give me the answer

$($a$)$ What is the Gibbs free energy of mixing of binary components in a system to form a mole of a regular solution $G^M?$ Please derive the critical temperature, $T_{or}$ is $T_{cr}=\frac{}{2R}$ for a regular solution. $(6\%)($b$)$ For an A$-$B binary regular solution, please draw the diagram for the magnitude of on the zero$-,$ first$-,$ second$-,$ and third$-$order derivatives of the integral Gibbs free energy of mixing with respect to composition. $(12\%)($c$)$ Please plot a diagram regarding the molar Gibbs free energies of mixing of binary components in a system which exhibits a miscibility gap. In this diagram, please indicate the composition range that the phase separation may occur by spinodal decomposition; and at what composition ranges that the phase separation may occur by nucleation and growth. Why? $(8\%)$