A small$-$scale experiment requires the preparation of a $40$ mole $\%$ sulfuric acid solution

from pure water and $80$ mole $\%$ sulfuric acid. The mixture is to be prepared by metering

one fluid at a constant molar rate into a tank containing the second fluid. Cooling is to be

provided to maintain the bath at a constant temperature.

At the temperature of operation, $298K,$ partial molar enthalpies are listed below

$[$International Critical Tables $(1930),$ Vol. $7,$ McGraw$-$Hill, New York, p $237].$ The term

$H(H_{2}S{O}_4)$ refers to a state of infinite dilution $($i$.$e$.,$ where the mole fraction acid

approaches zero$).H(H_{2}O)$ is the enthalpy of pure water at $298K.x$ is mole fraction and

enthalpies are expressed in $\frac{J}{m}ol.$

Data:

$($a$)$ Which fluid should be charged to the reactor first in order to mininize the rate of

heat release?

$($b$)$ What is the peak differential heat load per mole of fluid added?

$($c$)$ What is the total heat of mixing per mole of final solution for both methods?