Thermodynamics and Chemistry

CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES

PROBLEMS 221

(a)Use the Clapeyron equation to calculate the slope dp=dTof the liquid–gas coexistence

curve at this point.

(b)Repeat the calculation using the Clausius–Clapeyron equation.

(c)Use your results to estimate the standard boiling point of water. (Note: The experimental

value is99:61C.)

8.8 At the standard pressure of 1 bar, liquid and gaseous H 2 O coexist in equilibrium at372:76K,

the standard boiling point of water.

(a)Do you expect the standard molar enthalpy of vaporization to have the same value as the

molar enthalpy of vaporization at this temperature? Explain.

(b)The molar enthalpy of vaporization at372:76K has the valueÅvapHD40:67kJ mol^1.

Estimate the value ofÅvapHat this temperature with the help of Table7.5and the fol-

lowing data for the second virial coefficient of gaseous H 2 O at372:76K:

BD4:60 10 ^4 m^3 mol^1 dB=dTD3:4 10 ^6 m^3 K^1 mol^1

(c)Would you expect the values ofÅfusHandÅfusHto be equal at the standard freezing

point of water? Explain.

8.9 The standard boiling point of H 2 O is99:61C. The molar enthalpy of vaporization at this

temperature isÅvapHD40:67kJ mol^1. The molar heat capacity of the liquid at temperatures

close to this value is given by

Cp;mDaCb.tc/

wheretis the Celsius temperature and the constants have the values

aD75:94J K^1 mol^1 bD0:022J K^2 mol^1 cD99:61C

Suppose100:00mol of liquid H 2 O is placed in a container maintained at a constant pressure

of 1 bar, and is carefully heated to a temperature5:00C above the standard boiling point, re-

sulting in an unstable phase of superheated water. If the container is enclosed with an adiabatic

boundary and the system subsequently changes spontaneously to an equilibrium state, what

amount of water will vaporize? (Hint: The temperature will drop to the standard boiling point,

and the enthalpy change will be zero.)