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# In a chemical reaction run at a certain temperature, the ISBN: 9780073401331 38

## Solution for problem 20E Chapter 3.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 20E

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-by-Step Solution:

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  =2 0.0001

=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%.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “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.” is broken down into a number of easy to follow steps, and 150 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 20E from chapter: 3.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: estimate, concentration, rate, constant, uncertainty. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 20E from 3.3 chapter was answered, more than 244 students have viewed the full step-by-step answer.

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