Two gaseous reactants, \text{X}(g) and \text{Y}(g), undergo a bimolecular reaction inside … — JAMB UTME

Two gaseous reactants, $\text{X}(g)$ and $\text{Y}(g)$ , undergo a bimolecular reaction inside a rigid container at constant volume. When the temperature of the reaction vessel is raised from $300\text{ K}$ to $310\text{ K}$ , the rate of reaction approximately doubles. According to collision theory, which statement correctly explains the primary molecular factor responsible for this marked increase in rate?

The fraction of colliding molecules with kinetic energy equal to or exceeding the activation energy ( $E_a$ ) increases exponentially.Answer
B
The total collision frequency between reactant molecules increases proportionally with the absolute temperature.
C
The activation energy ( $E_a$ ) of the reaction is lowered as thermal energy increases in the system.
D
The molecular orientation requirements become negligible as thermal motion increases.

Answer

The primary factor responsible for the rate increase is that the fraction of colliding molecules possessing energy greater than or equal to the activation energy increases exponentially with temperature.

Increasing the temperature shifts the Maxwell-Boltzmann kinetic energy distribution toward higher energies. Because the proportion of molecules exceeding the activation energy is determined by the exponential factor

e^{-E_a/RT}

, a small temperature increase causes a dramatic, exponential increase in the fraction of collisions that are energetically successful.

Step-by-Step Solution

Analyze collision theory requirements for a chemical reaction to occur.

Effective collisions require both proper steric orientation and collision energy

E \ge E_a

Collision theory states that rate depends on collision frequency, steric factor, and the fraction of collisions exceeding activation energy.

Evaluate the effect of a

10\text{ K}

temperature rise on total collision frequency versus the fraction of energetic molecules.

Collision frequency increases only slightly (

∝ \sqrt{T}

, about

1.6\%

rise), whereas the fraction of molecules with

E \ge E_a

given by

e^{-E_a/RT}

increases exponentially.

The Maxwell-Boltzmann distribution curve shifts to higher kinetic energies, greatly expanding the area under the curve beyond

E_a

Select the option that identifies the exponential increase in energetic molecules as the governing cause.

The option describing an exponential increase in the fraction of energetic collisions is correct.

This exponential increase directly explains why a small temperature increase leads to a massive (often doubled) reaction rate.

Key Concept

Collision Theory and Temperature Dependence of Reaction Rate

Estimated Time:1m 30s

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Answer

Step-by-Step Solution

Key Concept

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