Solve itThe tank shown below is used to adjust the concentration of a salt solution with the volume $V.$

The inlet stream, flowing at a volumetric flow rate of $F_1,$ contains salt with a concentration $x_1.$

The volumetric flow rate and the salt concentration of the outlet stream are $F$ and $x,$

respectively. Initially, the tank holds a residual solution from a prior operation, with a volume

$V_0$ containing the same salt at a concentration $x_0.$ The tank can be assumed to be well$-$mixed

and the density remains constant during the process.

a$)$ Write the necessary mass balance equations and derive a

general expression for the salt concentration of the liquid in

tank as a function of time. Specify the initial conditions.

b$)$ Write the necessary mass balance equations and derive a

general expression for the salt concentration of the liquid in

tank as a function of time when volumetric flow rates of

inlet and outlet streams are equal $(F_1=F).$

c$)$ Calculate the volume of the solution and salt

concentration after $30$ minutes if $F_1=20\frac{L}{m}in,x_1=$

$0\mathrm{.}02k\frac{g_{\text{s}\text{a}\text{l}\text{t}}}{L},F=10\frac{L}{m}in,V_0=3000L$ and $x_0=$

$0\mathrm{.}005k\frac{g_{\text{s}\text{a}\text{l}\text{t}}}{L}.$