Question

For the gaseous reaction \[2A + B \to C + D\] , the rate is given by k[A][B]. the volume of the container containing the reaction mixture is suddenly reduced to one-fourth of its original volume with respect to the original rate, now the rate would be:
A. \[\dfrac{1}{{16}}\] times the original rate
B. \[\dfrac{1}{8}\] times the original rate
C.16 times the original rate
D.8 times the original rate

Answer 1

Hint: Rate law is given by \[r = k\left[ A \right]\left[ B \right]\] as provided in the question. We know that concentration is inversely proportional to the volume. So, we can equate between initial rate law and final rate law to obtain the answer which will either increase or decrease by the factor of 4.
Formula used:
 \[r = k\left[ A \right]\left[ B \right]\]

Complete step by step answer:
We already know that the rate law is given by \[r = k\left[ A \right]\left[ B \right]\] , where A and B are reactants. When volume is reduced by one-fourth then we can say that the concentration becomes four times of the original. This is because concentration is inversely proportional to the volume. It can also be explained by the fact that concentration is equal to the number of moles divided by the volume.
So, when volume is reduced by one-fourth, we can write the concentration of A and B in the rate law formula as four times of the original concentration.
 $r' = k[A][B]$
 $r' = k[A][B]$
 $r' = 16r$
  i.e., the rate of the reaction will become 16 times the initial reaction rate of the reaction.

Hence the correct option is (C).

Additional information:
Chemical kinetics is one such branch of chemistry which deals with the rate of a chemical reaction, factors affecting the rate and their mechanism. Rate law is a mathematical equation which will give the actual rate of a chemical reaction in terms of concentration of reactants, raised to some power, which may or may not be equal to their respective stoichiometric coefficients. Factors affecting the rate of reaction are, concentration, temperature, pressure, catalyst, surface area and light in photochemical reactions.

Note:
It is given in the question that the volume of the reaction vessel is reduced to one-fourth which ultimately means that the volume of all the reactants is getting reduced to one-fourth. Order of a reaction is the sum of powers of concentration terms used in the rate law of a reaction. They can be zero, integers or even fractional values.