Question

The constant 'k' in a rate law expression of a reaction is

• A. is dependent on the concentration of reactants.
• B. is dimensionless.
• C. dependent on temperature.
• D. called the Arrhenius constant.

Hint:

The rate constant \(k\) changes only with:
1. Temperature (exponential increase via Arrhenius equation).
2. Presence of a catalyst (lowers \(E_a\)).
It is completely independent of the concentrations of reactants and products.

Answer 1

The Correct Option is C

Concept:
The rate constant (\(k\)), also called the specific reaction rate, is the proportionality constant in the rate law equation that relates the rate of a chemical reaction to the molar concentrations of the reactants.
It serves as an intrinsic quantitative measure of the inherent speed of a chemical reaction under fixed experimental conditions.

Step 1: Independence from Reactant Concentration:
In a general rate expression:
\[ \text{Rate} = k [\text{A}]^x [\text{B}]^y \] When \([\text{A}] = [\text{B}] = 1\text{ mol L}^{-1}\), the rate of the reaction equals \(k\).
The value of \(k\) is a characteristic property of a given reaction and does not change with varying concentrations of reactants.
Hence, statement (A) is incorrect.

Step 2: Dependence on Reaction Order for Units:
The dimensions of \(k\) depend on the overall order \(n\) of the reaction:
\[ \text{Units of } k = \left(\text{mol L}^{-1}\right)^{1-n} \text{s}^{-1} \] It is dimensionless only when \(n = 1\) (where units reduce to \(\text{s}^{-1}\)), but not in general. Thus, statement (B) is incorrect.

Step 3: Dependence on Temperature via the Arrhenius Law:
The temperature dependence of the rate constant is described by the Arrhenius equation:
\[ k = A e^{-E_a / RT} \] As temperature increases, the fraction of colliding molecules with kinetic energy exceeding the activation energy \(E_a\) increases exponentially, causing \(k\) to increase.
Generally, for every \(10^\circ\text{C}\) increase in temperature, the rate constant approximately doubles or triples.
Thus, \(k\) is strongly dependent on temperature. Hence, statement (C) is correct.
The pre-exponential factor \(A\) is the Arrhenius constant, not \(k\), making statement (D) incorrect.
Final Answer:
The constant \(k\) is dependent on temperature, which corresponds to option (C).