M dyCDL t

which, after solving for NA, gives

For an instantaneous reaction with XA2 = 0 equation 43 can be simplified to

For a first-order reaction, substituting equation 39 into equation 43 gives

Equation 45 can be solved by trial and error, but it is appropriate to point out that the reaction rate in equation 45 is lower than that in equation 44, because (1 + NJnC) > 1.

ways begins with an unsteady-state condition. Steady-state conditions may be established only after some time has elapsed. In unsteady-state mass transfer, the concentrations or partial pressures and consequently the mass transfer rate are functions of time and position. Fick's second law can be used to describe the concentration changes with time and position. For one dimension, Fick's second law can be written as dC _ D d2C

To solve equation 46, a set of initial and boundary conditions must be given. A simple example is the diffusion through a membrane with known initial and boundary conditions (4,5), stated as at t = 0, C = C0, for 0 < y < Y

The solution of equation 46 is then

The total amount of substance diffused through the membrane in time t, Qt, is

When t approaches infinity, the exponential terms vanish and equation 49 simplifies to a linear form

A plot of Qt versus t gives an intercept L on the i-axis (where Qt = 0) as

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