Book Cover Chemistry 8th Edition / Chang
Student Study Guide

Chapter 13: Chemical Kinetics


Index | 13.1 | 13.2 | 13.3 | 13.4 | 13.5 | 13.6 |

THE RATE OF REACTION (13.1)

STUDY OBJECTIVES
  1. Define the rate of reaction.
  2. Express the rate of a given reaction in terms of the change in concentration with time of a reactant or a product.
  3. Calculate the average rate of reaction from given concentration vs. time data.

Expressing the Rate of Reaction. Chemical kinetics is the area of chemistry concerned with the study of the rates of chemical reactions. The purposes of kinetic studies are to find the factors that affect reaction rates and determine the reaction mechanism. Knowledge of the factors that affect reaction rates enables chemists to control rates. Finding the reaction mechanism means we can identify the intermediate steps by which reactants are converted into products.

A rate is a change in some quantity with time. The rate of population growth is the change in population per change in time. The change in a quantity such as population is always equal to the the difference, population (after) minus population (before). The symbol for "the change in" is .

(population) = populationfinal – populationinitial

The change in time is some appropriate time interval, t, where

t = tfinal – tinitial

The rate of population change is

As a chemical reaction proceeds the concentrations of reactants and products change with time. For instance, as the reaction A + B C progresses, the concentration of C increases. The rate is expressed as the change in the molar concentration of C, [C], during the time interval t.

For a specific reaction we need to take into account the stoichiometry; that is, we need the balanced equation. For example, let's express the rate of the following reaction in terms of the concentrations of the individual reactants and products.

2NO(g) + O2(g) 2NO2(g)

These concentrations can be monitored experimentally as a function of time. Notice from the balanced equation, that 2 mol NO reacts with 1 mol O2; therefore, the concentration of NO will decrease twice as fast as that of O2.

Since the rates of change of individual reactants and products may differ the convention is to make the reaction rate come out to be the same no matter which reactant or product is used to calculate it. First we divide each concentration change by the coefficient from the balanced equation

Second, a negative sign is inserted before terms involving reactants. The change in NO concentration, [NO], is negative because the concentration of NO decreases with time. Inserting a negative sign in the expression makes the rate of reaction a positive quantity.

For a general equation:

aA + bB cC

the rate can be expressed in terms of any individual reactant or product.

No matter which reactant or product we use, the reaction rate will be positive and have the same value.

EXAMPLE Expressing the Rate of Reaction

Remember to put subscripts in brackets and superscripts in braces -- x2 = x[2]; x3 = x{3}
In addition, use a capital D for delta, and place the denominator in parentheses, as shown below:

= D[C]/(Dt)

Write expressions for the rate of the following reaction in terms of each of the reactants and products.

2N2O5(g) 4NO2(g) + O2(g)
N2O5 rate =
NO2 rate =
O2 rate =

EXAMPLE Rate of Reaction

Oxygen gas is formed by the decomposition of nitric oxide:

2NO(g) O2(g) + N2(g)

If the rate of formation of O2 is 0.054 M/s, what is the rate of change of NO concentration?
M/s

Calculating an Average Rate. The average rate of reaction over any time interval is equal to the change in the concentration of a reactant [A], or of a product [C] divided by the time interval, t, during which the change occurred.

The concentration term [A]2 is the concentration of A at time t2, and [A]1 is the concentration of A at time t1.

EXAMPLE Calculation of the Average Rate

Experimental data for the hypothetical reaction:

A 2B

are listed in the following table.

Time (s) [A] (mol/L)
0.00 1.000
10.0 0.891
20.0 0.794
30.0 0.707
40.0 0.630

a. Calculate the average rates of change of [A], and the average reaction rates for the two time intervals from 0 to 10 s and from 30 to 40 s.

0 to 10 s 30 to 40 s
average rate of change mol/L·s mol/L·s
average reaction rate mol/L·s mol/L·s

b. Why does the rate decrease from one time interval to the next?

OBJECTIVE CHECK

Complete the following questions to check your understanding of the material. Select the check button to see if you answered correctly.

  1. Write expressions for the rate of reaction in terms of each of the reactants and products.
    N2(g) + 3H2(g) 2NH3(g)


  2. Thiosulfate ion is oxidized by iodine in aqueous solution according to the equation
    2S2O32–(aq) + I2(aq) S4O62–(aq) + 2I–(aq)
    If 0.025 mol of is consumed in 0.50 L solution per minute:
    1. Calculate the rate of removal of S2O32– in M/s.
    2. What is the rate of removal of I2?
  3. N2O5 is an unstable compound that decomposes according to the following equation.
    2N2O5 4NO2 + O2
    The following data was obtained at 50°C.
      4. [N2O5] (M) Time (s)
      1.00 0
      0.88 200
      0.78 400
      0.69 600
      0.61 800
      0.54 1000
      0.48 1200
      0.43 1400
    1. What is the average rate of N2O5 disappearance in the time interval 200-400 s?
    2. What is the average rate of N2O5 disappearance in the time interval 800-1000 s?
    3. What is the rate of O2 production in the time interval 800-1000 s?

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