Introduction to Rate Law (College Board AP® Chemistry): Study Guide

Rate law

Experimental data and the rate of reaction

• Experiments monitor the amount of a reactant or product over time (for example by measuring the volume or pressure of a gas, or the color intensity of a solution) to find the rate

• Measuring the rate at several concentrations of a reactant shows how the rate depends on that concentration

• The following general reaction will be used as example

D → E + F

• The rate of reaction at different concentrations of D was tabulated and plotted

• A line is plotted and the slope of the line is calculated using the formula below

slope = $\frac{\mathrm{∆}\mathrm{y}}{\mathrm{∆}\mathrm{x}}$

Graph to show rate against [D]

Rate of reaction over various concentrations of D

• As shown in the diagram, there is a directly proportional relation between the rate of reaction and the concentration of D

• This relation can be written as a mathematical equation as shown below

Rate ∝ [D]

Rate = k [D]

• From the slope of the graph, k = 6.67 × 10^-4 s^-1

• This equation means that if the concentration of D doubles, the rate will double

• The constant of proportionality (k) is called the rate constant

  • The value of k depends on temperature: at one temperature k is fixed, and changing a concentration changes the rate, not k

  • The units of k reflect the overall order of the reaction

The rate equation

• The following general reaction will be used to discuss the rate equation:

A + B → C + D

• The general rate equation is:

Rate = k[A]^m[B]ⁿ

• Where:

  • [A] and [B] are the concentrations of the reactants

  • m and n are the orders with respect to each reactant

• The rate law (the orders m and n) can only be found from experimental data

  • It cannot be read from the coefficients in the balanced equation

  • In the worked example below, N₂O₅ has a coefficient of 2 but is first order

• Reaction intermediates do not appear in the rate law

The order of reactants

• The order with respect to a reactant shows how the rate depends on that reactant’s concentration

  • It is represented as the power to which the concentration is raised in the rate equation

• The most common orders are listed below:

• Zero order occurs when the order with respect to a reactant is 0

  • This means that changing the concentration has no effect on the rate

  • Therefore, it is not included in the rate equation

• First order occurs when the order with respect to a reactant is 1

  • This means that the concentration is directly proportional to the rate

  • E.g. Doubling the concentration will double the rate

• Second order occurs when the order with respect to a reactant is 2

  • This means that the rate is directly proportional to the square of the concentration

  • E.g. Doubling the concentration increases the rate by a factor of 4, since 2² = 4

• Overall order  is just the sum of the powers of the reactants that appear in the rate equation

Initial rates & orders of reaction

• The order of the reactants can be determined with experimental data from the initial rates of reaction

  • This information is usually displayed in a table

• The following steps must be followed to determine the order for each reactant:

1. Identify two experiments where the concentration of this reactant changes, but the concentration of the other reactants is the same

2. Identify what has happened with the concentration

3. Determine the effect of the concentration in the rate of reaction

4. Deduce the order of reaction

5. Repeat this procedure with all the reactants, one at a time

• Once all the orders are determined the rate equation can be built

  • Zero order reactants are not included

  • First order reactants are included with no power written (the power is 1)

  • Second order reactants are raised to the power of 2