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## Q. 9.5

What is the form of equation 9.2-22 for liquid-film control?

$N_{A}\equiv(-r_A) = \frac{p_{A}+\frac{D_{B\ell }H _{A}}{D_{A\ell }b} c_{B}}{\frac{1}{k_{Ag}}+\frac{H_{A}}{k_{A\ell }} }$                           (9.2-22)

## Verified Solution

For liquid-film control, there is no gas-phase resistance to mass transfer of A. Thus, in equation 9.2-14, $1/k_{A\ell } \gg 1/H_{A}k_{Ag} and K_{A\ell} = k_{A\ell}$ so that equation 9.2-22b may be written

$\frac{1}{K_{Ag}}=\frac{1}{H_A k_{Ag}}+{1}{k_{A\ell}}$       (9.2-14)

$(-r_A)=K_{A\ell}(\frac{P_A}{H_A}+\frac{D_{B\ell}}{D_{A\ell}b}c_{B})$       (9.2-22b)

$(-r_{A})=(1+\frac{D_{B\ell } H_{A}}{D_{A\ell }b}\frac{c_{B}}{p_{A}} )\frac{k_{A\ell }}{H_{A}} p_{A}$                      (9.2-25)