Page 220 - Physical Chemistry

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(a) Show that the equilibrium mole fractions are x 2(P P*)/ NO O should also be included. Show that each of these re-
I
2
P and x (2P* P)/P. (b) Show that K° 4(P P*) / actions can be written as a combination of the first three reac-
I 2 P
(2P* P)P°, where P° 1 bar. (c) Find H° for I (g) ∆ 2I(g) tions and so these two reactions need not be included. (b) NIST-
2
at 1100 K. JANAF-table G° 4000 values for N(g), O(g), and NO(g) are
f
210.695, 13.270, and 40.132 kJ/mol, respectively. Use a
atm
bar
6.39 If K P and K P are the K° values with P° 1 bar and
P
with P° 1 atm, respectively, show that K P bar K P atm spreadsheet (or Mathcad, Maple V, or Mathematica) to calcu-
(1.01325) n/mol . late the composition of dry air at 4000 K and 1 bar. Take the ini-
tial composition as 0.78 mol N , 0.21 mol O , and 0.01 mol Ar.
2
2
6.40 For the ideal-gas reaction N 3H ∆ 2NH , suppose
2 2 3 Neglect the ionization of NO. (c) Vary the pressure over the
1 mol of N and 3 mol of H are present initially in a system
2 2 range 0.001 bar to 1000 bar and plot the results.
held at constant T and P; no other gases are present initially.
Let x be the number of moles of N that have reacted when
2 Section 6.6
equilibrium is reached. (x j .) Show that
eq 6.48 For the ideal-gas reaction PCl (g) ∆ PCl (g) Cl (g),
2
5
3
x 1 31 s>1s 424 1>2 where s 127K° P 2 1>2 P>P° state whether the equilibrium shifts to the right, left, or neither
when each of the following changes is made in an equilibrium
6.41 When the ideal-gas reaction A B ∆ C D has mixture at 25°C. You may use Appendix data. (a) T is de-
reached equilibrium, state whether or not each of the following creased at constant P. (b) V is decreased at constant T. (c) Some
relations must be true (all quantities are the values at equilib- PCl is removed at constant T and V. (d) He(g) is added at con-
5
rium). (a) n n n n ; (b) P P P P ; (c) n stant T and V. (e) He(g) is added at constant T and P.
C D A B C D A B A
n ; (d) n n ; (e) n n ; (f ) if only A and B are present
B C A C D
initially, then n n ; (g) if only A and B are present initially, 6.49 Suppose the temperature of an equilibrium ideal-gas re-
C A
then n n ; (h) if only A and B are present initially, then n action mixture is increased at constant volume. Under what
C D C
n n n ; (i) m m m m no matter what the condition does the equilibrium shift to the right? (Hint: Use the
D A B A B C D
initial composition. result of an earlier problem in this chapter.)
6.42 If in a gas-phase closed system, all the N and H come 6.50 (a) Show that
2 2
from the dissociation of NH according to 2NH ∆ N 3H ,
3 3 2 2 n j x j ¢n>mol
which one of the following statements is true at any time dur- a 0 ln Q x b 1 a 0Q x b
ing the reaction? (a) x 3x ; (b) 3x x ; (c) neither (a) 0n j n i j Q x 0n j n i j n j
N 2 H 2 N 2 H 2
nor (b) is necessarily true.
n
where Q (x ) i. (b) Use the result of part (a) to show that
i
i
x
Section 6.5 addition at constant T and P of a small amount of reacting
6.43 (a) Set up the spreadsheet of Fig. 6.9 and compute the species j to an ideal-gas equilibrium mixture will shift the equi-
900 K equilibrium composition of this system at 0.01, 0.1, 1.0, librium to produce more j when the following two conditions
10, 30, 100, and 1000 bar. Use the spreadsheet to graph the re- are both satisfied: (1) The species j appears on the side of the
sults. (b) Revise the spreadsheet of Fig. 6.9 to calculate the reaction equation that has the greater sum of the coefficients;
equilibrium composition at 1200 K and 0.20 bar. Use the NIST- (2) the equilibrium mole fraction x is greater than n /( n/mol).
j
j
JANAF tables (Sec. 5.9). (c) For the reaction N 3H ∆ 2NH , when will addition of
3
2
2
N to an equilibrium mixture held at constant T and P shift the
2
6.44 In the Fig. 6.9 spreadsheet, the Solver was used to make equilibrium to produce more N ? Answer the same question for
2
the fractional errors in the calculated equilibrium constants H and for NH . Assume ideal behavior.
very small. Explain why the alternative procedure of having 2 3
the Solver make the absolute errors very small might produce 6.51 For the gas-phase ammonia-synthesis reaction: (a) Sup-
very inaccurate results in certain circumstances. pose a system is in equilibrium with 3 mol of N , 1 mol of H ,
2
2
and 1 mol of NH . If 0.1 mol of N is added at constant T and
3
2
6.45 For reactions (1) and (2) of (6.47) and the initial compo- P, find n(N ) and x(N ) at the new equilibrium position. (You
2
2
sition of Fig. 6.9, give the minimum and maximum possible can use the Solver in a spreadsheet.) (b) Suppose the system is
values of j and of j and give the minimum and maximum in equilibrium with 2 mol of N , 4 mol of H , and 4 mol of NH .
1
2
2
2
3
possible numbers of moles of each species. (These conditions If 10 mol of N is added at constant T and P, find n(N ) and
could be added as constraints.) 2 2
x(N ) at the new equilibrium position.
2
6.46 (a) For the 0.01 bar calculation shown in Fig. 6.10, find 6.52 For the reactions (1) and (2) in (6.47), suppose the pres-
j for reactions (1) and (2) in (6.47). (b) Suppose that instead sure at 900 K is increased from 10 bar to 30 bar. (a) Explain
eq
of reactions (1) and (2), we describe the system by reaction (1) why the changes in extents of reaction are j n and j
CO
1
and the reaction CO H ∆ CO H O, which is reaction n Use the results of Prob. 6.43(a) to show that j 2
2
2
2
.
1
(1) minus (2). What is j for reaction (1) with this choice? 0.333 mol, j 0.173 mol, n H 2 O j 2 j
CO 2
eq
1
2
2
6.47 (a) For air up to 4000 K, one must consider the reactions 0.013 mol, and n tot 0.320 mol. Thus the pressure in-
N ∆ 2N, O ∆ 2O, and N O ∆ 2NO. Suppose some- crease has shifted reaction (2) to the side with the greater num-
2
2
2
2
one suggests that the reactions N O ∆ NO and N O ∆ ber of moles of gas.
2