Physical Chemistry 1st Midterm Test 2016下.pdf

# Physical Chemistry 1st Midterm Test 2016下.pdf - Physical...

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Physical Chemistry 1 st Midterm Test (2017/03/17) 1. a. Please follow two gases arrangement (see below) to derive the Gibbs energy ( Δ mix G = nRT( x A ln x A + x B ln x B ) ) of mixing of two perfect gases. (hint: P ln RT for perfect gas) (5 points) b. Consider a container of volume 5.0 dm 3 that is divided into two compartments of equal size. In the left compartment there is nitrogen at 1.0 atm and 25°C; in the right compartment there is hydrogen at the same temperature and pressure. Calculate the entropy and Gibbs energy of mixing when the partition is removed. Assume that the gases are perfect. (6 points) 2. a. A polynomial fit to measurements of the total volume of a binary mixture of A and B is ν =700-20 x + 0.5 x 2 + 0.01 x 3 , where ν=V/cm 3 , x =n B /mol, and n B is the amount of B present. Please determine the partial molar volumes of A and B. (hint: A n T P B B n V V , , ) (5 points) b. The partial molar volumes of two liquids A and B in a mixture in which the mole fraction of A is 0.3 are 180 cm 3 mol −1 and 150 cm 3 mol −1 , respectively. The molar masses of A and B are 240 g mol −1 and 200 g mol −1 . What is the volume of a solution of mass 1.000 kg? (hint: V = n A V A + n B V B , m (mass) = n A M A + n B M B ) (5 points) 3. a. Please derive the Gibbs-Duhem equation (n A d n B d  ), starting from G = n A n B (hint: dG= dn A  dn B ) (5 points) b. Suppose that n

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