Question

please use the temperature adjustment listed at the bottom for part b as well. assume: steady state, constant temp and pressure, ideal gas solution, B is insoluble in A, and Nb,z in gas phase =0.

Evaporation of volatile liquid.  A tank with its top open to the atmosphere contains liquid benzene.   The tank and atmosphere are at 25 oC.  The inner diameter of the cylindrical tank is 1.0 m, the height of the tank is 3.0 m, and the liquid level is at 0.5 m from the inside bottom of the tank.   Assume the gas space inside the tank is stagnant and that the methanol vapor is immediately dispersed into the atmosphere once outside of the tank.  

    a)  What is the evaporation rate of benzene from the tank, in kg/day, at 25 oC?

    b)  What is the evaporation rate of benzene from the tank, in kg/day, at 35 oC?

    c)   Would you expect the evaporation rate to be a linear function of temperature?  Explain.

Hints: Note that the quantity P•DAB for binary gas systems are given in Appendix J, at specified temperatures, where P is the pressure in the system.  To calculate the DAB at a different temperature, you can use the correction of (T2/T1)1.75.  

Answer 1

In this case, the system is a liquid A (benzene) evaporating into Gas B (air) i.e. diffusion through a stagnant gas film model.

Apply the above assumptions to the equation of continuity of species for rectangular coordinates (Equation 10-7 Griskey):

To obtain:

    

Therefore   is independent of z i.e. it is a constant

Modified Eg. 10-6 gives:

+ Y_A (N_A + N_B)

N_B=0 (Stagnant air)

Then rearranging gives:

                       

                               Equation 1

knowing

Replace the above equation into equation 1, we can derive the molar flux of A molecule in term of mole fraction Y_A:

Since P, R and T are constant, the can be factored out of the derivative to obtain:

                            Equation 2

The equation obtained above (equation 2) can be integrated over the following boundary conditions:

z =z₁               Y_A= Y_A1

z =z₂               Y_A= Y_A2

Letting (thickness) and rearranging the equation above we obtain:

                  Equation 4

The above equation of flux (Equation 4) can be written in terms of mole fraction for the stationary molecule i.e. Y_B as follows:

                                     Equation 5

At the surface of benzene liquid:

The vapour pressure of benzene = 0.132 atm therefore:

=0.132 and