$3\mathrm{.}7$ The temperature variation of rate of a chemical reaction which involves mass transfer is

sometimes used to determine whether the rate of mass transfer or that of the chemical reaction

controls, or is the dominating mechanism. Consider a fluid flowing through a $25-mm-$ID $(1\mathrm{.}0-$in$)$

circular tube, where the transferred solute is ammonia in dilute solution. Compute the mass$-$transfer

coefficient for each of the following cases:

$($a$)$ The fluid is a dilute solution of ammonia in air, $25C,1$ std atm, flowing at a Reynolds

number $=10000.D_{AB}=2\mathrm{.}26{10}^{-5}\frac{m^2}{s}(0\mathrm{.}226c\frac{m^2}{s}).$

$($b$)$ Same as part $($a$)($same mass velocity$),$ but temperature $=35C.$

$($c$)$ The fluid is a dilute solution of ammonia in liquid water, $25C,$ flowing at a Reynolds

number $=10000.D_{AB}=2\mathrm{.}65{10}^{-9}\frac{m^2}{s}(2\mathrm{.}65{10}^{-5}c\frac{m^2}{s}).$

$($d$)$ Same as part $($c$)($same mass velocity$)$ but temperature $=35C.$

In the case of both gas and liquid, assuming that the mass$-$transfer coefficient follows an

Arrhenius$-$type equation, compute the "energy of activation" of mass transfer. Are these high or low

in comparison with the energy of activation of typical chemical reactions? Note that, for dilute

solutions, the identity of the diffusing solute need not have been specified in order to obtain the

"energy of activation" of mass transfer. What other method might be used to determine whether

reaction rate or mass$-$transfer rate controls?