The Rate of Reaction: Definition, Expression, and Graphical Determination
What Is the Rate of Reaction?
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.
- The slope of the tangent is given by: $$\text{Slope} = \frac{\Delta[\text{Concentration}]}{\Delta t}$$
Instantaneous Rate from a Graph
- Suppose the concentration of hydrogen gas ($\text{H}_2$) produced in a reaction is recorded over time, and the data is plotted as a curve.
- At $t = 20 \, \text{s}$, the tangent to the curve passes through the points $10, 0.05$ and $30, 0.20$ on the graph.
- The slope of the tangent is: $$\text{Slope} = \frac{0.20 - 0.05}{30 - 10} = \frac{0.15}{20} = 0.0075 \, \text{mol dm}^{-3} \, \text{s}^{-1}$$
- Thus, the instantaneous rate at $t = 20 \, \text{s}$ is $0.0075 \, \text{mol dm}^{-3} \, \text{s}^{-1}$.
Experimental Methods for Measuring Rates
- In practice, concentrations are not always measured directly.
- Instead, experimental data such as changes in volume, mass, pressure, or color is often used to infer reaction rates.
Volume of Gas Produced
For reactions that produce a gas, the volume can be measured using a gas syringe or by collecting the gas over water.
$$\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)$$
The rate of reaction can be calculated by measuring the volume of hydrogen gas ($\text{H}_2$) produced over time.
Change in Mass
For reactions involving gases, the loss of mass can be measured using a balance.
$$\text{CaCO}_3(s) + 2\text{HCl}(aq) \rightarrow \text{CaCl}_2(aq) + \text{CO}_2(g) + \text{H}_2\text{O}(l)$$
The decrease in mass corresponds to the release of carbon dioxide ($\text{CO}_2$) gas.
Color Change
For reactions involving colored substances, a colorimeter or spectrophotometer can monitor changes in absorbance, which is proportional to concentration.
- The choice of method depends on the nature of the reaction and the substances involved.
- For example, gas volume is ideal for reactions producing gases, while electrical conductivity may be used for reactions involving ionic compounds.
- Confusing average and instantaneous rates: Remember that average rates provide an overall rate over a time period, while instantaneous rates focus on a specific moment.
- Incorrect units: Always ensure concentrations are in $\text{mol dm}^{-3}$ and time is in seconds when calculating rates.
- Misinterpreting graphs: When determining instantaneous rates, ensure tangent lines are drawn accurately and only touch the curve at the desired point.
To draw tangent lines accurately, use a ruler and ensure the line touches the curve at only one point without crossing it.
- Define the rate of reaction and write its mathematical expression.
- Explain the difference between average and instantaneous rates.
- Given a curved concentration vs. time graph, how would you determine the rate at a specific time?
