Question

The value of R in energy of activation is

• A. 1.98 cal/deg.molecule
• B. 1.89 cal/deg.molecule
• C. 8.91 cal/deg.molecule
• D. 9.18 cal/deg. molecule

Answer 1

The Correct Option is A

To solve this question, we need to understand the concept of activation energy and the gas constant (ℝ).

The gas constant ℝ is an important constant utilized in various equations in physical chemistry. Particularly, it appears in the Arrhenius equation, which is used to calculate the energy of activation (𝔼_a). The Arrhenius equation is:

\(k = A \exp{\left( -\frac{E_a}{RT} \right)}\)

Here: 

• \(k\) = rate constant
• \(A\) = pre-exponential factor
• \(E_a\) = activation energy
• \(T\) = temperature (in Kelvin)
• \(R\) = gas constant

In the context of activation energy, ℝ is often given in calories per degree per mole (cal/deg.mol or cal/K.mol). The standard value of ℝ in such units is approximately 1.987 cal/deg.mol.

The closest option provided to the standard value of the gas constant relevant for activation energy is:

• Option 1: 1.98 cal/deg.molecule

Thus, the correct answer is Option 1. The other options do not match the standard value of ℝ for these units and can be eliminated as incorrect.