7.66 (a) Consider a two-phase system, where one phase is pure liquid A and the second phase is an ideal gas mixture of A vapor with inert gas B (assumed insoluble in liquid A). The presence of gas B changes μA, the chemical potential of liquid A, because B increases the total pressure on the liquid phase. However, since the vapor is assumed ideal, the presence of B does not affect μg, the chemical potential of A in the vapor phase [see Eq. (6.4)]. Because of its effect on μ¼, gas B affects the liquid-vapor equi- librium position, and its presence changes the equilibrium vapor pressure of A. Imagine an isothermal infinitesimal change dP in the total pressure P of the system. Show that this causes a change dPA in the vapor pressure of A given by А dPA V¹m.A Vm.APA const. T (7.38) dP V8 m,A RT Equation (7.38) is often called the Gibbs equation. Because V m,A' m,A is much less than Vg the presence of gas B at low or moder- ate pressures has only a small effect on the vapor pressure of A. (b) The vapor pressure of water at 25°C is 23.76 torr. Calculate the vapor pressure of water at 25°C in the presence of 1 atm of inert ideal gas insoluble in water.

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7.66 (a) Consider a two-phase system, where one phase is pure
liquid A and the second phase is an ideal gas mixture of A vapor
with inert gas B (assumed insoluble in liquid A). The presence of
gas B changes μA, the chemical potential of liquid A, because B
increases the total pressure on the liquid phase. However, since
the vapor is assumed ideal, the presence of B does not affect μg,
the chemical potential of A in the vapor phase [see Eq. (6.4)].
Because of its effect on μ¼, gas B affects the liquid-vapor equi-
librium position, and its presence changes the equilibrium vapor
pressure of A. Imagine an isothermal infinitesimal change dP in
the total pressure P of the system. Show that this causes a change
dPA in the vapor pressure of A given by
А
dPA
V¹m.A
Vm.APA
const. T
(7.38)
dP
V8
m,A
RT
Equation (7.38) is often called the Gibbs equation. Because V
m,A'
m,A
is much less than Vg the presence of gas B at low or moder-
ate pressures has only a small effect on the vapor pressure of A.
(b) The vapor pressure of water at 25°C is 23.76 torr. Calculate
the vapor pressure of water at 25°C in the presence of 1 atm of
inert ideal gas insoluble in water.
Transcribed Image Text:7.66 (a) Consider a two-phase system, where one phase is pure liquid A and the second phase is an ideal gas mixture of A vapor with inert gas B (assumed insoluble in liquid A). The presence of gas B changes μA, the chemical potential of liquid A, because B increases the total pressure on the liquid phase. However, since the vapor is assumed ideal, the presence of B does not affect μg, the chemical potential of A in the vapor phase [see Eq. (6.4)]. Because of its effect on μ¼, gas B affects the liquid-vapor equi- librium position, and its presence changes the equilibrium vapor pressure of A. Imagine an isothermal infinitesimal change dP in the total pressure P of the system. Show that this causes a change dPA in the vapor pressure of A given by А dPA V¹m.A Vm.APA const. T (7.38) dP V8 m,A RT Equation (7.38) is often called the Gibbs equation. Because V m,A' m,A is much less than Vg the presence of gas B at low or moder- ate pressures has only a small effect on the vapor pressure of A. (b) The vapor pressure of water at 25°C is 23.76 torr. Calculate the vapor pressure of water at 25°C in the presence of 1 atm of inert ideal gas insoluble in water.
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