Question

In: Civil Engineering

6. A certain contaminant was studied in the laboratory by measuring over time the concentration in...

6. A certain contaminant was studied in the laboratory by measuring over time the concentration in a sample placed in a closed container. The values of the observed concentrations are given below. Determine the reaction order and the decay rate for this contaminant.

Time (hrs)

0

1

3.5

6.5

10

Conc (mg/L)

100

80

50

26

10

Solutions

Expert Solution

As both the reaction order and decay rate is unknown let us go for trial and error method .

STEP 1 : Assume it is a zero order reaction

Zero order reaction : graph of A versus time is straight line plot

Thus Af = -Kt + Ai

Here the slope is negative because concentration decreases as time increases

where Af = final concentration

K = decay rate

t = time taken to decrease from initial to final concentration

Ai = initial concentration

let us find K from the above table (values taken from first and last columns )

10 = -K(10) + 100

-90 = -K(10)

K = 9mg/L hrs-1

Check for K (values taken from first and second columns)

80 = -K(1) + 100

-20 = -K

K = 20 mg/L hrs-1

As the K value is different in both the cases, our assumption is wrong.

STEP 2 : Assume it as a first order reaction

First order reaction : graph of ln [A] versus time is a straight line plot

Thus ln Af = -Kt + ln Ai

ln [Af / Ai ] = -Kt

Here the slope is negative because ln of concentration decreases as time increases

where Af = final concentration

K = decay rate

t = time taken to decrease from initial to final concentration

Ai = initial concentration

let us find K from the above table (values taken from first and last columns )

ln [ 10 / 100 ] = -K(10)

K = 0.23 hrs-1 = 0.2 hrs-1

check for K (values taken from first and second columns)

ln [ 80/ 100 ] = - K (1)

K= 0.223hrs-1 = 0.2 hrs-1

Double check the value of K (values taken from first and third column)

ln [ 50 / 100] = -K (3.5)

K = 0.198 hrs-1 = 0.2 hrs-1

Thus , as the value of K is constant it can be concluded that it is a first order reaction and the decay rate is 0.2 hrs-1


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