PS5KEYF07 - Chemistry 391 PS5 KEY 1. Write the differential...

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1 Chemistry 391 Fall 2007 PS5 KEY 1. Write the differential VT AA dA dT dV TV ∂∂ ⎛⎞ =+ ⎜⎟ ⎝⎠ Take its derivative with respect to T at fixed p : pVT p AAA V TTV T ∂∂∂ ⎛⎞⎛⎞ ⎜⎟⎜⎟ ⎝⎠⎝⎠ Combine with () ( ) ( ) ,, , ) , GTp ATVTp pVTp to get p p GAA V V p T T + Now use the definition T A p V =− to obtain the desired result pV GA S TT −= = . 2. mixing mixing GT S Δ= Δ = nRT ( x 1 ln x 1 + x 2 ln x 2 ) -1 -1 -1 -1 1111 a) 20 mol 8.314 J K mol 298 K ln ln 34.4 kJ 2222 1122 b) 30 mol 8.314 J K mol 298 K ln ln 47.3 kJ 3333 mixing mixing G G × ×× + = × + = c) Physically, you should expect equal amounts of the two gases, x 1 = x 2 =1/2, to produce the lowest mixing G Δ because it will produce the largest mixing S Δ . The largest mixing S Δ because there is the greatest expansion of each gas for the amount of gases you have. If you plot mixing G Δ for a few x 1 values you will see that it is the case. To prove it, call 12 ;1 x xx x == and take the derivative of mixing G Δ with respect to x to get
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This note was uploaded on 07/25/2008 for the course CEM 391 taught by Professor Cuckier during the Fall '08 term at Michigan State University.

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PS5KEYF07 - Chemistry 391 PS5 KEY 1. Write the differential...

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