Ninety kilograms of sodium nitrate is dissolved in 110 kg of water. When the dissolution is complete (at time r = 0), pure water is fed to the tank at a constant rate m (kg/min), and solution is withdrawn from the tank at the same rate. The tank may be considered perfectly mixed.

(a) Write a total mass balance on the tank and use it to prove that the total mass of liquid in the tank remains constant at its initial value.

(b) Write a balance on sodium nitrate, letting x(t.th equal the mass fraction of NaNO3 in the tank and outlet stream. Convert the balance into an equation for dx/dt and provide an initial condition.

(c) On a single graph of x versus r, sketch the shapes of the plots you would expect to obtain for m = 50 kg/min, 100 kg/min, and 200 kg/mm. (Don’t do any calculations.) Explain your reasoning, using the equation of part (b) in your explanation.

(d) Separate variables and integrate the balance to obtain an expression for x(t, m). Check your solution. Then generate the plots of x versus t for m = 50 kg/mm. 100 kg/mm. and 200 kg/mm and show them on a single graph. (A spreadsheet is a convenient tool for carrying out this step.)

(e) If m = 100 kg/mm. how long will it take to flush out 90% of the sodium nitrate originally in the tank? How long to flush out 99%? 99.9%?