$9\mathrm{.}2.$ We are faced with the problem of diluting a $90wt\%H_{2}S{O}_4$ solution with water in the

following manner. A tank contains $500kg$ of pure water at $298K$; it is equipped with a

cooling device to remove any heat of mixing. This cooling device operates with a boiling

refrigerant reflux condenser system to maintain the temperature at $298K.$ Because of the

peculiarities of the system, the rate of heat transfer $(\frac{W}{m^2})$ must be constant. We wish to

add $1500kg$ of acid solution $($at a variable rate$)$ in $1$ hour. The acid is initially at $298K.$

Eothalpy data are given in Problem $9\mathrm{.}1.$

$($a$)$ Plot the heat of solution $(k\frac{J}{k}g$ solution$)$ versus weight fraction $H_{2}S{O}_4$ with the

reference states as pure water and pure $H_{2}S{O}_4,$ liquid, at $298K.$

$($b$)$ What is the total heat transferred in the dilution process described?

$($c$)$ Derive a differential equation to express the mass flow of $90wt\%$acid,$k\frac{g}{m}in,$ as

a function of the acid concentration in the solution.

$($d$)$ Using the result from part $($c$),$ determine the mass flow of $90wt\%$ acid when the

overall tank liquid is $64\mathrm{.}5wt\%$ acid.

Data: