Question

Please explain how to do this question (please explain about the concept also)
Sketch the entropy of mixing, S mix, for a binary system as a function composition, and identify (1) the slope at Xb=0 and (2) the maximum of S mix.

Answer 1

for gases entropy of mixing = -R{x_alnx_a+x_blnx_b)

R=8.314 joules/mole.K

The calculations are tabulated and shown below

xa	xb	lnxa	lnxb	Entropy of mixing
0.1	0.9	-2.30259	-0.105360516	2.702739841
0.2	0.8	-1.60944	-0.223143551	4.160345749
0.3	0.7	-1.20397	-0.356674944	5.078725807
0.4	0.6	-0.91629	-0.510825624	5.595419
0.5	0.5	-0.69315	-0.693147181	5.762825659
0.6	0.4	-0.51083	-0.916290732	5.595419
0.7	0.3	-0.35667	-1.203972804	5.078725807
0.8	0.2	-0.22314	-1.609437912	4.160345749
0.9	0.1	-0.10536	-2.302585093	2.702739841
0.001	0.999	-6.90776	-0.0010005	0.065740919
0.0001	0.9999	-9.21034	-0.000100005	0.008488835
0.0000001	1	-16.1181	-1E-07	1.4232E-05

Maximum entropy occurs when xa=0.5=xb and xb-à1 entropy change= 0