Question

For a reaction, ${E_a} = 0$, $K = 4.2 \times {10^5}{\sec ^{ - 1}}$ at $300K$ , the value of $K$ at $310K$ will be:
A.$4.2 \times {10^5}{\sec ^{ - 1}}$
B.$8.4 \times {10^5}{\sec ^{ - 1}}$
C.$8.4 \times {10^{ - 5}}{\sec ^{ - 1}}$
D.$4.2 \times {10^{ - 5}}{\sec ^{ - 1}}$

Answer 1

Hint: Energy of activation is defined as the minimum amount of extra energy that is required by a reacting molecule to get converted into the product. It is denoted by ${E_a}$ . It is measured in terms of joules or kilojoules per mol.

Complete step by step answer:
Arrhenius equation is the expression that shows the relationship between the rate constant, the absolute temperature and the pre exponential factor
Arrhenius equation is given as follows: $k = A{e^{\dfrac{{ - Ea}}{{RT}}}}$
Where, $k = $ rate constant.
$R = $ Universal gas constant.
$T = $ Temperature
${E_a} = $ Activation energy
$A = $ pre exponential factor.
$e = $ base of the natural logarithm.

Given data:
${E_a} = 0$ , $K = 4.2 \times {10^5}{\sec ^{ - 1}}$, $T = 300K$ .
Formula to be used: $k = A{e^{\dfrac{{ - Ea}}{{RT}}}}$ .
$k = A{e^{\dfrac{{ - Ea}}{{RT}}}}$
Substituting the value we get,
Since the energy of activation is equal to zero then the whole term ${e^{\dfrac{{ - Ea}}{{RT}}}}$ will become equal to $1$ .
From this it implies that whatever collision takes place will result in the chemical reaction which is not possible.
Therefore the value of $k$ at temperature $310K$ will be the same as that of value of $k$ at temperature $300K$ which is $K = 4.2 \times {10^5}{\sec ^{ - 1}}$ .
So, the correct answer is option A.

Additional information:
-Energy of activation depends on two factors:
-effect of catalyst
-A positive catalyst (that increases the rate of reaction) makes the energy of activation low whereas a negative catalyst ( which decreases the rate of reaction) increases the energy of activation.
-Nature of reactants.
-In ionic reactant energy of activation will be low whereas in case of covalent reactant the energy of activation will be high.

Note:If the activation energy is expressed in terms of energy per reactant molecule then the universal gas constant that is $R$ must be replaced by the Boltzmann constant ${K_b}$ . The reaction can never have its activation energy as zero.