A liquid is contained in a tapered conical flask with a taper angle of \(30^{\circ}\). The radius in the flask for the liquid level at the bottom is \(7 \mathrm{~cm}\) and the vapor height above this is \(10 \mathrm{~cm}\).

Find an expression for the rate of evaporation and the mole-fraction profile in the vapor space and compare your answer with the case of a straight cylinder.

Assume that the liquid is benzene under the conditions stated in Problem 3.

The bulk gas is at zero concentration.

Problem 3:

Benzene is contained in an open beaker of height \(6 \mathrm{~cm}\) and filled to within \(0.5 \mathrm{~cm}\) of the top. The temperature is \(298 \mathrm{~K}\) and the total pressure is \(1 \mathrm{~atm}\). The vapor pressure of benzene is \(0.131 \mathrm{~atm}\) under these conditions, and the diffusion coefficient is \(9.05 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\).

Find the rate of evaporation based on (a) the low-flux model, (b) exact solutions, and (c) the low-flux model corrected for the drift flux.