When the temperature of a gas is raised by 10 °C, the collision frequency increases by only about 2%, but the reaction rate increases by 100% (a factor of 2) or more. Explain.

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Understand that the collision frequency of gas molecules is related to the kinetic theory of gases, which states that as temperature increases, molecules move faster and collide more often.

Recognize that the reaction rate is influenced not only by the frequency of collisions but also by the energy of those collisions, specifically whether they have enough energy to overcome the activation energy barrier.

Recall the Arrhenius equation: \( k = A e^{-E_a/RT} \), where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Note that a small increase in temperature can significantly increase the fraction of molecules with energy greater than the activation energy, thus increasing the reaction rate exponentially.

Conclude that while collision frequency increases slightly with temperature, the exponential increase in the number of effective collisions (those with sufficient energy) leads to a much larger increase in reaction rate.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Collision Theory

Collision theory states that for a reaction to occur, reactant particles must collide with sufficient energy and proper orientation. While increasing temperature raises the collision frequency, it is the energy of these collisions that significantly influences reaction rates. A small increase in temperature can lead to a large increase in the number of effective collisions, thus enhancing the reaction rate.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. As temperature increases, more molecules have kinetic energy that exceeds this threshold, allowing more collisions to result in successful reactions. This explains why a relatively small increase in temperature can lead to a dramatic increase in reaction rate, as more molecules can overcome the activation energy barrier.

Arrhenius Equation

The Arrhenius equation quantitatively describes how reaction rates depend on temperature and activation energy. It shows that the rate constant increases exponentially with temperature, indicating that even a small temperature change can lead to a significant increase in the rate of reaction. This relationship helps explain why the reaction rate can double with a modest temperature increase, despite only a slight rise in collision frequency.

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Arrhenius Equation

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Textbook Question

Why don't all collisions between reactant molecules lead to a chemical reaction?

Textbook Question

Two reactions have the same activation energy, but their rates at the same temperature differ by a factor of 10. Explain.

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What fraction of the molecules in a gas at 300 K collide with an energy equal to or greater than Ea when Ea equals 50 kJ/mol? What is the value of this fraction when Ea is 100 kJ/mol?

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The values of Ea = 248 kJ>mol and ΔE = 41 kJ>mol have been measured for the reaction H21g2 + CO21g2S H2O1g2 + CO1g2 (b) Considering the geometry of the reactants and products, suggest a plausible structure for the transition state.

Textbook Question

Consider three reactions with different values of E_a and ΔE:

Reaction 1. E_a = 20 kJ>mol; ΔE = -60 kJ/mol

Reaction 2. E_a = 10 kJ>mol; ΔE = -20 kJ/mol

Reaction 3. E_a = 40 kJ>mol; ΔE = +15 kJ/mol

(b) Assuming that all three reactions are carried out at the same temperature and that all three have the same frequency factor A, which reaction is the fastest and which is the slowest?