Chapter 16, Problem 61A

Interpretation Introduction

Interpretation:

To explain the rate law for a chemical reaction is based on experimental evidence rather than the balanced equation for the reaction.

Concept introduction:

Consider the general reaction

$\text{aA+bB}\to \text{Products}$

Rate law of the reaction is as follows:

$\text{rate=}k{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}$

Here, $\left[\text{A}\right]$, $\left[\text{B}\right]$ concentration of reactant A and B, k represents rate and m, n are the orders of their corresponding reactant. They are determined by experimentally and are found by examining how altering the initial concentrations affects the initial reaction rate.

Answer to Problem 61A

The rate law for chemical reactions is based on experimental evidence rather than the balanced equation because most chemical reactions are not single-step reactions. Only single-step reactions have orders that are equal to their reaction coefficients.

Explanation of Solution

Consider the general reaction

$\begin{array}{l}\text{aA+bB}\to \text{Products}\\ \text{rate=}k{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}\end{array}$

In order to determine the rate law of a reaction, the method of initial rate is used. This method is used for at least three trials with different amounts of the reactants A and B to determine the affect that each reactant has on the reaction rate.

In the first experiment, a common control concentration is used for each reactant to assess the initial reaction rate. In the second trial, reactant B has the same initial concentrations as the first trial, but the concentration of reactant A is doubled.

By comparing the initial rates measured by doubling the concentration of A from trials 1 to 2, the order of reactant A is determined.

This can be repeated to determine the impact of reactant B on the rate. In one trial, keep the concentration of reactants A and B constant, and in another trial hold reactant A constant but double the concentration of the B and examine the effect of doubling on initial rate. The order by which the change in the concentration of B changed the reaction rate is the order of reactant B.

The method of initial rate is used at least for three trials for the different amounts of the reactants.

Conclusion

A rate law describes the relationship between the rate of a chemical reaction and reactants concentration.