Chemical Kinetics: Rates of Chemical Reactions

Chapter 15: Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the speed (rate) at which chemical processes occur. It also provides insight into the mechanisms by which reactions proceed and the factors that influence reaction rates.

• Reaction rate refers to the change in concentration of a reactant or product per unit time.

• Kinetics helps explain not only how fast a reaction occurs, but also why some reactions are fast and others are slow.

The Average Rate of the Reaction

Definition and Calculation

The average rate of a reaction is the change in concentration of a reactant or product over a specific time interval.

• For a general reaction: H2(g) + I2(g) → 2 HI(g)

• The average rate can be calculated as:

$\text{Rate} = -\frac{\Delta [\text{H}_2]}{\Delta t} = -\frac{[\text{H}_2]_{t_2} - [\text{H}_2]_{t_1}}{t_2 - t_1}$ $\text{Rate} = \frac{\Delta [\text{HI}]}{\Delta t} = \frac{[\text{HI}]_{t_2} - [\text{HI}]_{t_1}}{t_2 - t_1}$

• Negative sign for reactants indicates a decrease in concentration; positive for products indicates an increase.

Example Table: Average Rate Calculation

The following table shows how the concentration of H2 changes over time and how the average rate is calculated:

Δ[H2] (M)	Δt (s)	Rate = -Δ[H2]/Δt (M/s)
-0.181	10.000	0.0181
-0.149	10.000	0.0149
-0.121	10.000	0.0121
-0.100	10.000	0.0100
-0.080	10.000	0.0080
-0.067	10.000	0.0067
-0.054	10.000	0.0054
-0.046	10.000	0.0046
-0.030	10.000	0.0030

Note: The rate decreases as the reaction proceeds because the concentration of reactants decreases.

Visualizing Reaction Progress

Reactant to Product Conversion

Consider a reaction A → B, where A is the reactant and B is the product. The rate of disappearance of A and appearance of B can be measured over time.

• Example: If [A] decreases from 1.00 M to 0.54 M in 20 s, and [B] increases from 0.00 M to 0.46 M in the same time:

$\text{Rate of disappearance of A} = -\frac{\Delta [A]}{\Delta t} = -\frac{0.54 - 1.00}{20} = 0.023\ \text{M/s}$ $\text{Rate of appearance of B} = \frac{\Delta [B]}{\Delta t} = \frac{0.46 - 0.00}{20} = 0.023\ \text{M/s}$

• As time progresses, the rate typically decreases due to lower reactant concentrations.

The Instantaneous Rate of the Reaction

Definition and Determination

The instantaneous rate is the rate at a specific moment in time, found by taking the slope of the tangent to the concentration vs. time curve at that point.

• For the reaction: C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)

• Instantaneous rate at t = 600 s:

$\text{Rate} = -\frac{\Delta [\text{C}_4\text{H}_9\text{Cl}]}{\Delta t} = -\frac{0.017 - 0.042}{800 - 400} = 6.2 \times 10^{-5}\ \text{M/s}$

• Instantaneous rate at t = 0 s:

$\text{Rate} = -\frac{0.06 - 0.10}{200 - 0} = 2.0 \times 10^{-4}\ \text{M/s}$

Average Rate versus Instantaneous Rate

The average rate is calculated over a time interval, while the instantaneous rate is the slope at a single point in time. The instantaneous rate at t = 0 is called the initial rate.

• Graphically, the average rate is the slope of a secant line between two points; the instantaneous rate is the slope of a tangent line at a point.

Reaction Rate and Stoichiometry

Relating Rates for Different Substances

For reactions with different stoichiometric coefficients, the rates of disappearance and appearance are related by those coefficients.

• Example: 2 HI(g) → H2(g) + I2(g)

$\text{Rate} = -\frac{1}{2}\frac{\Delta [\text{HI}]}{\Delta t} = \frac{\Delta [\text{H}_2]}{\Delta t} = \frac{\Delta [\text{I}_2]}{\Delta t}$

• General case: aA + bB → cC + dD

$\text{Rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t}$

Relating Rates at Which Products Appear and Reactants Disappear

For the reaction 2 O3(g) → 3 O2(g):

• If O2 appears at a rate of 6.0 × 10−5 M/s, the rate at which O3 disappears is:

$\text{Rate} = \frac{1}{2}\frac{\Delta [\text{O}_3]}{\Delta t} = \frac{1}{3}\frac{\Delta [\text{O}_2]}{\Delta t}$ $-\frac{\Delta [\text{O}_3]}{\Delta t} = \frac{2}{3}\frac{\Delta [\text{O}_2]}{\Delta t}$ $-\frac{\Delta [\text{O}_3]}{\Delta t} = \frac{2}{3}(6.0 \times 10^{-5}) = 4.0 \times 10^{-5}\ \text{M/s}$

Summary Table: Rate Relationships

Substance	Coefficient	Rate Expression
Reactant A	a	$-\frac{1}{a}\frac{\Delta [A]}{\Delta t}$
Reactant B	b	$-\frac{1}{b}\frac{\Delta [B]}{\Delta t}$
Product C	c	$\frac{1}{c}\frac{\Delta [C]}{\Delta t}$
Product D	d	$\frac{1}{d}\frac{\Delta [D]}{\Delta t}$

Key Points

• Reaction rates are always positive values.

• Rates for reactants are given negative signs to indicate consumption.

• Stoichiometric coefficients must be considered when relating rates of different substances in a reaction.