Page 311 - Physical Chemistry

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9.49 The vapor in equilibrium with a solution of ethanol (eth) water increase or decrease from 20°C to 30°C? (b) Use (9.72)
l
v
l
and chloroform (chl) at 45°C with x chl 0.9900 has a pressure to estimate H i ° H i ° for O in water in the range 20°C to
2
v
l
v
of 438.59 torr and has x chl 0.9794. The solution can be as- 30°C. (c) Use data in Sec. 9.8 to find G i ° G i ° for O in water
2
l
v
sumed to be essentially ideally dilute. (a) Find the vapor-phase at 25°C. (d) Estimate S i ° S i ° for O in water at 25°C.
2
partial pressures. (b) Calculate the vapor pressure of pure chlo-
roform at 45°C. (c) Find the Henry’s law constant for ethanol 9.61 Show that the temperature and pressure variations of the
in chloroform at 45°C. Henry’s law constant are
q l
v l H° i H i
v
9.50 Use Fig. 9.21 to find (a) the vapor pressure of CS 2 a 0 ln K i b H° i H° i (9.72)
v
at 29°C; (b) x chl in the vapor in equilibrium with a 35°C 0T P RT 2 RT 2
l
acetone–chloroform solution with x chl 0.40. (The horizontal 0 ln K i V° i V i
ql
l
scale is linear.) a b (9.73)
0P T RT RT
9.51 From Fig. 9.21b, estimate K for acetone in CS and for
2
i
CS in acetone at 29°C. General
2
9.62 The normal boiling points of benzene and toluene are
9.52 Use the definition (9.62) of K and K chl 145 torr (Fig. 80.1°C and 110.6°C, respectively. Both liquids obey Trouton’s
i
l v
rule well. For a benzene–toluene liquid solution at 120°C with
9.21a) to find m° chl m° chl for chloroform in acetone at 35°C.
v
l
9.53 At 20°C, 0.164 mg of H dissolves in 100.0 g of water x C 6 H 6 0.68, estimate the vapor pressure and x C 6 H 6 . State any
2
when the H pressure above the water is 1.000 atm. (a) Find the approximations made. (The experimental values are 2.38 atm
2
Henry’s law constant for H in water at 20°C. (b) Find the mass and 0.79.)
2
of H that will dissolve in 100.0 g of water at 20°C when the H 2 9.63 Derive (9.41) for the chemical potentials in an ideal
2
pressure is 10.00 atm. Neglect the pressure variation in K . of the
i
solution by taking 10>0n C 2 T,P,n B mix G equation (9.39),
9.54 Air is 21% O and 78% N by mole fraction. Find the noting that mix G G G* G n m* n m*.
2
C
C
B
2
B
masses of O and N dissolved in 100.0 g of water at 20°C that 9.64 The process of Fig. 9.6 enables calculation of G.
2
2
mix
is in equilibrium with air at 760 torr. For aqueous solutions at (a) Find expressions for G of each step in Fig. 9.6, assuming
7
7
20°C, K 2.95 10 torr and K 5.75 10 torr.
O 2 N 2 all gases are ideal. To find G , use a result stated at the end of
4
9.55 Explain why the partial molar properties of the solvent Sec. 6.1 and derived in Prob. 9.20. (b) Explain why G and
1
A in an ideally dilute solution obey the same equations as for G are quite small unless P is very high. (c) Show that if G 1
6
the components of an ideal solution. From Prob. 9.44, we have and G are assumed negligible, then
6
for the solvent in an ideally dilute solution
¢ mix G n A RT ln 1P A >P*2 n B RT ln 1P B >P*2 (9.74)
B
A

(d) Verify that if Raoult’s law is obeyed, (9.74) reduces to the
S A S* m,A R ln x A , V A V* m,A , H A H* m,A
ideal-solution G equation.
9.56 (a) Use Eq. (9.31) to show that V i V i ° for a solute in mix
an ideally dilute solution. Explain why V i ° is independent of 9.65 For ethanol(eth)–chloroform(chl) solutions at 45°C,

concentration in the ideally dilute range and why V i ° V i . vapor pressures and vapor-phase ethanol mole fractions as a
q
q
(b) Use Fig. 9.8 to find V H 2 O in a water–ethanol solution at function of solution composition are [G. Scatchard and C. L.
20°C and 1 atm. Raymond, J. Am. Chem. Soc., 60, 1278 (1938)]:
9.57 Derive the following equations for partial molar proper- x eth 0.2000 0.4000 0.6000 0.8000
ties of a solute in an ideally dilute solution v
q x eth 0.1552 0.2126 0.2862 0.4640
S i S ° i R ln x i , H i H° i H i
P/torr 454.53 435.19 391.04 298.18
9.58 Show that for an ideally dilute solution
At 45°C, P* 172.76 torr and P* 433.54 torr. Use
chl
eth

¢ mix V a n i 1V° i V* 2, ¢ mix H a n i 1H° i H* m,i 2 Eq. (9.74) of Prob. 9.64 to calculate and plot mix G/(n n ).
A
B
m,i
i A i A
9.66 A simple two-component solution is one for which
9.59 Substitute m m° RT ln x into the equilibrium con-
i i i
dition n m 0 to derive G° RT ln K for an ideally di- ¢ mix G
i i i x
n
lute solution, where G° n m° and K (x ) i. n A RT ln x A n B RT ln x B 1n A n B 2x A x B W1T, P2
i i i x i i,eq
9.60 The definition (9.62) of the Henry’s law constant K at constant T and P, where W(T, P) is a function of T and P.
i
l
shows that if we know K in a solvent A, we can find m° Statistical mechanics indicates that when the A and B mole-
i
i
l
v
m° G i ° G i ° , the change in standard-state partial molar cules are approximately spherical and have similar sizes, the
v
i
Gibbs energy of gas i when it dissolves in liquid A. If we know solution will be approximately simple. For a simple solution,
l v
K as a function of T, we can find H i ° H i ° using Eq. (9.72) (a) find expressions for H, S, and V; (b) show that
i mix mix mix
l
v
l
v
2
of Prob. 9.61. Knowing G i ° G i ° and H i ° H i ° , we can find m m* RT ln x Wx , with a similar equation for m ;
A
B
B
A
A
l v 7
S i ° S i ° . (a) For O in water, K 2.95 10 torr at 20°C (c) find expressions for the vapor partial pressures P and P ,
2 i A B
and K 3.52 10 torr at 30°C. Does the solubility of O in assuming ideal vapor.
7
i 2