PChemFinalExamKey - NAME and Section No. Chemistry 391...

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––––––––––––––––––––––––––––––– NAME and Section No. 1 Chemistry 391 Fall 2006 Final Exam KEY (There are 125 points on this Exam) 1. (35 Points) *Do 7 out of 9 * (If more than 7 are done only the first 7 will be graded) a). A Carnot cycle operates between T H and T C taking in q H at T H and rejecting q C at T C . Write an expression for the efficiency / H ew q = − in terms of q C and q H, and also T C and T H . What is the possible range of values of e ? Since 0 CH dU w q q ==+ + v , () // 1 / 1/ H HCH C H q qqq q q TT =− = + = + The temperatures are positive numbers and / 1 < , so 01 e < < b). Why can you evaluate, for example, S Δ for an irreversible process by using a reversible process between the same final and initial states? S is a state function. Therefore, as long as the endpoints are the same, it doesn’t matter whether the process is reversible or irreversible. c). Show how to get the Gibbs equation for dH from the combined first and second law expression for dU . dH d U pV dU d pV dU pdV Vdp TdS pdV pdV Vdp TdS Vdp =+ + = + + = +
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––––––––––––––––––––––––––––––– NAME and Section No. 2 d). What quantity determines phase equilibrium (at fixed thermal and mechanical equilibrium), what is its direction of flow and what is the equilibrium condition? The chemical potential of each component in each phase i α μ determines phase equilibrium. Its direction of flow is from higher to lower chemical potential with equality for each component ( i , j , ) between each phase ( α , β , ) at equilibrium: ii β = . e). Order in size the translational, rotational, and vibrational partition functions for a typical diatomic molecule. Why do you get the order you present? tr rot vib zz z >> . The energy levels are more closely spaced for translational versus rotational versus vibrational, leading to this ordering. f). What is the mathematical definition of the partial molar volume of species i in a solution with r components? What does it depend on? () ,, ji Tpn n VV n =∂ It depends on T,p, and the mole fractions, x 1 , x 2 , ,x r for a r- component system.
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––––––––––––––––––––––––––––––– NAME and Section No. 3 g). Which of the translational, rotational, vibrational and electronic partition functions depend on the system volume? Physically explain your answer.
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PChemFinalExamKey - NAME and Section No. Chemistry 391...

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