R2.2.1 Rate of reaction

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:

$Rate = \frac{Δ [Reactant or Product]}{Δ t}$

Where:

$Δ [Reactant or Product]$ is the change in concentration (in ${mol dm}^{- 3}$ ).
$Δ t$ is the time interval over which the change occurs (in seconds).

Hint

If the concentration of a reactant decreases, $Δ [Reactant]$ will be negative. However, since reaction rates are always expressed as positive values, we take the absolute value.

Example

Calculating the Rate of Reaction

Consider the reaction:

$4 {NH}_{3} (g) + 5 O_{2} (g) \to 4 NO (g) + 6 H_{2} O (g)$

Over a period of 5 seconds, the concentration of $NO (g)$ increases from $0$ to $6.0 \times 10^{- 3} {mol dm}^{- 3}$ .

The rate of reaction with respect to $NO (g)$ is:

$Rate = \frac{Δ [NO]}{Δ t}$ $= \frac{6.0 \times 10^{- 3} {mol dm}^{- 3}}{5 s} = 1.2 \times 10^{- 3} {mol dm}^{- 3} s^{- 1}$

To find the rate of reaction with respect to $O_{2} (g)$ , we use the stoichiometric relationship.

For every 5 moles of $O_{2}$ consumed, 4 moles of $NO$ are produced.

Thus:

$Rate with respect to O_{2} = Rate with respect to NO \times \frac{5}{4}$ $= 1.2 \times 10^{- 3} \times \frac{5}{4} = 1.5 \times 10^{- 3} {mol dm}^{- 3} s^{- 1}$

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.

Schematic drawing of calculating average rate of reaction.

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:

$Slope = \frac{Δ [Concentration]}{Δ t}$

Example

Example: Instantaneous Rate from a Graph

Suppose the concentration of hydrogen gas ( $H_{2}$ ) produced in a reaction is recorded over time, and the data is plotted as a curve.

At $t = 20 s$ , 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:

$Slope = \frac{0.20 - 0.05}{30 - 10} = \frac{0.15}{20} = 0.0075 {mol dm}^{- 3} s^{- 1}$

Thus, the instantaneous rate at $t = 20 s$ is $0.0075 {mol dm}^{- 3} s^{- 1}$ .

Schematic drawing of calculating instantaneous rate of reaction.

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.

1. 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.

Example

$Mg (s) + 2 HCl (a q) \to {MgCl}_{2} (a q) + H_{2} (g)$

The rate of reaction can be calculated by measuring the volume of hydrogen gas ( $H_{2}$ ) produced over time.

2. Change in Mass

For reactions involving gases, the loss of mass can be measured using a balance.

Example

${CaCO}_{3} (s) + 2 HCl (a q) \to {CaCl}_{2} (a q) + {CO}_{2} (g) + H_{2} O (l)$

The decrease in mass corresponds to the release of carbon dioxide ( ${CO}_{2}$ ) gas.

3. Color Change

For reactions involving colored substances, a colorimeter or spectrophotometer can monitor changes in absorbance, which is proportional to concentration.

Note

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.

Common Mistakes in Determining Rates

Common Mistake

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 ${mol dm}^{- 3}$ 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.

Tip

To draw tangent lines accurately, use a ruler and ensure the line touches the curve at only one point without crossing it.

Reflection and Practice

Self review

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?

Theory of Knowledge

The concept of instantaneous rates involves changes over infinitesimally small time intervals. How does this abstraction compare to other scientific models, such as the ideal gas law or absolute zero in thermodynamics?

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R2.2.1 Rate of reaction

The Rate of Reaction: Definition, Expression, and Graphical Determination

What Is the Rate of Reaction?

Calculating the Rate of Reaction

Determining Reaction Rates Graphically

1. Average Rate

2. Instantaneous Rate

Experimental Methods for Measuring Rates

1. Volume of Gas Produced

2. Change in Mass

3. Color Change

Common Mistakes in Determining Rates

Reflection and Practice

You've read 2/2 free chapters this week.

Introduction to Rate of Reaction