Raising the temperature of a reaction mixture from 300\text{ K} to 310\text{ K} often doub… — JAMB UTME

Raising the temperature of a reaction mixture from $300\text{ K}$ to $310\text{ K}$ often doubles the rate of reaction, despite the average kinetic energy of the reactant molecules increasing by only about $3.3\%$ . Which of the following best explains this disproportionate increase in reaction rate according to collision theory?

A
The total collision frequency between reactant particles doubles with a $10\text{ K}$ rise in temperature.
B
The activation energy ( $E_a$ ) of the reaction is lowered significantly by the increase in thermal energy.
The fraction of reactant molecules possessing kinetic energy equal to or exceeding the activation energy increases exponentially.Answer
D
The average kinetic energy of all reactant molecules doubles due to an increase in molecular velocity.

Answer

The fraction of reactant molecules possessing kinetic energy equal to or exceeding the activation energy increases exponentially.

According to collision theory and the Maxwell-Boltzmann distribution, reaction rate depends on the frequency of effective collisions—collisions possessing energy greater than or equal to the activation energy (

E \ge E_a

). The fraction of molecules satisfying this condition is expressed by

f = e^{-E_a / RT}

. Because of this exponential factor, a small increase in absolute temperature (

T

) substantially increases the proportion of high-energy molecules in the tail of the curve, roughly doubling the effective collision frequency for typical activation energies.

Step-by-Step Solution

Analyze the relationship between temperature and average kinetic energy.

Average kinetic energy is directly proportional to temperature in Kelvin (

E_k = \frac{3}{2}RT

). A rise from

300\text{ K}

310\text{ K}

yields

\frac{310 - 300}{300} = 3.33\%

increase.

This rules out explanations claiming that average kinetic energy or velocity doubles.

Analyze total collision frequency versus effective collision frequency.

Total collision frequency increases only slightly (

\propto \sqrt{T}

\approx 1.6\%

increase), whereas effective collision frequency increases dramatically.

For a collision to lead to reaction, particles must collide with energy

E \ge E_a

and correct orientation.

Apply the Maxwell-Boltzmann distribution model.

The fraction of molecules with

E \ge E_a

is proportional to

e^{-E_a / RT}

. Because of the exponential dependence on

T

, even a modest

10\text{ K}

rise significantly expands the tail of the energy distribution curve beyond

E_a

, leading to roughly double the number of successful high-energy collisions.

This accounts for the dramatic increase in reaction rate.

Key Concept

Collision Theory and Maxwell-Boltzmann Energy Distribution

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics