# “Physical chemistry please help me answer this…

### Question Description:

“Physical chemistry please help me answer this in the easiest way, break down step by step and please include the calculation. thank you. Refer to attached file with corresponding number 7. In class, we said that the entropy of mixing for two ideal gases is: Δ = − + S R n x n x mixing ( A A B B ln( ) ln( )) Say we have nA moles of gas A initially at 1 atm pressure mix with nB moles of gas B also at 1 atm pressure to form 1 mole of a mixture of A and B at a final pressure of 1 atm. The entire process occurs at a constant temperature T. a. Show that the entropy change is given by : mixing ln( ) ln( ) A A B B Δ = − − S Rx x Rx x b. What can you say about the sign of ΔS? Is it in keeping with the second law? c. Gibbs Free Energy can be written as dG = dH – d(TS). Given that temperature is constant in this problem, what is the sign of dG? Based upon this, is the mixing process spontaneous? 2Chem 452 – HW 6 Winter 2012 3 d. Given that xA + xB = 1, what values of xA and xB give the largest entropy of mixing? (Prove it). Hint: Recall how to prove that a function is at its maximum