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.
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.
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter11: Solutions
Section: Chapter Questions
Problem 46P
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