Problem 3; 10 points) The diffusivity of methane in CO2 is to be measured in a "two-bulb" cell at 298K and 1 atm. Specifically, two vessels are connected by a capillary 20 cm in length and 0.3 cm in diameter. Vessel 1 has a volume of 2.5 liters, and at the start of the experiment is filled with pure CO2. Vessel 2 has a volume of 1.5 liter, and at the start of the experiment is filled with a gas mixture comprised of 15% methane, 85% CO2 (molar basis). a (a) Develop a general expression which relates the diffusivity (DAB) to the diffusion time (t), the various geometric aspects of the cell (V1, V2, L, Ac), and the mole fractions of methane; yo, yt, and Yave. (b) If the mole fraction of methane in vessel 2 is measured as y= 0.1413 after 40 hours, calculate the diffusivity, DAB (cm /s)