I was wondering what is the difference between the Clausius-Clapeyron equation and the Van't Hoff equation. They appear to have the exact same physical meaning and are often used interchangeably.


They're two forms of the same equation, but Clausius-Clapeyron uses vapor pressure ($p^*$) where Van 't Hoff uses the reaction equilibrium constant ($K$).

Why does this work out? Well, think of vaporization as a chemical reaction:

$$ \text{X} (l) \longrightarrow \text{X} (\text{g}) $$

The equilibrium constant is defined in terms of activity (a):

$$ K=\left.\frac{a_\text{X(g)}}{a_{\text{X}(l)}}\right|_\text{equil} $$

For an ideal liquid solution at modest pressure, a is just the mole fraction x. And for an ideal gas, a is just its partial pressure in bar:

$$ K=\left.\frac px\,\right|_\text{equil}$$

One equilibrium condition is $x=1\ $ and $p=p^*,\ $ so...

$$ K=p^* $$

Or $p^*$ is the equilibrium coefficient for vaporization. Now since K is characteristic of a reaction at a given temperature, this would imply that if we change x, then the new partial pressure at equilibrium would change according to

$$ K=p^*=\frac{p}{x} \qquad\Rightarrow\qquad p=xp^*$$

And that's exactly what happens. Neat, huh?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.