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# The conversion of cyclobutane (C4 H8) to ethylene (C2 H4)

## Problem 18SE Chapter 3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 18SE

The conversion of cyclobutane (C4 H8) to ethylene (C2 H4) is a first-order reaction. This means that the concentration of cyclobutane at time t is given by In C = In C0 − kt, where C is the concentration at time t, C0 is the initial concentration, t is the time since the reaction started, and k is the rate constant. Assume that C0 = 0.2 mol/L with negligible uncertainty. After 300 seconds at a constant temperature, the concentration is measured to be C = 0.174 ± 0.005 mol/L. Assume that time can be measured with negligible uncertainty.

a. Estimate the rate constant k, and find the uncertainty in the estimate. The units of k will be s-1.

b. Find the relative uncertainty in k.

c. The half-life t1/2 of the reaction is the time it takes for the concentration to be reduced to one-half its initial value. The half-life is related to the rate constant by t1/2= (In 2)/k. Using the result found in part (a), find the uncertainty in the half-life.

d. Find the relative uncertainty in the half-life.

Step-by-Step Solution:

Step 1 of 4:

(a)

In this question, we are asked to estimate the rate constant and find the uncertainty in the estimate.

The concentration of cyclobutane at time t is given by where  is the concentration at time is the initial concentration, is the time since the reaction is started, and is the rate constant.

Given concentration equation

………..(1)

Hence estimated rate constant is .

Uncertainty in the estimated rate constant k:

If is a measurement whose uncertainty is is small, and is a function of , then we can write

……………..(2)

Given

Given concentration equation

Substitute into the equation (2)

=

=

=

=

Substitute the value

=  =

Hence uncertainty  in

Therefore

Step of 2 of  4:

(b)

In this question, we are asked to find the relative uncertainty in

Relative uncertainty  =

In our case

Relative uncertainty  = ………………(3)

Substitute the values of and into the equation (3)

Relative uncertainty  =  = 0.2065

Relative uncertainty =

Hence relative uncertainty in  =

We can therefore express the  =

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The answer to “The conversion of cyclobutane (C4 H8) to ethylene (C2 H4) is a first-order reaction. This means that the concentration of cyclobutane at time t is given by In C = In C0 ? kt, where C is the concentration at time t, C0 is the initial concentration, t is the time since the reaction started, and k is the rate constant. Assume that C0 = 0.2 mol/L with negligible uncertainty. After 300 seconds at a constant temperature, the concentration is measured to be C = 0.174 ± 0.005 mol/L. Assume that time can be measured with negligible uncertainty.a. Estimate the rate constant k, and find the uncertainty in the estimate. The units of k will be s-1.________________b. Find the relative uncertainty in k.________________c. The half-life t1/2 of the reaction is the time it takes for the concentration to be reduced to one-half its initial value. The half-life is related to the rate constant by t1/2= (In 2)/k. Using the result found in part (a), find the uncertainty in the half-life.________________d. Find the relative uncertainty in the half-life.” is broken down into a number of easy to follow steps, and 177 words. The full step-by-step solution to problem: 18SE from chapter: 3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 18SE from 3 chapter was answered, more than 251 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: uncertainty, concentration, half, constant, Find. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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The conversion of cyclobutane (C4 H8) to ethylene (C2 H4)

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