   Chapter 12, Problem 105CP

Chapter
Section
Textbook Problem

# The reaction NO ( g ) + O 3 → NO 2 ( g ) + O 2 ( g ) was studied by performing two experiments. In the first experiment the rate of disappearance of NO was followed in the presence of a large excess of O3. The results were as follows ([O3] remains effectively constant at 1.0 × 1014 molecules/cm3): Time(ms) [NO] (molecules/cm3) 0 6.0 × 108 100 ± 1 5.0 × 108 500 ± 1 2.4 × 108 700 ± 1 1.7 × 108 1000 ± 1 9.9 × 107 In the second experiment [NO] was held constant at2.0 × 1014 molecules/cm3. The data for the disappearance of O3 are as follows: Time(ms) [O3] (molecules/cm3) 0 1.0 × 1010 50± 1 8.4 × 109 100 ± 1 7.0 × 109 200 ± 1 4.9 × 109 300 ± 1 3.4 × 109 a. What is the order with respect to each reactant?b. What is the overall rate law?c. What is the value of the rate constant from each set of experiments? Rate  =   k ' [ NO ] x         Rate  =   k " [ O 3 ] y d. What is the value of the rate constant for the overall rate law? Rate =   k [ NO ] x [ O 3 ] y

(a)

Interpretation Introduction

Interpretation: The order of the reaction with respect to each reactant is to be calculated. The overall rate law is to be stated. From each set of the given experiments the value of rate constants are to be calculated. The overall rate constant is to be stated.

Concept introduction: The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

To determine: The order of the reaction with respect to each reactant.

Explanation

Explanation

Given

The given reaction is stated as,

NO(g)+O3(g)NO2(g)+O2(g)

There are two reactants are present in the given reaction. Therefore to calculate the order of the reaction with respect to each reactant the following steps are observed.

With the help of the given data the value of ln[NO] is determined and are given by the following expression,

 Time (ms) [NO] (molecules/cm3) ln[NO] 0 6.0×108 20.21 100 5.0×108 20.03 500 2.4×108 19.29 700 1.7×108 18.95 1000 9.9×107 18.41

Table 1

With the help of the above determined values the plot of ln[NO] Vs time is drawn as,

Figure 1

The above figure clearly indicates that in the ln[NO] Vs time plot the straight line is observed therefore, the given reaction is first order with respect to reactant [NO]

(b)

Interpretation Introduction

Interpretation: The order of the reaction with respect to each reactant is to be calculated. The overall rate law is to be stated. From each set of the given experiments the value of rate constants are to be calculated. The overall rate constant is to be stated.

Concept introduction: The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

To determine: The overall rate law for the given reaction.

(c)

Interpretation Introduction

Interpretation: The order of the reaction with respect to each reactant is to be calculated. The overall rate law is to be stated. From each set of the given experiments the value of rate constants are to be calculated. The overall rate constant is to be stated.

Concept introduction: The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

To determine: The value of rate constant from each set of experiments.

(d)

Interpretation Introduction

Interpretation: The order of the reaction with respect to each reactant is to be calculated. The overall rate law is to be stated. From each set of the given experiments the value of rate constants are to be calculated. The overall rate constant is to be stated.

Concept introduction: The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

To determine: The value of rate constant for overall rate law.

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