Chapter 4, Problem 4.34SP

The following reaction is a common synthesis used in the organic chemistry laboratory course.

$\underset{\text{1-bromobutane}}{{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}\text{Br}}\text{ + }{\underset{\text{methoxide ion}}{\text{CH3O}}}^{-}\stackrel{\to }{\underset{\text{(methanol solvent)}}{{\text{CH}}_{\text{3}}\text{OH}}}\underset{\text{methoxybutane}}{{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{OCH}}_{\text{3}}}+\underset{\text{bromide ion}}{{\text{Br}}^{-}}$

When we double the concentration of methoxide ion (CH₃O⁻), we find that the reaction rate doubles. When we triple the concentration of 1-bromobutane, we find that the reaction rate triples.

1. a. What is the order of this reaction with respect to 1-bromobutane? What is the order with respect to methoxide ion? Write the rate equation for this reaction. What is the overall order?
2. b. One lab textbook recommends forming the sodium methoxide in methanol solvent, but before adding 1-bromobutane, it first distills off enough methanol to reduce the mixture to half of its original volume. What difference in rate will we see when we run the reaction (using the same amounts of reagents) in half the volume of solvent?

Interpretation Introduction

To determine: The order of the given reaction with respect to 1-bromobutane and methoxide ion, rate equation and overall order of the reaction.

Interpretation: The order of the given reaction with respect to 1-bromobutane and methoxide ion, rate equation and overall order of the reaction is to be predicted.

Concept introduction: The order of the reaction is the sum of stoichiometric coefficients of reactants that governs the rate of the reaction. When rate of the reaction is independent to the concentration of the reactants, it called zero order reaction.

Answer to Problem 4.34SP

The order of the given reaction with respect to 1-bromobutane and methoxide ion is $1$ and the overall order of the given reaction is $2$.

Explanation of Solution

The given balanced chemical equation is,

$\begin{array}{ccccccc}{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}\text{Br}& +& {\text{CH}}_{\text{3}}{\text{O}}^{-}& \underset{\begin{array}{c}{\text{CH}}_3\text{OH}\\ \left(\text{Methanol}\text{solvent}\right)\end{array}}{\to }& {\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{OCH}}_{\text{3}}& +& {\text{Br}}^{-}\\ 1-\text{bromobutane}& & \text{methoxide}\text{ion}& & \text{methoxybutane}& & \text{bromide}\text{ion}\end{array}$

It is given that the rate of the reaction changes when concentration of 1-bromobutane and methoxide ion is changed. This shows that the rate of the reaction depends upon the concentration of reactants.

The rate equation of the given reaction is expressed as,

$rate=k_{\text{r}}\left[{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}\text{Br}\right]\left[{\text{CH}}_{\text{3}}{\text{O}}^{-}\right]$

Where,

$k_{\text{r}}$ is the rate constant of the reaction.

The rate equation shows that the rate of reaction depends upon the concentration of 1-bromobutane and methoxide ion. The value of stoichiometric coefficient on 1-bromobutane and methoxide ion concentration term in rate equation is $1$. Therefore, the order of the given reaction with respect to 1-bromobutane and methoxide ion is $1$.

The order of the reaction is the sum of stoichiometric coefficient in rate equation. Therefore, the overall order of the given reaction is $2$.

Interpretation Introduction

To determine: The difference in the rate, when the reaction is run in half the volume of solvent.

Interpretation: The difference in the rate, when the reaction is run in half the volume of solvent is to be predicted.

Concept introduction: The order of the reaction is the sum of stoichiometric coefficients of reactants that governs the rate of the reaction. When rate of the reaction is independent to the concentration of the reactants, it called zero order reaction.

Answer to Problem 4.34SP

The rate of the reaction would not change if the reaction is run in half the volume of solvent because the rate of the reaction depends upon the concentration of 1-bromobutane and methoxide ion.

Explanation of Solution

The rate equation of the given reaction is expressed as,

$rate=k_{\text{r}}\left[{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}\text{Br}\right]\left[{\text{CH}}_{\text{3}}{\text{O}}^{-}\right]$

Where,

$k_{\text{r}}$ is the rate constant of the reaction.

The rate equation shows that the rate of  reaction depends upon the concentration of 1-bromobutane and methoxide ion. There is no effect on the rate of the reaction if concentration of solvent is changed. Therefore, the rate of the reaction would not change if the reaction is run in half the volume of solvent.