A 2000-liter tank initially contains 400 liters of pure water. Beginning at t = 0, an aqueous solution containing 1.00 g/L of potassium chloride flows into the tank at a rate of 8.00 L/s and an outlet stream simultaneously starts flowing at a rate of 4.00 L/s. The contents of the tank are perfectly mixed, and the densities of the feed stream and of the tank solution, rho (g/L), may be considered equal and constant. Let V (t) L denote the volume of the tank contents and C (t) (g/L) the concentration of potassium chloride in the tank contents and outlet stream. Required:
a. Write a total mass balance on the tank contents, convert it to an equation for dV/dt. and provide an initial condition.
b. Without solving either equation, sketch the plots you would expect to obtain for V versus t and C versus t. Briefly explain your reasoning. Solve the mass balance equation to obtain an expression for V(t).

A) 8 l/s - 4 l/s = dv/dt

initial conditions : t = 0 , v = 400 L

B) Vt = 4t + 400

Explanation:

Given data :

volume of tank = 2000 liter

volume of water in tank = 400 liters

aqueous solution contains = 1 g/l potassium chloride

flow rate of solution = 8.00 L/s  ( v1 )

outlet stream flow rate = 4.00 L/s  ( v2 )

t = 0

density of the whole content of the tank ( feed stream and tank solution )= rho (g/l )

assuming

v (t) liters = volume of tank  contents

C (t) g/l =  concentration of potassium chloride in tank contents and outlet stream

A ) Total mass balance on the tank contents

mass inlet - mass outlet = mass accumulation   1

note : mass accumulation = dm/dt

         mass = density * v

hence equation 1 becomes

( D1 * v1 ) - (D2 *v2) = dM/dt

D1 * (8 l/s) - D2 * (4 l/s) = dM/dt   2

since D1 = D2 = Dm and M = ( D*v )

hence equation 2 becomes

8 l/s - 4 l/s = dv/dt

initial conditions : t = 0 , v = 400 l

B) attached below is the required sketch

solving the mass balance equation to obtain an expression for V(t)

8 l/s - 4 l/s = dv/dt

= 8 - 4 = dv/dt

=  4 = dv/dt

hence dv = 4dt

integrating

Vt - vi = 4*t

input the initial volume ( vi ) = 400

Vt = 4t + 400

The reason behind the sketch is that the volume increase because the inflow is greater than the outflows

also the concentration increases because of the addition of a concentrated mixture

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the seeing the electronic configuration we can say that the element is fluorine.

fluorine is the most electronegative element in the periodic table.

but by only seeing the configuration we cannot say about its reactivity because we don't know if its configuration after excitation or by addition of electrons.

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