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Quiz03 - Physical Chemistry(I Quiz 03 Nov 08 2007 a PVm...

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Physical Chemistry (I) Quiz 03 Nov. 08, 2007 1. (15%) Show that ( ) m T PV a b P RT - for a van der Waals gas in the limit of zero pressure, where the van der Waals equation is given by 2 m m RT a P V b V = - - . 2. (20%) Assume that a sealed vessel at constant pressure of 1 bar initially contains 2.00 mol of NO 2 ( g ). The system is allowed to equilibrate with respect to the reaction 2 NO 2 ( g ) ° N 2 O 4 ( g ). The number of moles of NO 2 ( g ) and N 2 O 4 ( g ) at equilibrium is 2.00 – 2 ξ and ξ , respectively, where ξ is the extent of reaction. (a) Derive an expression for the entropy of mixing as a function of ξ . (5%) (b) Write an expression for G pure as a function of ξ . (5%) (c) Write an expression for G mix of the reaction as a function of ξ . (5%) (d) What’s the criterion to determine the equilibrium position of the reaction? (5%) 3. (10%) The reaction A + B C + D is at equilibrium with ξ being the extent of the reaction. In the class, we learned that if the m G for the products were less than those for the reactants, ξ would be near 1; on the other hand, if the m G for the reactants were less than those for the products, ξ would be much smaller than 0.5. (a) What does it tell you about the r G Δ with ξ = 0.1? (5%) (b) What does it tell you about the r G Δ with ξ = 0.5? (5%) 4. (15%) The pressure dependence of G is quite different for gases and condensed phases. Calculate G m (C, solid , graphite , 100 bar, 298.15 K, ρ = 2.25 kg L -3 ) and G m (He, g , 100 bar, 298.15 K) relative to their standard state values. By what factor is the change in G m greater for He than for graphite?
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