# How do I make a phase diagram for water?

Jan 17, 2017

By knowing where the normal boiling and freezing points are (at $\text{1 atm}$), critical point and triple point are, and the slope of the liquid-solid, liquid-vapor, and solid-vapor coexistence curves.

Note that the phase diagram is simply a pressure vs. temperature graph.

We know that ${T}_{f} = {0}^{\circ} \text{C}$ at $\text{1 atm}$ and ${T}_{b} = {100}^{\circ} \text{C}$ at $\text{1 atm}$ are the normal freezing and boiling points, respectively.

The critical point is when the liquid and vapor exist at the same time, at some $\left({P}_{c} , {T}_{c}\right)$ on a $P$ vs. $T$ graph. For water, ${P}_{c} = \text{218.3 atm}$ and ${T}_{c} = {374.2}^{\circ} \text{C}$.

The triple point is when the solid, liquid, and vapor exist at the same time, at some $\left({P}_{\text{trpl", T_"trpl}}\right)$. For water, ${T}_{\text{trpl" = 0.01^@ "C}}$, and ${P}_{\text{trpl" = "0.006032 atm}}$.

The Clapeyron equation describes the slope of a coexistence curve, (dP)/(dT) = (DeltabarH_"trs")/(TDeltabarV_("trs")). We omit the derivation, but:

• $\Delta {\overline{H}}_{\text{trs}}$ is the molar enthalpy of the phase transition.
• $\Delta {\overline{V}}_{\text{trs}}$ is the change in molar volume due to the phase transition.
• $T$ is the temperature in $\text{K}$.

Using the Clapeyron equation:

• For the liquid-solid coexistence curve in the phase diagram of water, $\frac{\mathrm{dP}}{\mathrm{dT}} < 0$, since $\Delta {\overline{V}}_{\left(l\right) \to \left(s\right)} > 0$, and $\Delta {\overline{H}}_{\text{frz}} < 0$, which indicates that water expands when it freezes (this is unusual).
• For the liquid-vapor coexistence curve, $\frac{\mathrm{dP}}{\mathrm{dT}} > 0$, since $\Delta {\overline{V}}_{\left(l\right) \to \left(g\right)} > 0$, and $\Delta {\overline{H}}_{\text{vap}} > 0$, which indicates that water expands when it vaporizes (as usual).
• For the solid-vapor coexistence curve, $\frac{\mathrm{dP}}{\mathrm{dT}} > 0$, since $\Delta {\overline{V}}_{\left(s\right) \to \left(g\right)} > 0$, and $\Delta {\overline{H}}_{\text{sub}} > 0$, which indicates that water expands when it sublimates (clearly).

Put all that together into a phase diagram:

Simply note where each point is, and you should be able to at least sketch its general shape. Note that the phase diagram is simply a pressure vs. temperature graph.