Question

A first order reaction is $20\% $ complete in $10\min $. Calculate the specific rate constant of the reaction.
A) \[0.0970mi{n^{ - 1}}\]
B) \[0.009mi{n^{ - 1}}\]
C) \[0.0233mi{n^{ - 1}}\]
D) \[2.223mi{n^{ - 1}}\]

Answer 1

Hint: We need to know that a first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants.

Complete answer:
We have to remember that a first-order reaction can be defined as a chemical reaction for which the reaction rate is entirely dependent on the concentration of only one reactant. In such reactions, if the concentration of the first-order reactant is doubled, then the reaction rate is also doubled. For first-order reactions, the rate constant is expressed in s1 (reciprocal seconds). We have to know a reaction that depends on the concentration of only one reactant ( uni molecular reaction). Other reactants can be present, but each will be zero-order.
Let the specific rate of reaction be x:
\[k = \left( {\dfrac{{2.303}}{t}} \right)log{\text{ }}\dfrac{a}{{a - x}}\]
Let the initial concentration be a be $100g$ and $t = 10\min $
So, \[\left( {a - x} \right) = 80g\]
As the reaction is $20\% $ complete
\[k = \left( {\dfrac{{2.303}}{{10}}} \right){\text{ }}log{\text{ }}\dfrac{{80}}{{100}}\]
On simplification we get,
\[k = 0.0233mi{n^{ - 1}}\]

Hence, option (C) is correct.

Note:
We have to remember that the Order of Reaction refers to the power dependence of the rate on the concentration of each reactant. Thus, for a first-order reaction, the rate is dependent on the concentration of a single species. The overall order of reaction is the sum of the individual orders of reaction of the reactants and it measures the sensitivity of the reaction to changes in the concentrations of all the reactants.