The well-stirred tank of volume V = 2 m3 shown in figure is initially filled wit

Question

The well-stirred tank of volume V = 2 m3 shown in figure is initially filled with brine, in which the initial concentration of sodium chloride at t = 0 is c0= 1 kg/rn3. Subsequently, a flow rate of Q = 0.01 m3/s of pure water is fed steadily to the tank, and the same flow rate of brine leaves the tank through a drain. Derive an expression for the subsequent concentration of sodium chloride c in terms of c0, t, Q, and V. Make a sketch of c versus t and label the main features. How long (minutes and seconds) will it take for the concentration of sodium chloride to fall to a final value of cf = 0.0001 kg/rn3?

Explanation / Answer

we use M1V1 = M2V2 , M-molarity , V - vol , hence Co(V) = C(V+Qt) , C = Co(V)/(V+Qt) , as time increases C decreases , Co=1 , C= 0.0001 , Q=0.01, V=2 , t = ?, 1(2) = 0.0001(2+0.001t) , t = 1.9998 x10^ 7 sec = 333300 min

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