Question

Engineers do a treatment study on an industrial waste containing Chemical X. In a batch reactor, the concentration of Chemical X drops from 150 mg/L to 75 mg/L in 14 hours.

(a) What is the half-life?
(b) What is the decay constant if the reaction is first order?
(c) What is the decay constant if the reaction is zero order?
(d) How would you determine whether the reaction is zero or first order? If you had a set of concentration

Answer 1

(a) 14 hours is the half life.

(b) The rate constant, k = 0.0495 hour⁻¹

(c) The rate constant, k = 5.36 mg/L.hour⁻¹

(d) The kinetics of a reaction can be known graphically by plotting the concentration vs time experimental data on a sheet of graph.

Step-by-step explanation:

(a) Given that:-

Initial concentration = 150 mg/L

Final concentration = 75 mg/L (Half)

Time taken = 14 hours

Half life is the time at which the concentration of the reactant reduced to half. So, 14 hours is the half life.

(b) Half life expression for first order kinetic is:

Half life = 14.0 hours

`t_(1/2)=\frac {ln\ 2}{k}`

Where, k is rate constant

So,

`k=\frac {ln\ 2}{t_(1/2)}`

`k=\frac {ln\ 2}{14.0}\ hour^(-1)`

The rate constant, k = 0.0495 hour⁻¹

(c) Half life expression for zero order kinetic is:

Half life = 14.0 hours

`t_(1/2)=([A]_0)/(2k)`

Where, k is rate constant

`[A]_0`is the initial concentration = 150 mg/L

So,

`k=(150\ mg/L)/(2* 14\ hour)\\\\k=(150)/(2* 14)\ mg/L.hour^(-1)`

The rate constant, k = 5.36 mg/L.hour⁻¹

(d) The kinetics of a reaction can be known graphically by plotting the concentration vs time experimental data on a sheet of graph.

The concentration vs time graph of zero order reactions is linear with negative slope.

The concentration vs time graph for a first order reactions is a exponential curve.

The concentration vs time graph for a second order reaction is a hyberbolic curve.