Unit 1 Exam - Chemistry 158b Unit 1 Exam Partial...

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Chemistry 158b – Unit 1 Exam: Partial Differentiation & Equations of State This is a closed-book one hour exam. The use of a calculator is permitted. There are four problems, each worth 25%. Try to spend no more than 15 minutes on each problem. You are not required to answer the Bonus question. Some Useful constants: R = 8.314510 J K -1 mol -1 = 0.0831451 dm 3 bar K -1 mol -1 = 0.0820578 dm3 atm K -1 mol -1 Also: + + + = ! x x e x 2 1 2 , and the binomial expansion + + + = - 2 1 1 1 x x x This entire exam concerns the van der Waals equation of state: 2 V a b V RT P - - = 1. (a) Pressure ( P ) is a function of the independent variables temperature ( T ), volume ( V ), and the number of moles ( n ), i.e. P ( T , V , n ). Write down the total differential of P . (b) Obtain the two relevant partial derivatives for the van der Waals equation. Write down the total differential of P for the van der Waals equation of state. (c) Obtain the second partial derivatives: V T P 2 2 and T V P 2 2
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