Answer to Question #151933 in General Chemistry for Piyush Mishra

Question

A tank contains 20 kg of a salt solution at a concentration of 4% by weight. Fresh solution enters the tank at a rate of 2.5 kg/min at a salt concentration of 3% by weight. The contents are stirred well and the mixture leaves the tank at a rate of 2.0 kg/min. (a) Express the salt concentration as a function of time and (b) At what instant of time the salt concentration in the tank will reach 3.75 % by weight?

Answer 1

stream entering into the tank having mass flow rate of = 2.5kg/min

C is the stream leaving the tank at the rate of = 2.0kg/min

B is the mass of solution in the tank = 20kg

Xf is the salt concentration in the feed by mass = 0.03

Xc is the salt concentration in the product = X which is the salt concentration in the tank which is changing with time

Because the leaving stream have same concentration as in the tank due to well mixing

Apply mass balance of salt

Rate of mass of salt in --- rate of mass of salt out = rate of mass of salt accumulate in the tank

A*Xf -- C*X = B*(dX/dt)------(1) where x is the concentration of salt in the tank at any time t.

eq(1) becomes

2.5*0.03 -- 2X = 20*(dX/dt)

dX/(0.075 -- 2X) = 1/(20) *dT on integrate this equation

From X = 0.04 to 0.0375 and at time t= 0 to t

Because at time t=0 concentration of salt in the tank is 4% and we have to calculate the time at which concentration is 3.75%