The latent heat of vaporisation of benzene at its boiling point (80 °C) is 7413 cal mol^–1. What is the vapor pressure of benzene at 27 °C.

Question

The latent heat of vaporisation of benzene at its boiling point (80 °C) is 7413 cal [latex]\mathrm{mol}^{–1}[/latex]. What is the vapor pressure of benzene at 27 °C.

Accepted Answer

[latex]\begin{array}{l}\Delta \mathrm{H}_{\mathrm{V}}=7413 \mathrm{~cal} \mathrm{~mol}^{-1} ; \mathrm{T}_{1}=80 ^{\circ} \mathrm{C}=353 \mathrm{~K} ; \quad \mathrm{P}_{1}=1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{~Hg} \ \ \mathrm{T}_{2}=27 ^{\circ} \mathrm{C}=300 \mathrm{~K} ; \quad \mathrm{P}_{2}=?\ \ \log \frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}=\frac{\Delta \mathrm{H}_{\mathrm{V}}}{2.303 \mathrm{~R}}\left[\frac{\mathrm{T}_{2}-\mathrm{T}_{1}}{\mathrm{~T}_{2} \mathrm{~T}_{1}} ight] \ \ \log \frac{\mathrm{P}_{2}}{760 \mathrm{~mm} \mathrm{~Hg}}=\frac{7413 \mathrm{~cal} \mathrm{~mol}^{-1}}{2.303 imes 1.987 \mathrm{~cal} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}}\left[\frac{300-353}{300 imes 353} ight] \ \ \quad \quad \quad \quad =\frac{7413 imes(-53)}{2.303 imes 1.987 imes 300 imes 353}=-0.8107 \ \ \log \frac{760 \mathrm{~mm} \mathrm{~Hg}}{\mathrm{P}_{2}}=0.8107\ \ ext { or } \frac{760 \mathrm{~mm} \mathrm{~Hg}}{\mathrm{P}_{2}}= ext { Antilog } 0.8107=6.4670\ \ ext { Hence } P_{2}=760 / 6.4670=117.52 \mathrm{~mm} \mathrm{~Hg} \end{array}[/latex]

Question 15.10.1: The latent heat of vaporisation of benzene at its boiling po......

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