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

`k =0.101 \ min^(-1)`

Step-by-step 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= (V)/(V_o)`

`t= (500 \ m^3)/(0.42 \ m^3/sec)`

t = 1190.47 sec

t ≅ 19.8 min

∴

The rate of the decay constant is:

`kt= (C_(AO)-C_(A))/(C_A) \\ \\ k = (1)/(19.8)( (15-5)/(5))`

`k =0.101 \ min^(-1)`