For the continuous stirred tank reactor $($CSTR$)$ shown in the figure below, two liquid streams are fed to the reactor. Inside the reactor, a reversible liquid phase reaction occurs according to the following stoichiometric equation:

$C+DE+G$

One concentrated feed with flow rate $F_l(\frac{m^3}{s}),$ density ${}_{\text{I}}(\frac{kg}{m^3})$ concentration $C_{EI}(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3})$ and two dilute streams with flow rates $F_2$&$F_3(\frac{m^3}{s}),$ densities ${}_2$&${}_3(k\frac{g}{m}3)$ and concentrations $C_{E2}$&$0\mathrm{.}22C_{E2}(mol\frac{e}{m^3}),$ respectively. The effluent has a flow rate $F_o(\frac{m^3}{s}),$ density ${}_o(k\frac{g}{m}3)$ and concentration $C_E(mol\frac{e}{m^3}).$ The density and concentration of the liquid inside the tank are $(k\frac{g}{m}3)$ and $C_E(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3}),$ respectively. Based on the data and assumptions given below, write the following:

i$)$ The equation of total mass balance.

ii$)$ The equation of component $E$ balance

iii$)$ The degree of freedom

Data

The reaction is isothermal. The reactor is a cylindrical tank of a radius $R.$ The liquid level inside the tank is variable and $=h.$ The variables $C_{E1},C_{E2},F_{\text{I}}$&$F_o$ are forced variables. The outlet flow $F_o$ is related to the liquid level inside the tank by the following equation: $F_{}=\sqrt[\phantom{2}]{h}*$ is a constant.

Assumptions

Well mixing. The reactant $C,D$ and $G$ are in excess. The densities and specific heat capacities of the three inlet streams are equal and not affected by the temperature. The three streams are of equal temperature. The magnitude of the reaction rate is: