Question

The rate constant, the activation energy and the Arrhenius parameter (A) of a chemical reaction at $25{}^\circ C$are$3.0\times {{10}^{-22}}{{s}^{-1}}$,$104.4KJmo{{l}^{-1}}$, $6.0\times {{10}^{14}}{{s}^{-1}}$and respectively. The value of rate constant at $T\to \infty $is:
A. $2.0\times {{10}^{18}}{{s}^{-1}}$
B. $6.0\times {{10}^{14}}{{s}^{-1}}$
C. infinity
D. $3.6\times {{10}^{30}}{{s}^{-1}}$

Answer 1

Hint: Rate constant also known by the name proportionality constant which gives the relationship between molar concentration of the reactants and chemical reaction. This is generally denoted by the symbol K.

Complete answer:
Rate constant can be easily calculated with the help of Arrhenius equation. This equation gives us the formula for the temperature dependence of reaction rates. The Arrhenius equation has many applications but the main and very important application of the Arrhenius equation is it is useful in determination of rate of chemical reaction and for the calculation of energy of activation.
The Arrhenius equation gives the dependence of the rate constant of a chemical reaction on the absolute temperature and the equation is given by the following formula:
$K=A{{e}^{-{{E}_{a}}/RT}}$
Where K = Rate constant
A = Constant of chemical reaction
T = Absolute temperature
${{E}_{a}}$= Activation energy of the reaction
R = Universal gas constant
In the given question the value of rate constant i.e. K at $T\to \infty $,
$RT\to \infty $
$\dfrac{-{{E}_{A}}}{RT}\to 0$
${{e}^{-{{E}_{a}}/RT}}\to 1$
Hence $K\to A$because $T\to \infty $
Therefore we can conclude that the value of K as $T\to \infty $= $6.0\times {{10}^{14}}{{s}^{-1}}$.

Hence option B is the correct answer.

Note:
Arrhenius activation energy fails to tell about threshold energies and about the success of individual collisions at the molecular level and also not give any information in the case of heterogeneous catalysis.