Question

The rate constant of a reaction depends upon:
(A) temperature of the reaction
(B) extent of the reaction
(C) initial concentration of the reactants
(D) the time of completion of reaction

Answer 1

Hint: Recall the rate law given in the chapter chemical kinetics. The rate law has a constant called rate constant whose value is determined by the Arrhenius equation. The factors in the Arrhenius equation alone can change the value of rate constant. The Arrhenius equation is given below:
$k\text{ }=\text{ }A{{e}^{-\dfrac{{{E}_{a}}}{RT}}}$
Where,
k is the rate constant for the reaction,
A is the Arrhenius constant
${{E}_{a}}$ is the activation energy
R is Universal gas constant
T is the temperature at which rate law is determined.

Complete step by step answer:
In chemical kinetics, rate constant or rate coefficient for the reaction helps to determine the rate and direction of the chemical reaction.
Let us consider a simple reaction in which compound A gives compound B.
$aA\text{ }\to \text{ }bB$
Where,
a and b are stoichiometric coefficients.
The rate law for the above reaction is written as,
$\text{r = k }\text{. }\!\![\!\!\text{ A}{{\text{ }\!\!]\!\!\text{ }}^{a}}$
Where,
[A] is the concentration of the reactant
Concentration of reactants or products are in standard form only i.e. only molar concentration are used for calculation of rate.
As mentioned in the hint, rate constant is determined by the Arrhenius theory. The Arrhenius theory gave an equation to find the factors on which rate constant depends. The equation is,
$k\text{ }=\text{ }A{{e}^{-\dfrac{{{E}_{a}}}{RT}}}$
Rate constant of a reaction depends on
- Activation energy of the reactant particles
- Temperature at which reaction is taking place.
So, the correct answer is “Option A”.

Note: Along with Arrhenius theory, there exists another theory that is derived using more sophisticated statistical mechanical considerations. This theory is called transition state theory or collision theory and gives the Eyring equation.
The main difference between the two theories is that Arrhenius theory attempts to model the reaction as a whole however the latter models and considers the individual elementary steps involved.