Question

The activation energy for a reaction is $ 9.0kcal{(mol)^{ - 1}} $ . The increase in the rate constant when its temperature is increased from 298 K to 308 K is
A. 63%
B. 50%
C. 100%
D.10%

Answer 1

Hint :The minimal amount of extra energy needed by a reacting molecule to transform into substance is known as activation energy. It's also known as the smallest amount of energy used to activate or energise molecules or atoms in order for them to undergo a chemical reaction or transformation.

Complete Step By Step Answer:
We have the Arrhenius equation,
 $ \log \dfrac{{{k_1}}}{{{k_2}}} = \dfrac{{{E^a}}}{{2.303R}}(\dfrac{{{T_2} - {T_1}}}{{{T_1}{T_2}}}) $
Where,
 $ {k_1} $ and $ {k_2} $ are rate constants,
 $ {E^a} $ is the activation energy ,
R the universal gas constant and
T the absolute temperatures in two stages
Substituting the values to the equation we get,
 $ = \dfrac{{9 \times {{10}^3}}}{{2.0303 \times 2}}(\dfrac{{308 - 298}}{{308 \times 298}}) $
 $ = 0.2129 $
Therefore,
We can find $ \dfrac{{{k_1}}}{{{k_2}}} $ by taking antilog
That is,
 $ \dfrac{{{k_1}}}{{{k_2}}} = anti\log (0.2129) $
 $ = 1.632 $
Therefore,
 $ {k_2} = 1.632{k_1} $
So, we can find the increase in rate constant by,
 $ {k_2} - {k_1} = 1.632{k_1} - {k_1} $
 $ = 0.632{k_1} $
 $ = \dfrac{{0.632{k_1}}}{{{k_1}}} \times 100 $
 $ = 63.2 $
Hence, the increase in the rate constant when its temperature is increased from 298 K to 308 K is option A, $ 63\% $ .

Note :
Remember the Arrhenius equation, $ \log \dfrac{{{k_1}}}{{{k_2}}} = \dfrac{{{E^a}}}{{2.303R}}(\dfrac{{{T_2} - {T_1}}}{{{T_1}{T_2}}}) $ ,
The amount of energy required for activation is determined by two factors.
1. Nature of Reactants
Since there is an attraction between reacting species, the value of ( $ {E_a} $ ) would be low in the case of an ionic reactant. The value of $ {E_a} $ would be high in the case of a covalent reactant since energy is needed to crack the older bonds.
2. Catalyst Effect
The positive catalyst creates an alternate path where the value of $ {E_a} $ is minimal, while the negative catalyst creates an alternate path where the value of $ {E_a} $ is high.