Chemistry 391 Fall 2007 Problem Set 5 (Due, Monday October 8) 1. The Gibbs differentials imply that pVGASTT∂∂⎞⎞=−⎟⎟⎠⎠. This is a remarkable result. Prove it from the defining relation ()(),,,),GTp ATVTppVTp=+. 2. You have containers of pure H2and He at 298 K and 1 atm pressure. CalculatemixingmixingGTSΔ=−Δrelative to the unmixed gases of a. a mixture of 10 mol of H2and 10 mol of He b. a mixture of 10 mol of H2and 20 mol of He c. For what composition (proportion of the two gases) does mixingGΔhave its minimum value? Explain physically and show it with calculus. 3. Show that PpVdHC dTV TdpT⎡⎤∂⎛⎞−⎢⎥⎜⎟∂⎝⎠⎣⎦. (These are all easily measurable properties for a gas and are useful for e.g. Joule-Thompson calculations). HINT – It will prove useful to consider GHTSand what this produces for TGp
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