Question

At $100K$, a reaction is $30\% $ complete in 10 minutes, while at $200K$, $30\% $ is complete in 5 minutes. The activation energy of the reaction is:
A. $2050$J
B. $4000$J
C. $3000$J
D. $1150$J

Answer 1

Hint: For solving the activation energy for the forward reaction is the amount of free energy that must be added to go from the energy level of the reactants to the energy level of the transition state. When a reactant molecule absorbs enough energy to reach the transition state, it can proceed through the remainder of the reaction.

Complete step by step answer:
From the Arrhenius equation we know that the rate constant of a reaction is a function of the temperature. It is related to temperature by the Arrhenius equation.
$k = A{e^{\dfrac{ - {E_a}}{RT}}}$
Here, K is said to be the rate constant.
A is the frequency factor or pre-exponential factor or Arrhenius constant.
$E_a$ is the activation energy of the reaction which is expressed in Joule per mole.
R is the gas constant (8.314J/mol/K)
So, according to Arrhenius equation,
${\log _{10}}\left( {\dfrac{{{k_2}}}{{{k_1}}}} \right) = \dfrac{{{E_a}}}{{2.303R}} \times \left( {\dfrac{1}{{{T_1}}} - \dfrac{1}{{{T_2}}}} \right)$
Substituting the known values we get,
$ \Rightarrow \log 2 = \dfrac{{{E_a}}}{{2.303R \times 8.314}} \times \left( {\dfrac{1}{{100}} - \dfrac{1}{{200}}} \right)$
On simplifying we get,
${E_a} = 1150J$
So, the activation energy of the reaction is $ We need to understand the role of activation energy that all chemical reactions, including exothermic reactions, need activation energy to get started. Activation energy is needed for the reactants to move together with the help of which it overcomes forces of repulsion that starts breaking bonds.

So, the correct answer is Option D.

Note: In a chemical reaction, we can define the transition state as the highest energy state of the system. When the molecules in the reactants side collide with enough kinetic energy and this energy is higher than the transition state energy, then the reaction occurs and the products are formed.