$2.$Assuming that a silver$-$gold alloy is a random mixture of gold and silver atoms, calculate the increase in entropy when $50$ g of gold are mixed with $30$ gram of silver to form a homogeneous alloy. The gram atomic weights of Au and Ag are, respectively, $198$ and $107\mathrm{.}9$ gr$/$mole$.R=8\mathrm{.}314\frac{J}{m}ol.$ K $.$

What is the maximum increase in the entropy for formation of Ag $-$Au alloys?