   # Consider the zero-, first-, and second-order integrated rate laws. If you have concentration versus time data for some species in a reaction, what plots would you make to “prove” a reaction is either zero, first, or second order? How would the rate constant, k , be determined from such a plot? What does the y-intercept equal in each plot? When a rate law contains the concentration of two or more species, how can plots be used to determine k and the orders of the species in the rate law? ### 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 5RQ
Textbook Problem
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## Consider the zero-, first-, and second-order integrated rate laws. If you have concentration versus time data for some species in a reaction, what plots would you make to “prove” a reaction is either zero, first, or second order? How would the rate constant, k, be determined from such a plot? What does the y-intercept equal in each plot? When a rate law contains the concentration of two or more species, how can plots be used to determine k and the orders of the species in the rate law?

Interpretation Introduction

Interpretation: An explanation regarding the various questions related to the integrated rate laws for a reaction is to be stated.

Concept introduction: The differential rate law provides the rate of a reaction at specific reaction concentrations. The dependence of the reaction rate on the concentration of the reactants is represented by a differential rate law, whereas the dependence on time is represented by an integrated rate law.

To determine: The plots in a concentration versus time data that would prove a reaction to be a zero-, first- or a second order reaction; the rate constant values from these plots and the quantity indicated by the y-intercept.

### Explanation of Solution

For a reaction of zero order,

The integrated rate law equation is, [A]=kt+[A]ο

This is similar to the equation for a straight line, that is y=mx+C.

Hence, a straight line obtained on plotting a [A] versus time graph corresponds to a zero order reaction. The slope of the obtained plot gives the value of the rate constant. The y-intercept corresponds to the value of [A]ο.

For a reaction of the first order,

The integrated rate law equation is, ln[A]=kt+ln[A]ο

This is similar to the equation for a straight line, that is y=mx+C.

Hence, a straight line obtained on plotting a ln[A] versus time graph corresponds to a first order reaction. The slope of the obtained plot gives the value of the rate constant

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