The twin-bulb method of measuring diffusion is shown below. The bulbs, which are well stirred and of equal volume, temperature, and pressure initially contain binary gas mixtures of different compositions. At time zero, the valve is opened; sometime later, the valve is closed, and the bulk contents are analyzed.

a. Derive the equation for the flux of component A through the tubes, and use this to get an explicit expression for the diffusion coefficient. Assume each bulb has a volume V (which is much larger than the volume of the tube), the cross-sectional area of the tube is S, and the length of the tube is L. The initial concentration of A in the left tube is CA,L, and in the right tube it is CA,R.

b. After 20 minutes, the concentrations in each bulb are measured and the results are shown below. If the length of the tube is 5 cm, the volume of each bulb is 1000 cm3 and the cross-sectional area is 5 cm2, what is the value of the diffusion coefficient for this system?

At time = 0 CAL = 30 CAR = 5 After 20 minutes CAL = 20 = CAR = 10 =