The limiting condition for the appearance of the miscibility gap in a binary solution is
Where, G is the Gibbs free energy and X is the mole fraction of component Z.

A. $$\left( {\frac{{{\partial ^2}G}}{{\partial {X^2}}}} \right) = 0$$

B. $$\left( {\frac{{{\partial ^3}G}}{{\partial {X^3}}}} \right) = 0$$

C. $$\left( {\frac{{{\partial ^2}G}}{{\partial {X^2}}}} \right) + \left( {\frac{{{\partial ^3}G}}{{\partial {X_3}}}} \right) = 0$$

D. $$\left( {\frac{{{\partial ^2}G}}{{\partial {X^2}}}} \right) - \left( {\frac{{{\partial ^3}G}}{{\partial {X^3}}}} \right) = 0$$

Answer: Option A