6.19 (a) For 2CO(g) O (g) ∆ 2CO (g), assume ideal-gas 6.29 For the gas-phase reaction N 3H ∆ 2NH , a closed
2 2 2 2 3
behavior and use data in the Appendix and the expression for system initially contains 4.50 mol of N , 4.20 mol of H , and
2
2
H° found in Example 5.6 in Sec. 5.5 to find an expression for 1.00 mol of NH . Give the maximum and minimum possible
3
ln K°(T) valid from 300 to 1500 K. (b) Calculate K° at 1000 K values at equilibrium of each of the following quantities: j; n ;
P P N 2
for this reaction. n ; n .
H 2 NH 3
6.20 Consider the ideal-gas dissociation reaction A ∆ 2B. 6.30 (a) For the ideal-gas reaction A ∆ 2B reaching equilib-
2
2
For A and B, we have C° P,m,A a bT cT and C° P,m,B e rium at constant T and P, show that K° [x /(1 x )](P/P°),
P
B
B
2
fT gT , where a, b, c, e, f, g are known constants and these where x is the equilibrium mole fraction. (b) Use the result of
B
1
equations are valid over the temperature range from T to T . (a) to show that x [(z 4z) 1/2 z], where z K° P°/P.
2
2
1
P
B
2
Further, suppose that H° and K°(T ) are known. Find an ex- (c) A system that is initially composed of 0.200 mol of O
T 1 P 1 2
pression for ln K°(T) valid between T and T . reaches equilibrium at 5000 K and 1.50 bar. Find the equilib-
P
2
1
rium mole fraction and moles of O and O, given that K°
6.21 Prove that for an ideal-gas reaction 2 P
49.3 for O (g) ∆ 2O(g) at 5000 K. (d) Find the equilibrium
2
¢U° mole fractions in an equilibrium mixture of NO and N O
d ln K° c 2 2 4

dT RT 2 gases at 25°C and 2.00 atm. Use Appendix data.
6.31 At 727°C, K° 3.42 for 2SO (g) O (g) ∆ 2SO (g).
2
2
P
3
6.22 Prove that for an ideal-gas reaction If 2.65 mmol of SO , 3.10 mmol of O , and 1.44 mmol of SO
2 3 2 3
0 ln K x ¢H° 0 ln K x ¢n>mol are placed in an empty 185-cm vessel held at 727°C, find the
a b , a b equilibrium amounts of all species and find the equilibrium
0T P RT 2 0P T P pressure.
6.23 True or false? (a) If H° is positive, then K° must in- 6.32 For the ideal-gas reaction A B ∆ C, a mixture with
P
crease as T increases. (b) For an ideal-gas reaction, H° must n 1.000 mol, n 3.000 mol, and n 2.000 mol is at
C
B
A
be independent of T. equilibrium at 300 K and 1.000 bar. Suppose the pressure is
isothermally increased to 2.000 bar; find the new equilibrium
Section 6.4 amounts.
6.24 A certain gas mixture held at 395°C has the following 6.33 For the reaction PCl (g) ∆ PCl (g) Cl (g), use data
5
2
3
initial partial pressures: P(Cl ) 351.4 torr; P(CO) 342.0
2 in the Appendix to find K° at 25°C and at 500 K. Assume ideal-
P
torr; P(COCl ) 0. At equilibrium, the total pressure is 439.5
2 gas behavior and neglect the temperature variation in H°. If
torr. V is held constant. Find K° at 395°C for CO Cl
P 2 ∆ we start with pure PCl , calculate the equilibrium mole frac-
5
COCl . [COCl (phosgene) was used as a poison gas in World
2 2 tions of all species at 500 K and 1.00 bar.
War I.]
6.34 At 400 K, K° 36 for N (g) 3H (g) ∆ 2NH (g).
P
3
2
2
1
3
6.25 Suppose 1.00 mol of CO and 1.00 mol of COF are Find K° at 400 K for (a) N (g) H (g) ∆ NH (g);
2
2
3
P
2
2
2
2
placed in a very large vessel at 25°C, and a catalyst for the gas- (b) 2NH (g) ∆ N (g) 3H (g).
2
2
3
phase reaction 2COF ∆ CO CF is added. Use data in the
2
2
4
Appendix to find the equilibrium amounts. 6.35 Given the G° 1000 gas-phase values 84.31 kcal/mol for
f
n-pentane, 83.64 kcal/mol for isopentane, and 89.21 kcal/mol
6.26 For the ideal-gas reaction A B ∆ 2C 2D, it is for neopentane, find the mole fractions present in an equilib-
1
given that G° 1250 cal mol . (a) If 1.000 mol of A and
500 rium mixture of these gases at 1000 K and 0.50 bar.
1.000 mol of B are placed in a vessel at 500 K and P is held
6.36 Use G° data in the NIST-JANAF tables (Sec. 5.9) to
fixed at 1200 torr, find the equilibrium amounts. (b) If 1.000 f

find K° at 6000 K for N(g) ∆ N (g) e (g).
mol of A and 2.000 mol of B are placed in a vessel at 500 K and P
P is held fixed at 1200 torr, find the equilibrium amounts. 6.37 Suppose that for a certain ideal-gas reaction, the error in
G° is 2.5 kJ/mol. What error in K° does this cause?
6.27 Suppose 0.300 mol of H and 0.100 mol of D are placed 300 P
2
2
in a 2.00-L vessel at 25°C together with a catalyst for the 6.38 At high temperatures, I vapor is partially dissociated to
2
isotope-exchange reaction H (g) D (g) ∆ 2HD(g), where I atoms. Let P* be the expected pressure of I calculated ignor-
2
2
2
2
D H is deuterium. Use Appendix data to find the equilib- ing dissociation, and let P be the observed pressure. Some val-
rium composition. ues for I samples are:
2
6.28 At 400 K, K° 36 for N (g) 3H (g) ∆ 2NH (g). T/K 973 1073 1173 1274
3
2
2
P
Find the equilibrium amounts of all species if the following P*/atm 0.0576 0.0631 0.0684 0.0736
amounts are placed in a 2.00-L vessel at 400 K, together with a
catalyst. (a) 0.100 mol of N and 0.300 mol of H . (Hint: P/atm 0.0624 0.0750 0.0918 0.1122
2
2