In a chemical reaction run at a certain temperature, the concentration C of a certain reactant at time t is given by 1/C = kt + l/C0, where C0 is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.04 mol/L exactly. Assume that time is measured with negligible uncertainty.

a. After 30 s, the concentration C is measured to be 0.0038 ± 2:0 × 10-4 mol/L. Estimate the rate constant k, and find the relative uncertainty in the estimate.

b. After 50 s, the concentration C is measured to be 0.0024 ± 2.0 × 10-4 mol/L. Estimate the rate constant k and find the relative uncertainty in the estimate.

c. Denote the estimates of the rate constant k in parts

(a) and (b) by and , respectively. The geometric mean is used as an estimate of k. Find the relative uncertainty in this estimate.

Step 1 of 4:

Here the experiment under consideration is a chemical reaction..

Concentration C of certain reactant at time t is given by,

=kt+

where, is the initial concentration of the reactant and k is the rate constant.

It is also given that the initial concentration is =0.04 mol/L.

Using these,we have to find the required values.

Step 2 of 4:

(a)

Here we have to find the rate constant k and relative uncertainty in estimate at time t=30 sec and concentration C=0.0038 mol/L.

We have,

=kt+

=

=

=

=7.9386

Now we have to find the uncertainty in estimate. It is given by,

=

=

Here

=2.0

=20.0001

=0.0002

So, becomes,

=(0.0002)

=(0.0002)

=(2308.40259)(0.0002)

=0.4617

Therefore,the relative uncertainty is given by,

=

=0.0582

=5.8158%

Hence,the rate constant k is k=7.9386 and relative uncertainty is 5.8158%.