Question

A chemical breaks down in a flow-balanced, steady-state CFMR according to first-order reaction kinetics. At steady state, the upstream and downstream concentration of the chemical are 15 mg/L and 5 g/m3. Water is being treated at a rate of 0.42 m3/sec. The volume of the tank is 500,000 liters. Assuming a first-order reaction, what is the rate constant

Answer 1

Answer:

$k =0.101 \ min^{-1}$

Explanation:

From the given information:

The initial concentration of a chemical $C_{AO} = 15 \ mg/L$

The final concentration is $C_A = 5 \ g/m^3$ = 5 mg/L

Volume flow rate $V_o = 0.42 \ m^3/sec$

Volume of the tank V = 500 000 L = 500 m³

The time t is determined by using the formula:

$t= \dfrac{V}{V_o}$

$t= \dfrac{500 \ m^3}{0.42 \ m^3/sec}$

t = 1190.47 sec

t ≅ 19.8 min

∴

The rate of the decay constant is:

$kt= \dfrac{C_{AO}-C_{A}}{C_A} \\ \\ k = \dfrac{1}{19.8}( \dfrac{15-5}{5})$

$k =0.101 \ min^{-1}$