Rate Of A Chemical Reaction

Average vs Instantaneous Rate

Chemical kinetics helps us understand how fast a reaction occurs. The speed of a reaction is measured by the change in concentration of a reactant or product over a period of time.

The average rate ($r_{av}$) is calculated over a measurable time interval, $\Delta t$. It is defined as:

$r_{av} = -\frac{\Delta[R]}{\Delta t} = +\frac{\Delta[P]}{\Delta t}$

Example 3.1: Average Rate Calculation

Problem. From the concentrations of $\text{C}_4\text{H}_9\text{Cl}$ (butyl chloride) at different times, calculate the average rate of the reaction:

$\text{C}_4\text{H}_9\text{Cl} + \text{H}_2\text{O} \rightarrow \text{C}_4\text{H}_9\text{OH} + \text{HCl}$

We need to find the average rate between $t_1 = 0\text{ s}$ and $t_2 = 50\text{ s}$.

• At $t_1 = 0\text{ s}$, $[\text{C}_4\text{H}_9\text{Cl}]_1 = 0.100\text{ mol L}^{-1}$
• At $t_2 = 50\text{ s}$, $[\text{C}_4\text{H}_9\text{Cl}]_2 = 0.0905\text{ mol L}^{-1}$

Stoichiometry and Rate

What happens when the stoichiometric coefficients in a balanced equation are not 1? Consider the decomposition of hydrogen iodide:

$2\text{HI (g)} \rightarrow \text{H}_2\text{ (g)} + \text{I}_2\text{ (g)}$

Notice that two moles of HI must decompose to produce just one mole of H$_2$ and one mole of I$_2$.

Example 3.2: Rate and Stoichiometry

Problem. The decomposition of $\text{N}_2\text{O}_5$ in $\text{CCl}_4$ at $318\text{ K}$ follows the equation:

$2\text{N}_2\text{O}_5\text{ (g)} \rightarrow 4\text{NO}_2\text{ (g)} + \text{O}_2\text{ (g)}$

Initially, $[\text{N}_2\text{O}_5] = 2.33\text{ mol L}^{-1}$. After $184\text{ minutes}$, it is reduced to $2.08\text{ mol L}^{-1}$. Calculate the average rate of this reaction. What is the rate of production of $\text{NO}_2$ during this period?