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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 33E

To determine

**To find:** The derivative of *t* with respect to *c* with the equation

Expert Solution

The derivative of *t* with respect to *c* is given as

**Given:**

The given equation is as below.

Calculation:

Use chain rule to differentiate the equation (1).

Assume the variable *u* as *t* as

Use the expression below.

Substitute

Refer equation (1), separate the term

Indicate it as

Differentiate

Assume the variable *l* as

Use the expression below.

Substitute

Substitute

Write the interpretation based on the result as below.

The rate of reaction will be fast with higher initial concentration value. The time taken for removing the unit concentration of the material will be lesser as the initial concentration increases.

The derivative of *t* with respect to *c* is given as