Real solutions

Excess functions represent the difference between the thermodynamic function of a solution and said function in a hypothetical ideal solution of the same composition. \begin{equation} G^{E}=G-G^{id}=G-G^{id}+G^{\ast}-G^{\ast}=G-G^{\ast}-(G^{id} -G^{\ast})=\Delta G_{mez}-\Delta G_{mez}^{id} \end{equation} Analogously: \begin{equation} S^{E}=\Delta S_{ mix}-\Delta S_{mez}^{id} \end{equation} \begin{equation} H^{E}=\Delta H_{mez}-\cancel{\Delta H_{mez}^{id}} \end{equation} \begin{equation} V^{E}=\Delta V_{mez}-\cancel{\Delta V_{mez}^{id}} \end{equation}