A synthetic blue dye (D) is known to decompose in aqueous solution according to the following reaction

World of Chemistry, 3rd edition
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ISBN:9781133109655
Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Chapter15: Solutions
Section: Chapter Questions
Problem 37A
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A synthetic blue dye (D) is known to decompose in aqueous solution according to the following
reaction
Transcribed Image Text:A synthetic blue dye (D) is known to decompose in aqueous solution according to the following reaction
Expert Solution
Step 1

In the second-order reaction, the length of the sequential half-life is increased as the concentration decreased whereas as in the zero-order, the length of the sequential half-life is decreased as the concentration decreased.

Step 2

The equation for the general reaction is shown below:

Chemistry homework question answer, step 2, image 1

The half-life duration for the above reaction will be 42 hours. The time span of the second half-life of the given reaction from the initiation of the reaction will be 84 hours. Thus, the length of the second half-life will be 42 hours. Therefore, the length of the successive half-life is remain constant as the reaction is progressed. Hence, the reaction will be first order reaction. Therefore, the third half-life duration will be 42 hours.

The rate law expression for the above equation is shown below:

Chemistry homework question answer, step 2, image 2

In the above equation, the rate is equivalent to the reactant concentration. As the concentration will be doubled then the initial rate for the given general reaction must be doubled.

Therefore, the correct option is the option (C).

 

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