$(20$ points$)$ For the same binary system, consider the mixing process of the pure species $1$ and $2\mathrm{.}2$ moles of species $1$ and $8$ moles of specics $2$ are mixed to form $10$ moles of the binary solution. Show the process schematically and calculate the change in Gibbs free energy for the system. Is the mixing process spontaneous?

$OC$ hix $=|{|}_T(RT{C}^{{?}^{?}}1-a_i)$