I explained the Clausius-Clapeyron equation in one of my posts (here) and so won’t repeat the details. HOWEVER, I didn’t definitively demonstrate via calculation why my hypothesis is valid.

Here’s the equation:

dP/dT = ∆H_vap / V_vT

wherein P is the saturated vapor pressure at T, ∆H_vap is the heat of vaporization per mole and V_v is the molar volume of the vapor. 

In my final physical explanation of why dP^sat/dT is proportional to ∆H_vap, I proposed that when temperature increases (dT), the Maxwell-Boltzmann shifts and the fraction of molecules with sufficient escape energy increases, thus increasing vapor pressure.

I then explained why, for a given dT, the relative increase in vapor pressure is higher for a higher the value of ∆H_vap because the initial fraction of vaporizing liquid molecules is lower.

BUT… what I didn’t do was use this explanation as the basis for a derivation that would lead to the Clauius-Clapeyron equation. So this is something that I still must do.

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