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Question: For a reaction, \({E_a} = 0\), \(K = 4.2 \times {10^5}{\sec ^{ - 1}}\) at \(300K\) , the value of \(...

For a reaction, Ea=0{E_a} = 0, K=4.2×105sec⁡−1K = 4.2 \times {10^5}{\sec ^{ - 1}} at 300K300K , the value of KK at 310K310K will be:
A.4.2×105sec⁡−14.2 \times {10^5}{\sec ^{ - 1}}
B.8.4×105sec⁡−18.4 \times {10^5}{\sec ^{ - 1}}
C.8.4×10−5sec⁡−18.4 \times {10^{ - 5}}{\sec ^{ - 1}}
D.4.2×10−5sec⁡−14.2 \times {10^{ - 5}}{\sec ^{ - 1}}

Explanation

Solution

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 Ea{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=Ae−EaRTk = A{e^{\dfrac{{ - Ea}}{{RT}}}}
Where, k=k = rate constant.
R=R = Universal gas constant.
T=T = Temperature
Ea={E_a} = Activation energy
A=A = pre exponential factor.
e=e = base of the natural logarithm.

Given data:
Ea=0{E_a} = 0 , K=4.2×105sec⁡−1K = 4.2 \times {10^5}{\sec ^{ - 1}}, T=300KT = 300K .
Formula to be used: k=Ae−EaRTk = A{e^{\dfrac{{ - Ea}}{{RT}}}} .
k=Ae−EaRTk = A{e^{\dfrac{{ - Ea}}{{RT}}}}
Substituting the value we get,
Since the energy of activation is equal to zero then the whole term e−EaRT{e^{\dfrac{{ - Ea}}{{RT}}}} will become equal to 11 .
From this it implies that whatever collision takes place will result in the chemical reaction which is not possible.
Therefore the value of kk at temperature 310K310K will be the same as that of value of kk at temperature 300K300K which is K=4.2×105sec⁡−1K = 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 RR must be replaced by the Boltzmann constant Kb{K_b} . The reaction can never have its activation energy as zero.