Question

For a reaction, ${{E}_{a}}=0$ and $k=3.2\times {{10}^{4}}{{s}^{-1}}$ at $300K$. The value of $k$ at $310K$ would be:
A. $k=6.4\times {{10}^{4}}{{s}^{-1}}$
B. $k=3.2\times {{10}^{4}}{{s}^{-1}}$
C. $k=3.2\times {{10}^{8}}{{s}^{-1}}$
D. $k=3.2\times {{10}^{5}}{{s}^{-1}}$

Answer 1

The rate of reaction can be expressed by the Arrhenius equation. The Arrhenius equation is used in the collision theory and is dependent on the temperature for determining the rate of reactions.An increase in Temperature can lead to proceeding the reaction in forward direction, as the molecules obtain energy for collision. But, for collision to occur the orientation of molecules is also important. Collisions do not occur if the orientation is not proper.

Complete step by step answer:
The collision theory of chemical reactions determines the rate of reaction with the help of Arrhenius equation. The Arrhenius equation is dependent on temperature for determining the rate of reaction.
The rate constant for the reaction is expressed as follows:

$k={{Z}_{AB}}{{e}^{\dfrac{-Ea}{RT}}}$
Where, $k$is the reaction constant
${{Z}_{AB}}$is the collision frequency of reactants A and B

${{e}^{\dfrac{-Ea}{RT}}}$is defined as fractions of molecules with energies equal to or greater than ${{E}_{a}}$

${{E}_{a}}$ is the activation energy.
$T$ is the absolute temperature, and
$R$ is the universal gas constant
We are given that the energy of activation i.e., ${{E}_{a}}$ is zero
Means, $k={{Z}_{AB}}{{e}^{0}}$
(anything to the power zero is 1)

Therefore, the fractional term ${{e}^{\dfrac{-Ea}{RT}}}$ becomes one.

This means that the rate of reaction constant becomes independent of the temperature. The rate constant does not change with change in temperature.
At $310K$ the value of rate constant, $k$ $=3.2\times {{10}^{4}}{{s}^{-1}}$

So, the correct answer is Option B.

Note: As we supply heat to a system, the atoms or the molecules of the system gain the minimum energy that is required for the collision, called the threshold energy. Once the threshold energy is achieved the reaction moves in forward direction.The heat supplied to the system is the activation energy.Such collisions are called effective collisions.