# Entropy of solid, liquid, and gas at triple point of water

At the triple point of water how do the entropies of solid, liquid, and gas compare?

I think that either they will be equal or it will be that gas > liquid > solid.

I don't know if entropy is influenced by the fact that it will be at the triple point. Can someone please elaborate?

Triple point defines a situation of simultaneous equilibrium between the solid, the liquid and the gas phases.

For such an equilibrium, you simply write:

$$\Delta S= \frac{\Delta H}{T}$$

that rises from the fact that $\Delta G=0$.

Considering water molar ($m$) enthalpies for each phase transition at $273\,K$:

$$\Delta H_{melting,m}=6.01\,kJ\,mol^{-1}$$ $$\Delta H_{vaporisation,m}=45.05\,kJ\,mol^{-1}$$ $$\Delta H_{sublimation,m}=51.06\,kJ\,mol^{-1}$$

one realises that

• the entropy of the gas phase is higher than the entropy of the liquid phase.
• the entropy of the liquid phase is higher than the entropy of the solid phase

In this respect the triple point has no peculiar behaviour compared to other points where a two-phase equilibrium is established.