# CfE: Pure Component Phase Equilibrium

### Equilibrium: Two (pure) Phases

We have shown that the criteria for equilibrium is:

\$dG \le 0\$

For a mixture of two phases we can write:

\$G = n_lg_l + n_vg_v\$

so that

\$dG = n_ldg_l + g_ldn_l + n_vdg_v + g_vdn_v\$

Since we are assuming thermal equilibrium (constant \$T\$) and mechanical equilibrium (constant \$P\$), the state postulate says that \$g\$ is fixed so that \$dg_l = dg_v = 0\$, so

\$dG = g_ldn_l + g_vdn_v\$

At equilibrium the rate of change of material from one phase must be balanced by the rate of change of material to that phase, so that \$dn_v = -dn_l\$ and

\$dG = (g_l-g_v)dn_v \le 0\$

Once we reach equilibrium the inequality takes on the value of zero, so

\$g_l=g_v\$

##### Outcome:

Write down the conditions for equilibrium for: a pure single phase system, a pure multi-phase system, and a multi-phase mixture