Question

[Problem 1.7.3) A tank whose volume is 200 L is initially half full of a solution that contains 100 g of chemical. A solution containing 0.5 g/L of the same chemical flows into the tank at a rate of 6 L/min, and the well-stirred mixture flows out at a rate of 4 L/min. Determine the concentration of chemical in the tank just before the solution overflows.

please explain and show work for my understanding.

Answer 1

Given that The Volume of the tauk is 200 letres. Half full Solution Contaius lo0grams of.chemical v Co) l00L. Flowrate Pn> rz.6L/min mixture rato out» 2=.4L/min ACO) = L00 g ACE) Find the Valuej of Alt). VLt) dv = 3idt - ½dt dv. TE-k = = 6-4 -2; By Voiable Seprable method. Sdv%=2Sdt.→ v-2lttc) V Co) = 100 > VCE)= 2(t+50) AA = Got - CY20E = 3-4C2 dA =3-4 Sime 'A By Substituting, dA 3-4 2lt+50) p. dA (A) = 3 t+50 dt

SPOndy Integrating facta IF)= S.EA50 2lu (t+50) (t+50) Integrating bsthside =3 (t+0) A = (t+y0)³+ d it. At) = ACO) = 100 grauw (Initial Condition) 100. = 100 x 50 = d = 125000 t+50j+12500 ACE) = (t+50% Substitut v= 200 tu VIE) = 2Ctt5) 200 = 2(tt50) > t=n 5omin. At t=50, A(50)=112:5 t=50, VC50)= 200 ACt) Now att=50. vet) Conceutatio f chanial (12,5 0.5625