Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 6, Problem 6.70E

Rearrange the Clausius-Clapeyron equation, equation 6.14 in terms of the pressure p 2 of a material. Plot the vapor pressures of H 2 O (the boiling point is 100 ° C , Δ vap H = 40.71 kJ/mol ), neon (the boiling point is 246 ° C , Δ vap H = 1.758 kJ/mol ), and Li (the boiling point is 1342 ° C , Δ vap H = 134.7 kJ/mol ). Although these three materials are very different, are there any similarities in the behavior of the vapor pressures as the temperature increases?

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Interpretation Introduction

Interpretation:

The vapor pressures of H2O, neon and Li are to be plotted and any similarities in the behavior of the vapor pressures with the increase in temperature is to be stated.

Concept introduction:

The Clausius-Clapeyron equation can be obtained from the rearrangement and integration of Clapeyron equation. The Clausius-Clapeyron equation is generally used for gas-phase equilibria, to predict the equilibrium temperatures and pressures and also for the determination of enthalpy for phase transition.

Answer to Problem 6.70E

The plot between vapor pressure and temperature for H2O, neon and Li is shown below.

Physical Chemistry, Chapter 6, Problem 6.70E , additional homework tip  1

Figure 1

From the plot, the common observation is that for the given substances the increase in vapor pressure is slow until the normal boiling point.

Explanation of Solution

The Clausius-Clapeyron equation 6.14 is,

lnp2p1=ΔHR(1T21T1)

Rearrange the given equation for the partial pressure p2 as shown below.

lnp2p1=ΔHR(1T21T1)p2p1=eΔHR(1T21T1)p2=p1eΔHR(1T21T1)

Given boiling point of H2O, neon and Li is 100°C, 246°C and 1342°C respectively and the enthalpy of vaporization is 40.71kJ/mol, 1.758kJ/mol and 134.7kJ/mol respectively.

Calculation of partial pressure p2 for H2O.

ΔH T1 p1 T2 p2
40.71kJ/mol 373K 1atm 300K 1.04×105atm
40.71kJ/mol 373K 1atm 500K 28.05atm
40.71kJ/mol 373K 1atm 750K 734.14atm

Calculation of partial pressure p2 for neon.

ΔH T1 p1 T2 p2
1.758kJ/mol 27K 1atm 20K 0.064atm
1.758kJ/mol 27K 1atm 100K 5.72atm
1.758kJ/mol 27K 1atm 200K 817.31atm

Calculation of partial pressure p2 for Li.

ΔH T1 p1 T2 p2
134.7kJ/mol 1615K 1atm 1500K 0.46atm
134.7kJ/mol 1615K 1atm 1600K 0.91atm
134.7kJ/mol 1615K 1atm 1800K 2.801atm

The plot between vapor pressure and temperature for H2O, neon and Li is shown below.

Physical Chemistry, Chapter 6, Problem 6.70E , additional homework tip  2

Figure 1

To observe the change in the plot of lithium, the values of vapor pressure is considered till 10atm as shown below.

Physical Chemistry, Chapter 6, Problem 6.70E , additional homework tip  3

Figure 2

From the plot, the common observation is that for the given substances the increase in vapor pressure is slow until the normal boiling point. After the normal boiling point, the increase in vapor pressure is exponential. As the temperature increases from lower normal boiling point to higher values, the exponent value changes from negative to positive.

Conclusion

From the plot, the common observation is that for the given substances, the increase in vapor pressure is slow until the normal boiling point.

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Chapter 6 Solutions

Physical Chemistry

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