Page 145 - Modern physical chemistry

136 Relationships between Phases

the total entropy is constant,
[6.97]

and the total energy is constant,
dE=O. [6.98]
Using equations (6.95) - (6.98) to eliminate dnp), dVC 2 l, cJS<2l, dEfrom equation (6.94)
leads to
0= (T(l) _ T(2)) dS(l) _ (p(l) _ p(2)) dV(l) + L(.u~l) _ .u~2)) dn~l). [6.99]

The fluctuations cJS<1), dVC1l, dnp) are all independent (uncoupled). So to satisfy equation
(6.99), we must have
[6.100]
p(l) =p(2), [6.101]

.u~l) = .u~2). [6.102]

At equilibrium, the temperatures, the pressures, and the chemical potentials in the two
phases must be equal.
A membrane placed between the two phases may prevent some of the constituents
from moving between them. The corresponding chemical potentials would then not equi-
librate. The membrane would also support a pressure difference tlP as we saw in the dis-
cussion of osmotic pressure.
Questions

6.1 Define phase, component, thennodynarnic degree of freedom.
6.2 Justify the Gibbs phase rule.
6.3 In a particular system, molecules of A".B" appear in two different electronic states. Can
these be considered as separate components? Explain.
6.4 Why are there so many different solid phases for water?
6.5 How may one measure the nonideality of a solution?
6.6 What is a regular solution?
6.7 Derive and interpret the lever rule.
6.8 When and how does a eutectic point arise?
6.9 Distinguish between first order, second order, and higher order phase transitions.
6.10 Identify and describe examples of the different kinds of phase transitions.
6.11 Derive the Clapeyron and Ehrenfest equations.
6.12 Describe the approximations made in deriving the Clausius Clapeyron equation.
6.13 Explain why and how the vapor pressure of a component varies with the total pressure on
the given system.
6.14 How may the vapor pressure of a component vary with its concentration in the condensed
phase? Explain.
6.15 How is the activity of a component in a solution defined?
6.16 Explain the effects of a solute on the boiling point and on the freezing point of a system.
6.17 How maya semipenneable membrane act?
6.18 What conditions govern the equilibria between phases?

Problems
6.1 (a) The principal constituents in a system are H 20, Na+, K+, Ct, and Bt". How many compo-
nents does it have? (b) Salts NaCI, NaBr, KCI, and KBr are mixed with water. How many
components does the system have?