# Equation to calculate the triple point

Is there any equation that can calculate the triple point of a substance? Because a method for calculating the critical temperature and the Boyle temperature of a substance that I posted in another question I recently found that it also seems to be able to predict the triple point for some substances.

I searched the Internet and couldn't find any other such equation, in fact I came across a site that said there was none. Is this true? My equation predicts it from the Lennard-Jones parameters. Source:

Here is an excerpt from a document that I'm putting together. It also predicts the reduced triple point temperature to be 0.5

• Well, there is no general relation between these temperatures. – Mithoron Jun 6 '16 at 18:56
• Oh, you copied those L-J constants... Well as you can see this constant isn't equal to triple point temp. – Mithoron Jun 6 '16 at 21:00
• @Mithoron What constant? – KingChem Jun 7 '16 at 2:23
• I agree. We can't predict the triple point from just liquid and vapor characteristics alone. The properties of the solid phase must enter in. In the case of water, you have many phases each of which would potentially make its own triple point with liquid and vapor, unless you know which solid phase to pick. – Oscar Lanzi Jun 7 '16 at 9:57

In principle, you can use the integrated Clapeyron and Clausius–Clapeyron equations to calculate $P$ vs. $T$ co-existence lines and find the crossing point which is at the triple point. You need the $\Delta H$ for fusion and evaporation and the densities of the solid and liquid phases. The equations are $$p_\text{liq-vap}=\exp\left(\frac{\Delta H_\text{vap}}R\left(1/T_1-1/T\right)\right)$$ and for the solid vapour line use $\Delta H_\text{fus} +\Delta H_\text{vap}$
For the solid-liquid line use $$p_\text{sol-liq} = P_1 + \frac{\Delta H_{\text{fus}}}{\delta V}\left(\ln\left(T\right)-\ln\left(T_1\right)\right)$$
where $\delta V = M\left(1/d_\mathrm l-1/d_\mathrm s\right)$ where $M$ is the molecular weight and $d$ the densities of liquid and solid. $T_1$ and $P_1$ are temperature and pressure at the triple point. Thus you have to iterate $T_1$ and $P_1$ by fitting (say by least squares) to the calculated curves to whatever data you have to find the triple point. Tricky!