Use of the Clausius-Clapeyron Equation The vapor pressure of liquid 2,2,4-trimethyl pentane at various temperatures is given below. Estimate the heat of vaporization of this compound at 25°C.

Question

Use of the Clausius-Clapeyron Equation

The vapor pressure of liquid 2,2,4-trimethyl pentane at various temperatures is given below. Estimate the heat of vaporization of this compound at 25°C.

Vapor pressure (kPa)	0.667	1.333	2.666	5.333	8.00	13.33	26.66	53.33	101.32
Temperature (°C)	-15.0	-4.3	7.5	20.7	29.1	40.7	58.1	78.0	99.2

Accepted Answer

Over a relatively small range of temperature (say from 20.7 to 29.1°C), [latex]\Delta_{ vap } \underline{H}[/latex] may be taken to be constant. Using Eq. 7.7-6, we obtain

[latex]\ln \frac{P^{ vap }\left(T_{2} ight)}{P^{\operatorname{vap}}\left(T_{1} ight)}=-\frac{\Delta_{ vap } \underline{H}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}} ight)[/latex] (7.7-6)

[latex]\frac{\Delta_{ vap } \underline{H}}{R}=\frac{-\ln \left[P^{ vap }\left(T_{2} ight) / P^{ vap }\left(T_{1} ight) ight]}{\frac{1}{T_{2}}-\frac{1}{T_{1}}}=\frac{-\ln (8.000 / 5.333)}{\frac{1}{302.25}-\frac{1}{293.85}}=4287.8 K[/latex]

so that

[latex]\Delta_{ vap } \underline{H}=35.649 kJ / mol[/latex]

One can obtain an estimate of the temperature variation of the heat of vaporization by noting that the integration of Eq. 7.7-5 can be carried out as an indefinite rather than definite integral. In this case we obtain

[latex]\frac{d \ln P^{ ext {vap }}}{d T}=\frac{\Delta_{ ext {vap }} \underline{H}}{R T^{2}}[/latex] (7.7-5a)

[latex]\ln \frac{P^{ ext {vap }}\left(T_{2} ight)}{P^{ ext {vap }}\left(T_{1} ight)}=\int_{T_{1}}^{T_{2}} \frac{\Delta_{ ext {vap }} \underline{H}}{R T^{2}} d T[/latex] (7.7-5b)

[latex]\ln P^{ vap }(T)=-\frac{\Delta_{ vap } \underline{H}}{R T}+C[/latex]

where C is a constant. Therefore, if we were to plot [latex]\ln P^{ ext {vap }}[/latex] versus 1/T , we should get a straight line with a slope equal to [latex]-\Delta_{ ext {vap }} \underline{H} / R[/latex] f the heat of vaporization is independent of temperature, and a curve if [latex]\Delta_{ vap } \underline{H}[/latex] varies with temperature. Figure 7.7-1 is a vapor pressure-temperature plot for the 2,2,4-trimethyl pentane system. As is evident from the linearity of the plot, [latex]\Delta_{ vap } \underline{H}[/latex] is virtually constant over the whole temperature range.

Question 7.7.1: Use of the Clausius-Clapeyron Equation The vapor pressure of...

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