In this problem you will determine an expression for the binary entropy of mixing. consider an isolated system composed of two types of particles a and b initially separated by a partition, as in fig. 3.13. the particles are constrained to occupy sites on a regular lattice, and there are exactly as many lattice sites as there are initial particles. the use of a lattice is an approximation, but it will give a very general expression for the entropy of mixing. there are no potential or kinetic energies, and swapping two particles of the same color is not considered a new configuration, i. e., particles of the same type are indistinguishable from each other. at some point the partition is removed, and particles freely mix. using its relationship to the density of states, write expressions for the entropy before and after the wall is removed. find the entropy difference, asmix = satter - sbefore. use stirling's approximation to simplify your answer. express your final answer in terms of the mole fractions, xana/n and xg = n/ny, and the total number of molecules nt = na + ng-