Question

The reaction \[2A + {B_2}\xrightarrow{{}}2AB\] is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of …………………. (Round off to the Nearest Integer).

Answer 1

Hint: An elementary reaction is a type of chemical reaction in which one or more chemical species immediately react with each other to produce products in a single step with a single transition state, i.e., reactants do not first form any intermediate compounds before reacting directly to produce products. The reaction only requires one step. There is only one transition state in this reaction. No reaction intermediates are needed for or produced during this process.

Complete Step by Step Solution:
The given elementary reaction is as follows:
\[2A + {B_2}\xrightarrow{{}}2AB\]
For the given reaction, the rate of reaction can be written as follows:
\[{\text{Rate of reaction}} = k{\left[ A \right]^2}\left[ {{B_2}} \right]\]
Now, we know that molarity is the number of moles per unit volume.
\[{\text{Concentration}} = \dfrac{{{\text{moles}}}}{{{\text{volume (lit)}}}}\]
By using this, the initial rate of given reaction can be written as follows:
\[{\text{initial rate}} = k{\left( {\dfrac{{{n_A}}}{{{V_0}}}} \right)^2}\left( {\dfrac{{{n_B}}}{{{V_0}}}} \right)\]
Now, the volume of the reaction vessel is reduced by a factor of 3.
\[
  {\text{final rate}} = k{\left( {\dfrac{{{n_A}}}{{\dfrac{{{V_0}}}{3}}}} \right)^2}\left( {\dfrac{{{n_B}}}{{\dfrac{{{V_0}}}{3}}}} \right) \\
   \Rightarrow {\text{final rate}} = 27k{\left( {\dfrac{{{n_A}}}{{{V_0}}}} \right)^2}\left( {\dfrac{{{n_B}}}{{{V_0}}}} \right) \\
   \Rightarrow {\text{final rate}} = 27 \times {\text{initial rate}} \\
 \]
Therefore, the rate of reaction increases by a factor of 27.

Additional Information:
The rate at which a chemical reaction takes place, sometimes referred to as the reaction rate or rate of reaction, is proportional to the rise in product concentration per unit time and the fall in reactant concentration per unit time. The reaction might move at many different speeds.
Examples of reaction rates: In contrast to the rapid combustion of cellulose in a fire, the gradual oxidative rusting of iron under Earth's atmosphere can take several years. Most reactions progress at a slower rate as they go along. Monitoring concentration changes over time allows one to determine the reaction's pace.

Note: The concentration (amount per unit volume) of a substance generated in a unit of time or the concentration (amount per unit volume) of a reactant consumed in a unit of time are two common ways to express the pace of a chemical reaction. It can also be defined in terms of the quantity of reactants used or goods created in a specific period of time.