Effective average driving forces in a gas absorber consider a packed-tower gas absorber of the type discussed in Example 23.5-2. Assume that the solute concentration is always low and that the equilibrium and operating lines are both very nearly straight. Under these conditions, both k⁰_ya and k⁰_x a may be considered constant over the mass-transfer surface 

(a) Show that (Y_A – Y_Ae) varies linearly with Y_A. Note that Y_A is the bulk mole ratio of A in the gas phase and Y_Ae is the equilibrium gas-phase mole ratio over a liquid of bulk composition XA (see Fig. 22.4-2). 

(b) Repeat part (a) for (Y_A – Y_A0). 

(c) Use the results of parts (a) and (b) to show that the overall mass transfer coefficient K⁰_y is defined by Eq. 22.4-4. Note that this part of the problem may be solved by analogy with the development in Example 15.4-1.

WARO = (K?a)ZS(Y A0 Yadn Y aha WAgo = Ka)ZS(Ye - Yadn %3!