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The decomposition of nitrogen dioxide (NO2) into nitrogen

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 19SE Chapter 3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 19SE

Problem 19SE

The decomposition of nitrogen dioxide (NO2) into nitrogen monoxide (NO) and oxygen is a second- order reaction. This means that the concentration C of NO2 at time t is given by 1/C = k t + 1/C0, where C0 is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.03 mol/L exactly. Assume that time can be measured with negligible uncertainty.

a. After 40 s, the concentration C is measured to be 0.0023 ± 2.0 x 10-4 mol/L. Estimate the rate constant k, and find the uncertainty in the estimate.

b. After 50 s, the concentration C is measured to be 0.0018 ± 2.0 ×10-4 mol/L. Estimate the rate constant k, and find the uncertainty in the estimate.

c. Denote ihe estimates of the rate constant k in parts (a) and (b) by  and  respectively. The average  is used as an estimate of k. Find the uncertainty in this estimate.

d. Find the value of c so that the weighted average  has the smallest uncertainty.

Step-by-Step Solution:

Answer :

Step 1 of 5:

         Given, the decomposition of nitrogen dioxide (into nitrogen monoxide (NO) and oxygen is a second order reaction.

         This means that the concentration C of at time ‘t’ is given by:

                                                          ….. (1)

          Where, is the initial concentration and k is the rate constant.

  Assume the initial concentration is known to be 0.03 mol/L exactly.


Step 2 of 5

Chapter 3, Problem 19SE is Solved
Step 3 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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