Water in a narrow, long test tube (0.6 cm in diameter) is held at a constant temperature of 293 k. the total pressure of air (assume dry) is 1 atm and the temperature is 293 k. water evaporates and diffuses through the air in the test tube and the initial diffusion path is 15 cm (the distance between the surface of water and the opening of the test tube). assume that the system is isothermal.

a. start from the total flux balance, show that the water flux, n_a is:
na= dab. p/rtδz ln (p-pa2)/(p-pa1)
where p is the total pressure, pa1 and pa2 are the partial pressure of water at the surface of water and at the opening of the test tube, delta z is the distance between the surface of water and the opening of the test tube, d_ab is the diffusivity of water vapor in air, t is the temperature (k) and r is the ideal gas law constant (= 82.057 cm^3-atm/g mol middot k).

b. if water in the test tube is evaporating at a rate of 2.4 times 10^-7 ml/s, what is the diffusivity of water vapor in air, d_ab? ( the vapour pressure of water at 293k is 17.54mmhg or 0.231atm. clearly state the assumptions used in estimating the diffusivity)