Question

Activation energy of a reaction is \[{\text{100 kJ/mol}}\]. By using a catalyst Ea​ decreases by \[75\% \] What will be the effect on the rate of reaction at \[{20^o}C\]?
Consider all other things as equal.
A.Increases by $1.12 \times {10^{18}}$
B.Increases by $3.22 \times {10^{16}}$
C.Increases by $4.21 \times {10^8}$
D.Increases by $2.34 \times {10^{13}}$

Answer 1

Hint: Catalyst is a very usual word that comes up in the topic of chemical reactions. This is where a catalyst comes in. Generally, a catalyst speeds up and increases the reaction rate. Catalysts break or rebuild the chemical bonds between the atoms which are present in the molecules of different elements or compounds.
The formula used:
\[2.303{\text{log}}\left( {\dfrac{{{{\text{k}}_{\text{1}}}}}{{{{\text{k}}_{\text{2}}}}}} \right) = (75/RT)\;\]where \[\dfrac{{{{\text{k}}_{\text{1}}}}}{{{{\text{k}}_{\text{2}}}}}\]is the ratio of rate constants

Complete step by step answer:
Catalysts make the whole reaction process easier and efficient. Key points of a catalyst are that it does not initiate a chemical reaction. It cannot be consumed in the reaction. It forms intermediates with reactants and at the same time facilitates the production of the final reaction product. We can find the ratio of rate constants as:
\[\dfrac{{{{\text{k}}_{\text{1}}}}}{{{{\text{k}}_{\text{2}}}}} = \dfrac{{{{\text{e}}^{ - 100/RT}}}}{{{{\text{e}}^{ - 25/RT}}}} = {{\text{e}}^{ - 75/RT}}\].
Further solving:
\[2.303{\text{log}}\left( {\dfrac{{{{\text{k}}_{\text{1}}}}}{{{{\text{k}}_{\text{2}}}}}} \right) = \dfrac{{75}}{{8.314 \times {{10}^{ - 3}}}} \times 298\;\].
The value we will get is:
\[\dfrac{{{{\text{k}}_{\text{1}}}}}{{{{\text{k}}_{\text{2}}}}} = 2.35 \times {10^{13}}\;\].
This will be the ratio of rates of the reaction
\[\dfrac{{{{\text{r}}_{\text{2}}}}}{{{{\text{r}}_{\text{1}}}}} = \dfrac{{{{\text{k}}_{\text{2}}}}}{{{{\text{k}}_{\text{1}}}}} = 2.35 \times {10^{13}}\].
Thus the rate of reaction will become \[2.35 \times {10^{13}}\]of the initial reaction rate.

Hence, the correct answer for this question option D.

Note:
There are four types of catalysts:
Positive Catalysts: Catalysts which increase the rate of a chemical reaction are positive catalysts. It increases the rate of reaction by lowering the activation energy barriers such that a large number of reaction molecules are converted into products, thereby the percentage of yield of products increases.
Negative Catalysts: Catalysts which decrease the rate of reaction and negative catalyst.
Promoter or Accelerators: A substance which increases the catalyst activity are known as Promoters or accelerators.
Catalyst Poisons or Inhibitors: Substances which decrease the catalyst activity are known as catalyst poisons or inhibitors.