7.3 Effect of Temperature on the Rate of Reactions

This topic explains how temperature affects the rate of chemical reactions. It describes the collision theory, the Maxwell-Boltzmann distribution, and the Arrhenius equation.

Definition

Arrhenius Equation: An equation that describes the effect of temperature on the rate constant of a reaction.

k = A e^{-E_a / RT}

• k = rate constant
• A = Arrhenius constant (frequency factor)
• E_a = activation energy
• R = gas constant (8.3143 J K⁻¹ mol⁻¹)
• T = temperature in Kelvin

Main Idea

The reaction rate generally increases with increasing temperature. According to collision theory, the rate of a reaction is proportional to the number of collisions between the reacting molecules. An increase in temperature increases the average kinetic energy of the molecules. This increases the average speed of the reacting molecules. An increase in the kinetic energy of the reacting molecules increases the collision frequency, i.e., the number of effective collisions, and thus the reaction speeds up.

Core Concept

• Temperature increase → rate increase.
• Collision theory: Rate depends on the number of effective collisions.
• Effective collisions: Molecules must have activation energy and correct orientation.
• Maxwell-Boltzmann distribution: Shows the distribution of kinetic energy among molecules.
• Arrhenius equation: Relates rate constant to temperature.

Detailed Explanation

Effect of Temperature on Reaction Rate

• The reaction rate generally increases with increasing temperature.
• According to collision theory, the rate of a reaction is proportional to the number of collisions between the reacting molecules.
• An increase in temperature increases the average kinetic energy of the molecules.
• This increases the average speed of the reacting molecules.
• An increase in the kinetic energy of the reacting molecules increases the collision frequency, i.e., the number of effective collisions, and thus the reaction speeds up.
• But only effective collisions produce a reaction.
• For the collision to be effective, the molecules must have activation energy and must be correctly oriented.
• At normal temperatures, very few molecules have this activation energy.
• Not all reactant molecules have the same energy at a given temperature.
• Most of them are of medium energy.
• Some molecules have a higher than average kinetic energy.
• The number of molecules with kinetic energy at least equal to E_a at temperature T is proportional to the shaded area under the Maxwell-Boltzmann kinetic energy curve.
• The Maxwell-Boltzmann distribution curve shows how the available energy is distributed between the molecules of a gas at a constant temperature.

Maxwell-Boltzmann Distribution Curve

• The distribution curve shows that most molecules do not have the required activation energy at T₁ or lower temperature.
• Only some of the molecules that required the activation energy are able to react.
• When the temperature increases (from T₁ to T₂), the energy of the molecules also increases.
• Thus, the proportion of molecules with the required activation energy increases.
• Thus, the reaction rate increases.

General Observation

- It was found that, in general, the reaction rate increases two to three times for every 10 K increase in temperature.

Arrhenius Equation

Arrhenius (1889) studied the effect of temperature on reaction rates. He found that the effect of temperature on rate of reaction is given by the following equation. This equation is known as the Arrhenius equation.

k = A e^{-E_a / RT}

• k = rate constant
• E_a = energy of activation
• R = gas constant (R = 8.3143 J K^-1 mol^-1)
• A = constant known as Arrhenius constant
• T = temperature in Kelvin

• A is related to the frequency of collision and orientation of the reacting molecules.
• Therefore, rate constant k varies with the temperature.
• It increases with temperature, which in turn increases rate of reaction.

Intermediate Level

Effect of Temperature

Collision Theory

• Rate ∝ number of collisions.
• Only effective collisions produce reaction.
• Effective collision: sufficient energy + correct orientation.

Maxwell-Boltzmann Distribution

• Shows distribution of kinetic energy.
• At higher T, more molecules have E ≥ E_a.
• Shaded area under curve = fraction of molecules with enough energy.

Arrhenius Equation

k = A e^{-E_a / RT}

• k = rate constant
• A = Arrhenius constant
• E_a = activation energy
• R = gas constant
• T = temperature

Key Points

• Rate increases 2–3 times per 10 K rise.
• Rate constant increases with temperature.
• Arrhenius equation relates k to T.

Important Points

• 1. Rate increases with temperature.
• 2. Collision theory: Rate depends on effective collisions.
• 3. Effective collision: activation energy + correct orientation.
• 4. Maxwell-Boltzmann distribution: Shows energy distribution.
• 5. Higher T → more molecules with E ≥ E_a.
• 6. Rate increases 2–3 times per 10 K.
• 7. Arrhenius equation: k = A e^{-E_a / RT}.
• 8. A = Arrhenius constant (frequency factor).

Remember

• - Temperature ↑ → Rate ↑
• - Collision theory: Effective collisions
• - Maxwell-Boltzmann: Energy distribution
• - Rate increases 2–3 times per 10 K
• - Arrhenius equation: k = A e^{-E_a / RT}
• - A: Arrhenius constant

Common Mistakes

• 1. Thinking all collisions are effective: Only those with enough energy and correct orientation.
• 2. Forgetting the role of activation energy: Molecules must have E ≥ E_a.
• 3. Mixing up A and E_a: A = frequency factor; E_a = activation energy.
• 4. Ignoring the Maxwell-Boltzmann distribution: It explains why rate increases with T.

Quick Revision

• Rate increases with temperature.
• Collision theory: Rate depends on effective collisions.
• Effective collision: activation energy + correct orientation.
• Maxwell-Boltzmann distribution: Shows energy distribution.
• Higher T → more molecules with E ≥ E_a.
• Rate increases 2–3 times per 10 K.
• Arrhenius equation: k = A e^{-E_a / RT}.
• A = Arrhenius constant (frequency factor).

60-Second Revision

• Temperature ↑ → Rate ↑
• Collision theory: Effective collisions
• Maxwell-Boltzmann: Energy distribution
• Rate increases 2–3 times per 10 K
• Arrhenius equation: k = A e^{-E_a / RT}
• A: Arrhenius constant

QUALITY VALIDATION

• Topic: 7.3 Effect of Temperature on the Rate of Reactions
• Chapter: 7 (Chemical Kinetics)

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