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PS5F07 - Chemistry 391 Problem Set 5(Due Monday October 8...

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Chemistry 391 Fall 2007 Problem Set 5 (Due, Monday October 8) 1. The Gibbs differentials imply that p V G A S T T = − = − . This is a remarkable result. Prove it from the defining relation ( ) ( ) ( ) ( ) , , , ) , G T p A T V T p pV T p = + . 2. You have containers of pure H 2 and He at 298 K and 1 atm pressure. Calculate mixing mixing G T S Δ = − Δ relative to the unmixed gases of a. a mixture of 10 mol of H 2 and 10 mol of He b. a mixture of 10 mol of H 2 and 20 mol of He c. For what composition (proportion of the two gases) does mixing G Δ have its minimum value? Explain physically and show it with calculus. 3. Show that P p V dH C dT V T dp T = + . (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 G H TS = and what this produces for T G p
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