   # Experimental data for the reaction A → 2 B + C have been plotted in the following three different ways (with concentration units in mol/L): What is the order of the reaction with respect to A, and what is the initial concentration of A? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 45E
Textbook Problem
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## Experimental data for the reaction A → 2 B + C have been plotted in the following three different ways (with concentration units in mol/L): What is the order of the reaction with respect to A, and what is the initial concentration of A?

Interpretation Introduction

Interpretation: The general reaction is given. The graph of [A] versus time, ln[A] versus time and 1/[A] versus time is given. The order of reaction with respect to A and its initial concentration is to be calculated.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate

law provides the rate of a reaction at specific reaction concentrations.

To determine: The order of reaction with respect to A .

### Explanation of Solution

The given reaction is,

A2B+C

The rate law gives the relation between reaction rate and concentration of reactants. The rate law is represented as,

Rate=k[A]a (1)

Where,

• k is rate constant.
• [A] is concentration of reactant.
• a is reaction order of A.

The order of the given reaction can be determined by using following parameters,

• For first order reaction, ln[A]vstime graph is straight line
• For second order reaction, 1[A]vstime graph is straight line.
• For zero order reaction, [A]vstime graph is straight line.

Theplot of 1[A]vstime graphis straight line. It means that the given reaction is second order (a=2) reaction.

To determine: The initial concentration of A .

The integral rate law equation of second order reaction is,

1[A]=kt+1[A]0 (2)

Where,

• k is rate constant.
• [A]0 is initial concentration.
• [A] is final concentration.
• t is time.

The graph of second order reaction is,

Figure 1

Data from graph,

At t=6 the value of concentration is [A]=70

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