Question

Correct statements regarding Arrhenius equation among the following are:
Factor \(e^{-E_a/RT}\) corresponds to fraction of molecules having kinetic energy less than \(E_a\).
At a given temperature, lower the \(E_a\), faster is the reaction.
Increase in temperature by about \(10^\circ\text{C}\) doubles the rate of reaction.
Plot of \(\log k\) vs \(\dfrac{1}{T}\) gives a straight line with slope \(= -\dfrac{E_a}{R}\).
Choose the correct answer from the options given below:

• A. A and C Only
• B. B and D Only
• C. A and B Only
• D. B and C Only

Hint:

Always remember the factor \(2.303\) appears in Arrhenius plots when logarithm to base 10 is used.

Answer 1

The Correct Option is A

The Arrhenius equation is a formula that expresses the rate constant k of a chemical reaction in terms of the temperature T and the activation energy E_a. The equation is given by:

k = A \cdot e^{-E_a/RT}

where:

• k is the rate constant.
• A is the frequency factor, representing the number of collisions resulting in a reaction.
• e^{-E_a/RT} is the exponential factor that gives the fraction of molecules with kinetic energy greater than or equal to E_a.
• R is the universal gas constant.
• T is the temperature in Kelvin.

Now, let's analyze the given statements:

1. Statement A: Factor e^{-E_a/RT} corresponds to fraction of molecules having kinetic energy less than E_a.
   This statement is incorrect. The factor e^{-E_a/RT} corresponds to the fraction of molecules having kinetic energy greater than E_a.
2. Statement B: At a given temperature, lower the E_a, faster is the reaction.
   This statement is correct. A lower activation energy E_a means that a greater fraction of molecules have enough energy to overcome the energy barrier, thus speeding up the reaction.
3. Statement C: Increase in temperature by about 10^\circ\text{C} doubles the rate of reaction.
   This statement is generally considered correct. It is an empirical rule of thumb, often observed in chemical kinetics.
4. Statement D: Plot of \log k vs \dfrac{1}{T} gives a straight line with slope = -\dfrac{E_a}{R}.
   This statement is correct. When taking the natural logarithm of both sides of the Arrhenius equation, the equation becomes linear: \log k = \log A - \dfrac{E_a}{RT}, with the slope being -\dfrac{E_a}{R}.

According to the analysis, the correct statements are B and D.

Therefore, the option "B and D Only" is correct, not "A and C Only," which was previously stated as correct. This should be carefully reviewed.