Page 262 - Physical Chemistry

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B may undergo reactions in the solution. In the solution, A and 7.72 From Eq. (7.34), a drop of liquid of radius r is at a
B react to form E and F according to higher pressure than the vapor it is in equilibrium with. This
increased pressure affects the chemical potential of the liquid
aA bB ∆ eE f F
and raises its vapor pressure slightly. (a) Use the integrated
If b 0, this reaction might be dissociation or association of form of Eq. (7.38) in Prob. 7.66 to show that the vapor pres-
the solvent. If b 0, the reaction might be solvation of the sure P of such a drop is
r
solute B. No E or F is added from the outside. Therefore, c ind P r P exp 12gV m,l >rRT2
c r a 4 1 1 2.
s
s
Let dn and dn moles of A and B be added to the solu- where V m,l is the molar volume of the liquid and P its bulk
B
A
tion from outside. This addition shifts the reaction equilibrium vapor pressure. This is the Kelvin equation. (b) The vapor pres-
to the right, and the extent of reaction changes by dj. Since sure and surface tension of water at 20°C are 17.535 torr and
dn n dj for a reaction, the actual change in number of 73 dyn/cm. Calculate the 20°C vapor pressure of a drop of
i
i
s
s
moles of A is dn dn n dj dn adj. The quantity water of radius 1.00 10 5 cm.
A
A
A
A
m dn that occurs in the Gibbs equation for dG is m dn i 7.73 True or false? (a) For a one-component system, the max-
i
i
i
i
i
m dn m dn m dn m dn . (a) Show that imum number of phases that can coexist in equilibrium is three.
F
E
F
E
A
B
A
B
(b) The equation dP/dT H/(T V) is exact. (c) The equation
s
a m i dn i m A dn A m B dn B s d ln P/dT H /RT is exact. (d) When three phases coexist
2
i m
in equilibrium in a one-component system, one of the phases
provided reaction equilibrium is maintained. Thus we can take must be a gas, one must be a liquid, and one must be a solid.
the sum over only the independent components A and B and (e) For a one-component system, the most stable phase at a
ignore solvation, association, or dissociation. (b) Use the result given T and P is the phase with the lowest G . (f ) Solid H O
m
2
of part (a) to show that cannot exist at 100°C as a stable phase. (g) For a pure
substance, the vapor pressure of the solid is equal to the
s
s
vapor pressure of the liquid at the triple-point temperature.
m A 10G>0n A 2 T,P,n B
4
7.71 For pressures under 10 atm, which of the following (h) Liquid water cannot exist at 1 atm and 150°C. (i) If phases
a
phases can exist at temperatures arbitrarily close to absolute a and b of a closed system are in equilibrium, then m must
b
zero: (a) H O(s); (b) H O(l); (c) H O(g)? equal m .
2
2
2