Question

A lake with the volume of 106 m3 receives 10 m3/s of inflow containing 0.1 mol/m3 of a chemical. The chemical reacts with a first-order rate constant of 0.02 h-1. The outflow from the lake is also 10 m3/s. Assume there was no chemical in the lake at the beginning.
What will be the concentration changing rate of this chemical in this lake? Assume the concentration of such chemical at certain time is x mol/m3 in the lake.

Answer 1

Given volume of lake 10^6 m^3 flow rate = 10^3m^3/sec concentration = 0.1 mol/m^3 and it is given a first order reaction with rate K = 0.02h^- 1 = 5.56 times 10^- 6 sec^- 1 out flow rate also 10^3m^3/sec so let Assume as me tank of volume 10^6m^3 Input flow rate = output molar flow rate + molar rate of decomposition of a + molar rate of accumulation of A F_Ao = F_Ao + C_1V + v d_cA/dt and have given concentration of chemical @certain time is N (10^3) (0.1) = 10^3 (m) + (5.56 times 10^- 6 times 10^6) + 10^6 dx/dt 100 = 10^3 + (5.56 * + 10^6 dx/dt) 10^6 dx/dt + 1005.56 times 10^- 6 - 10^- 4 = 0 The concentration changing rate of chemical in the take is dx/dt + 1005.56 times 10^- 6 - 10^- 4 = 0