Question

The rate of reaction increases to $ 2.3 $ times when the temperature is raised from $ 300{\text{K}} $ to $ 310{\text{K}} $ . If $ {\text{K}} $ is the rate constant at $ 300{\text{K}} $ , then the rate constant at $ 310{\text{K}} $ will be equal to:
(A) $ 2{\text{K}} $
(B) $ {\text{K}} $
(C) $ 2.3{\text{K}} $
(D) $ {\text{3}}{{\text{K}}^2} $

Answer 1

Hint: To answer this question, you must recall the rate law and its formula. We must find the relation with which the rate constant for a given reaction changes with change in the temperature. We shall analyse the equation below and find the relation between rate of reaction and rate constant.

Formula used: For a reaction: $ {\text{aA}} + {\text{bB}} \to {\text{cC}} + {\text{dD}} $
The rate law expression can be written as $ {\text{R}} = {\text{k}}{\left[ {\text{A}} \right]^{\text{a}}}{\left[ {\text{B}} \right]^{\text{b}}} $
Where, $ {\text{R}} $ represents the rate of the given reaction
 $ {\text{k}} $ represents the rate constant of the given reaction
 $ \left[ {\text{A}} \right] $ represents the concentration of the reactant A at any given time in the reaction mixture
 $ \left[ {\text{B}} \right] $ represents the concentration of the reactant B at any given time in the reaction mixture
 $ {\text{a}} $ and $ {\text{b}} $ are the stoichiometric coefficients of the reactants A and B in the chemical equation.

Complete step by step solution
We know that the rate of a reaction is the speed at which the reactants in a chemical reaction are converted into the products. There are various types of rate laws, but for solving this question we stick to the general rate law.
The rate constant is the proportionality factor in the rate law equation. It changes when the reaction is subjected to a change in temperature. The rate constant is directly proportional to the change in temperature.
We know that when temperature is increased, the rate of the reaction becomes $ 2.3 $ times. From the formula $ {\text{R}} = {\text{k}}{\left[ {\text{A}} \right]^{\text{a}}}{\left[ {\text{B}} \right]^{\text{b}}} $ , we can see that the only thing that causes the change in rate is the rate constant.
So, at temperature of $ 310{\text{K}} $ , the rate constant is given by $ 2.3{\text{K}} $
The correct answer is C.

Note
The rate law is a relation that gives us a relationship between the speed with which the reaction proceeds and the concentration of the reactants involved. According to it, the rate of the reaction is directly proportional to the product of the concentrations of the reactants raised to the power of their stoichiometric coefficients.