1) Derive the equilibrium conditions for an isolated system consisting of two regions separated by a membrane and with three components A, B, and C. The membrane is rigid, heat conducting, and only permeable to component A.
2) Derive the equilibrium conditions for a system of two phases with three components A, B and C in a closed container where the temperature, pressure and total number of moles of each component are fixed.
3) Extend the results from part ii) to the case where in addition to there being two phases the components take part in a chemical reaction with stoichiometry
A = B + C
and the initial number of moles of each component is fixed ?