The Rate of Reaction: Definition, Expression, and Graphical Determination
What Is the Rate of Reaction?
Definition
Rate of reaction
The rate of reaction measures how quickly reactants are consumed or products are formed during a chemical reaction. It is defined as:
The change in concentration of a reactant or product per unit time.
In mathematical terms, the rate of reaction is expressed as:
$$\text{Rate} = \frac{\Delta[\text{Reactant or Product}]}{\Delta t}$$
Where:
- $\Delta[\text{Reactant or Product}]$ is the change in concentration (in $\text{mol dm}^{-3}$).
- $\Delta t$ is the time interval over which the change occurs (in seconds).
- If the concentration of a reactant decreases, $\Delta[\text{Reactant}]$ will be negative.
- However, since reaction rates are always expressed as positive values, we take the absolute value.
Calculating the Rate of Reaction
- Consider the reaction: $$4 \text{NH}_3(g) + 5 \text{O}_2(g) \rightarrow 4 \text{NO}(g) + 6 \text{H}_2\text{O}(g)$$
- Over a period of 5 seconds, the concentration of $\text{NO}(g)$ increases from $0$ to $6.0 \times 10^{-3} \, \text{mol dm}^{-3}$.
- The rate of reaction with respect to $\text{NO}(g)$ is: $$\text{Rate} = \frac{\Delta[\text{NO}]}{\Delta t}$$ $$= \frac{6.0 \times 10^{-3} \, \text{mol dm}^{-3}}{5 \, \text{s}} = 1.2 \times 10^{-3} \, \text{mol dm}^{-3} \, \text{s}^{-1}$$
- To find the rate of reaction with respect to $\text{O}_2(g)$, we use the stoichiometric relationship.
- For every 5 moles of $\text{O}_2$ consumed, 4 moles of $\text{NO}$ are produced.
- Thus: $$\text{Rate with respect to } \text{O}_2 = \text{Rate with respect to } \text{NO} \times \frac{5}{4} $$ $$=1.2 \times 10^{-3} \times \frac{5}{4} = 1.5 \times 10^{-3} \, \text{mol dm}^{-3} \, \text{s}^{-1}$$
Determining Reaction Rates Graphically
- In experiments, the concentration of a reactant or product is often measured at regular time intervals.
- This data is plotted on a graph, with time on the x-axis and concentration on the y-axis.
- The resulting curve provides valuable insights into the reaction rate.
1. Average Rate
- The average rate of reaction over a time interval is determined by calculating the slope of a secant line connecting two points on the curve.
- This represents the overall rate during a specific time period.
2. Instantaneous Rate
- The instantaneous rate is the rate at a specific moment in time.
- To find this, a tangent line is drawn to the curve at the desired time, and its slope is calculated.
