Question

For a first order reaction rate constant is $1\times {{10}^{-5}}{{\sec }^{-1}}$ having ${{E}_{a}}=1800kj/mol$ . Then the value of $lnA$ at $T= 600K$ is:
A. 151.7
B. 349.3
C. 24.7
D. 11.34

Answer 1

Hint: Rate is defined as the speed at which a chemical reaction occurs. Rate is generally expressed in the terms of concentration of reactant which is consumed during the reaction in a unit of time or the concentration of product which is produced during the reaction in a unit of time.

Complete step by step solution:
Activation energy can be calculated using various methods. It can be calculated using the Arrhenius equation and also when then two temperatures and the rate constant at both temperatures are known. The temperature should be converted to kelvin while calculating activation energy using the Arrhenius equation.
Given in the question:
The rate constant for first order reaction= $1\times {{10}^{-5}}{{\sec }^{-1}}$
The value of activation energy = ${{E}_{a}}=1800kj/mol$
Temperature = 600k
Now, according to Arrhenius equation:
\[k=A{{e}^{-{{E}_{a}}/RT}}\]
We can also write it as:
\[\log K=\log A-\dfrac{{{E}_{a}}}{RT}\]
Putting all the given value in the above equation we get:
\[\begin{align}
& \log A=\log (1\times {{10}^{-5}})+\dfrac{1800}{1\times {{10}^{-5}}\times 600} \\
& =151.7 \\
\end{align}\]

Hence the correct answer is option (A) i.e. For a first order reaction rate constant is $1\times {{10}^{-5}}{{\sec }^{-1}}$ having ${{E}_{a}}=1800kj/mol$ . Then the value of $lnA$ at $T= 600K$ is $151.7$.

Note: If the reaction is a first order reaction, the unit for first order reaction is${{\sec }^{-1}}$ . The negative and positive sign in the expression of the rate or reaction only means the change in concentration. A negative charge indicates that the concentration of the reactant is decreasing, similarly a positive charge means that the concentration of product is increasing