7.3 Effect of Temperature on the Rate of Reactions | Chemical Kinetics | Chemistry 11

The rate of a chemical reaction is highly dependent on temperature. Generally, an increase in temperature leads to an increase in the reaction rate.

Collision Theory and Temperature

According to collision theory, a reaction occurs when reactant molecules collide with sufficient energy and in the correct orientation. The effect of temperature can be explained by this theory:

Increased Kinetic Energy: An increase in temperature raises the average kinetic energy of the molecules.
Increased Molecular Speed: As molecules gain kinetic energy, their average speed increases.
Increased Collision Frequency: Faster-moving molecules collide more frequently.

However, not all collisions result in a reaction. For a collision to be effective, two conditions must be met:

The colliding molecules must possess a minimum amount of energy, known as the activation energy ( $E_{a}$ ).
The molecules must be in the correct spatial orientation at the moment of impact.

Key insight: Collision frequency increases by only about $1$ – $2%$ for a $10 K$ rise in temperature. The dominant reason for the sharp increase in reaction rate is the exponential increase in the fraction of molecules possessing energy $\geq E_{a}$ .

The Maxwell-Boltzmann Distribution

At any given temperature, the reactant molecules do not all have the same kinetic energy. The Maxwell-Boltzmann distribution curve illustrates how kinetic energy is distributed among a population of molecules at a constant temperature.

Figure 7.2a: Maxwell-Boltzmann curve of kinetic energy distribution.

The peak of the curve represents the most probable kinetic energy.
The activation energy ( $E_{a}$ ) is a threshold on this curve. Only molecules with kinetic energy equal to or greater than $E_{a}$ can react upon collision.
The shaded area under the curve to the right of $E_{a}$ represents the fraction of molecules with sufficient energy to react.

Effect of Increasing Temperature

When the temperature is increased (e.g., from $T_{1}$ to $T_{2}$ , where $T_{2} > T_{1}$ ):

The distribution curve flattens and shifts to the right.
The fraction of molecules possessing the required activation energy ( $E_{a}$ ) increases significantly.
This leads to a higher number of effective collisions per unit time, thereby increasing the reaction rate.

Temperature Coefficient ( $Q_{10}$ )

A general rule of thumb is that for many reactions, the rate doubles or triples for every 10 K (or 10°C) increase in temperature. This is quantified by the Temperature Coefficient ( $Q_{10}$ ):

$Q_{10} = \frac{Rate at ( T + 10 K )}{Rate at T}$

For most reactions, $Q_{10} \approx 2$ – $3$ .

The Arrhenius Equation

In 1889, Svante Arrhenius quantitatively described the relationship between temperature, activation energy, and the rate constant ( $k$ ) with the Arrhenius equation:

$k = A e^{- E_{a} / R T}$

Where:

Symbol	Meaning
$k$	Rate constant
$A$	Pre-exponential factor (related to collision frequency and orientation probability)
$E_{a}$	Activation energy (J/mol)
$R$	Universal gas constant ( $8.314 J \cdot K^{- 1} \cdot m o l^{- 1}$ )
$T$	Absolute temperature (Kelvin)

This equation shows that $k$ increases exponentially as $T$ increases. Since reaction rate is directly proportional to $k$ , the reaction rate also increases with temperature.

Linearised Form

Taking the natural logarithm of the Arrhenius equation:

$ln k = ln A - \frac{E _{a}}{R} \cdot \frac{1}{T}$

A plot of $ln k$ vs $\frac{1}{T}$ gives a straight line with:

Slope $= - \frac{E _{a}}{R}$
Intercept $= ln A$

This allows experimental determination of $E_{a}$ from kinetic data.

The rate of a chemical reaction is highly dependent on temperature. Generally, an increase in temperature leads to an increase in the reaction rate.

Collision Theory and Temperature

According to collision theory, a reaction occurs when reactant molecules collide with sufficient energy and in the correct orientation. The effect of temperature can be explained by this theory:

Increased Kinetic Energy: An increase in temperature raises the average kinetic energy of the molecules.
Increased Molecular Speed: As molecules gain kinetic energy, their average speed increases.
Increased Collision Frequency: Faster-moving molecules collide more frequently.

However, not all collisions result in a reaction. For a collision to be effective, two conditions must be met:

The colliding molecules must possess a minimum amount of energy, known as the activation energy ( $E_{a}$ ).
The molecules must be in the correct spatial orientation at the moment of impact.

The Maxwell-Boltzmann Distribution

The peak of the curve represents the most probable kinetic energy.
The activation energy ( $E_{a}$ ) is a threshold on this curve. Only molecules with kinetic energy equal to or greater than $E_{a}$ can react upon collision.
The shaded area under the curve to the right of $E_{a}$ represents the fraction of molecules with sufficient energy to react.

Effect of Increasing Temperature

When the temperature is increased (e.g., from $T_{1}$ to $T_{2}$ , where $T_{2} > T_{1}$ ):

The distribution curve flattens and shifts to the right.
The fraction of molecules possessing the required activation energy ( $E_{a}$ ) increases significantly.
This leads to a higher number of effective collisions per unit time, thereby increasing the reaction rate.

Temperature Coefficient ( $Q_{10}$ )

$Q_{10} = \frac{Rate at ( T + 10 K )}{Rate at T}$

For most reactions, $Q_{10} \approx 2$ – $3$ .

The Arrhenius Equation

In 1889, Svante Arrhenius quantitatively described the relationship between temperature, activation energy, and the rate constant ( $k$ ) with the Arrhenius equation:

$k = A e^{- E_{a} / R T}$

Where:

Symbol	Meaning
$k$	Rate constant
$A$	Pre-exponential factor (related to collision frequency and orientation probability)
$E_{a}$	Activation energy (J/mol)
$R$	Universal gas constant ( $8.314 J \cdot K^{- 1} \cdot m o l^{- 1}$ )
$T$	Absolute temperature (Kelvin)

This equation shows that $k$ increases exponentially as $T$ increases. Since reaction rate is directly proportional to $k$ , the reaction rate also increases with temperature.

Linearised Form

Taking the natural logarithm of the Arrhenius equation:

$ln k = ln A - \frac{E _{a}}{R} \cdot \frac{1}{T}$

A plot of $ln k$ vs $\frac{1}{T}$ gives a straight line with:

Slope $= - \frac{E _{a}}{R}$
Intercept $= ln A$

This allows experimental determination of $E_{a}$ from kinetic data.