Question

A reactive contaminant decays according to first order kinetics with a rate constant of k. A waste stream containing this contaminant at a concentration of 100 mg/L is treated using an ideal completely mixed flow reactor having a volume 100 L. At steady state conditions, the effluent concentration of the contaminant from the reactor is 20 mg/L. The flow rate of the influent stream is 50 L/hr. The rate constant at which the contaminant decays (k) is

Answer 1

For a mixed flow reactor,the design equation is given as ,

V/F_A0 = /C_A0 = X_A/ -r_A

where V = reaction volume

F_A0 = Molar inlet flow rate

= Residence time = volume / volumetric flowrate

C_A0 = Inlet concentration

X_A = Conversion achieved.

-r_A = Rate of the reaction.

For our problem,

C_A0 = 100 mg/L

= V/Q = 100 L/ 50 L/hr = 2 hr

X_A = (C_A0 - C_A )/C_A0 = (100 - 20) /100 = 0.8

-r_A = kC_A = k*20

Substituting the above values,

2( hr) / 100 (mg/L) = 0.8 / k * 20 (mg/L)

k = 2 hr^-1

The units of rate constant for a first order reaction is time^-1 . For our problem, it is 2 hours^-1 .