The entropy change of mixing for a binary solution is given by $\backslash$Delta Sm $=-5$R $($XA ln XA $+$ XB ln XB$)$ J$/$molK$.$ One mole of a pure B is added to the solution with $2$ moles of A and $3$ moles of B$.$ Calculate the entropy change of the system upon this addition. Assuming the solution is behaving ideally calculate the change in the activity of B upon this addition.