Question

Consider the lattice model that consists of a two-dimensional mesh of N × N cells. N1 molecules of one type and N2 of another are placed on it. Calculate the entropy of mixing for this system

Answer 1

The total number of the sites are N x N.

The total number of microstates, when N1 molecules of one type and N2 molecules of N2 type are mixed together is

The entropy is therefore

The entropy of the original segregated arrangement is 0.

So, the entropy of mixing is

Now let us assume that all the sites are filled by the molecules. i.e

Now using Stirling's approximation

Further, we can reduce this to

Where X1 and X2 are mole fractions of the two molecules respectively.

answered by: anonymous