Ch 2 · Effect of temperature on reaction rates and the concept of activation energy · AS & A Level Chemistry 9701

Topic 2 of 3 in Reaction kinetics — AS & A Level Chemistry 9701 — 48 lessons.

Introduction

Temperature has a far larger effect on reaction rate than a simple increase in collision frequency would suggest; a rise of only 10 °C can roughly double the rate of many reactions. Explaining this fully requires the Boltzmann distribution of molecular energies, which shows why only a small, highly temperature-sensitive fraction of molecules can ever react.

Key ideas — Activation energy

The activation energy, E_a, is the minimum energy that colliding particles must possess for a collision between them to be effective, that is, for it to result in a reaction. Even when particles collide with the correct orientation, the collision fails to produce a reaction unless the combined kinetic energy of the colliding particles is at least equal to E_a; the size of E_a therefore reflects how much energy is needed to begin breaking the bonds of the reactants.

🧑‍🏫 Teacher's explanation

Imagine you are trying to push a heavy boulder over a steep hill. Even if you give the boulder a nudge (a collision), it won't roll down the other side unless you provide enough energy to get it to the very peak of the hill. That peak height is exactly like the activation energy. If you don't reach that height, the boulder just rolls back to you, and nothing 'happens'.

📖 Definitions

🔍 Worked example — Easy

A reaction has an activation energy of 80 ext kJ mol^-1. If the average kinetic energy of the molecules in the system is 40 ext kJ mol^-1, explain why the reaction rate is relatively low.

🔍 Worked example — Standard

Calculate the number of moles of O_2 in 5.0 ext g of O_2 gas.

🔍 Worked example — Exam-style

At 300 ext K, the fraction of molecules with energy ≥ E_a is 1 × 10^-4. If the temperature is increased to 310 ext K, the fraction increases to 5 × 10^-4. Calculate the factor by which the fraction of successful collisions has increased.

⚠️ Common errors

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🎯 Exam question

Key ideas — The Boltzmann distribution

The Boltzmann distribution is a graph of the number of molecules (on the vertical axis) against kinetic energy (on the horizontal axis) for a fixed sample of gas or liquid at a given temperature. The curve starts at the origin (no molecules have zero energy), rises to a single peak, and then falls with a long tail extending to high energies, never quite reaching zero; the total area under the curve represents the total number of molecules present, which does not change. The activation energy is marked as a vertical line on the horizontal axis, and only the small area under the curve to the right of this line represents molecules energetic enough to react on collision.

🧑‍🏫 Teacher's explanation

Imagine a crowded room where everyone is jumping on a trampoline. Some people jump very low, most jump at a medium height, and only a very few jump extremely high. If there is a high ceiling (the activation energy), only those few people who jump high enough will hit it.

📖 Definitions

🔍 Worked example — Easy

A sample of gas has a total of 1.0 × 10^24 molecules. If the area under the Boltzmann distribution curve to the right of the activation energy E_a represents 0.01\% of the total area, calculate the number of molecules capable of reacting upon collision.

🔍 Worked example — Standard

At 300 K, the fraction of molecules with energy ≥ E_a is f_1. At 350 K, the fraction is f_2. Qualitatively, which is larger, f_1 or f_2, and why?

🔍 Worked example — Exam-style

Explain why an increase in temperature leads to a disproportionately large increase in reaction rate, even if the collision frequency increases only slightly.

⚠️ Common errors

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🎯 Exam question

(a) Sketch the effect on the Boltzmann distribution curve when the temperature is increased to 310 K. [2 marks] (b) Explain, in terms of the Boltzmann distribution, why the rate of reaction increases when the temperature is raised. [3 marks] [5 marks]

Key ideas — Why only a small fraction of molecules exceed the activation energy

At any moment, molecules in a sample have a very wide spread of kinetic energies, from almost zero up to very high values, because of the huge number of random collisions constantly redistributing energy between them; most molecules have energy close to the average, near the peak of the curve. Since the activation energy for most reactions is considerably higher than this average energy, and the curve falls steeply beyond the peak, only the small minority of molecules in the long tail, at the extreme high-energy end of the distribution, possess energy equal to or greater than E_a at any given instant.

🧑‍🏫 Teacher's explanation

Imagine a crowded, chaotic dance floor where people are constantly bumping into each other. Some people are moving slowly, most are moving at a medium pace, and only a few are sprinting wildly. If 'success' in a dance move requires a certain amount of momentum, most people won't have enough energy to pull it off.

📖 Definitions

🔍 Worked example — Easy

A sample of gas has an average kinetic energy of 2.0 kJ/mol. If the activation energy for a specific reaction is 50 kJ/mol, qualitatively describe the fraction of molecules that can react.

🔍 Worked example — Standard

The temperature of a system is increased. How does the Boltzmann distribution curve change in terms of its peak and its tail?

🔍 Worked example — Exam-style

In a reaction, the activation energy is 100 kJ/mol. If the temperature is increased, explain why the rate increases even if the collision frequency increases only slightly.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

(a) Sketch a Boltzmann distribution curve for the kinetic energies of molecules in a sample at temperature T_1. (b) On the same axes, sketch the curve for the same sample at a higher temperature T_2. (c) Explain, in terms of the Boltzmann distribution, why the rate of reaction increases when the temperature is raised from T_1 to T_2. [4 marks]

Key ideas — Effect of temperature on rate

Raising the temperature increases the average kinetic energy of the molecules: the peak of the Boltzmann distribution curve moves to the right and becomes lower and broader, since the total area (total number of molecules) stays the same. Because the curve is shifted, a disproportionately larger area now lies beyond the fixed activation energy line, so the fraction of molecules with energy ≥ E_a increases sharply even for a small rise in temperature. Raising temperature also increases collision frequency slightly, since molecules move faster, but this effect is minor compared with the large increase in the fraction of collisions that are effective; the dominant reason reaction rate increases with temperature is the sharp rise in the proportion of molecules exceeding the activation energy.

🧑‍🏫 Teacher's explanation

Imagine a high jump competition. To clear the bar, an athlete needs a minimum amount of energy (the 'activation energy'). At a low temperature, most athletes are tired and can only jump a few inches high; very few can clear a bar set at 6 feet. If you give the athletes a boost (increase the temperature), they all jump slightly higher on average. While the average jump height increases only a little, the number of athletes who can suddenly clear that 6-foot bar increases massively.

📖 Definitions

🔍 Worked example — Easy

A reaction has an activation energy of 50 kJ mol^-1. At 298 K, only 2\% of collisions have energy ≥ E_a. If the temperature is raised to 308 K, the fraction of successful collisions increases to 5\%. Calculate the factor by which the reaction rate increases.

Ch 2 · Effect of temperature on reaction rates and the concept of activation energy · AS & A Level Chemistry 9701

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