# The rate of a gaseous reaction is equal to k[A][B]. The volume of the reaction vessel containing these gases is reduced by one-fourth of the initial volume. The rate of the reaction would be:

(A) 1/16

(B) 16/1

(C) 1/8

(D) 8/1

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**Hint:**Rate law is given by r = k[A][B]. Concentration is inversely proportional to volume. Equate between initial rate law and final rate law to reach the answer. It increases/decreases by the factor of 4.

**Formula used:**r = k[A][B]

**Complete step by step answer:**

We know that the rate law is given by

Rate(r) = k[A][B] (i)

Where A and B are reactants.

When volume is reduced by one fourth, then the concentration becomes 4 times. It is explained by the fact that concentration = number of moles/volume .And hence, concentration is inversely proportional to volume.

So, when volume is reduced by one fourth, then the concentration becomes 4 times.

Hence,${ r'\ =\ k[4A][4B]\\ \ \ =\ 16k[A][B]\\ \ \ =\ 16\ r } $ (r’ is the new rate)

(ii)

By dividing (i) and (ii), we will get:

$r’ = 16 r$

ie. rate of the reaction will become 16 times of the initial reaction rate.

**Therefore, option (B) 16/1 is the correct answer..**

**Additional Information:**

Chemical kinetics is the branch of chemistry that deals with rate (speed/velocity) of a chemical reaction, factors influencing rate and mechanism.

Rate law is a mathematical equation that will give the actual rate of a chemical reaction in terms of concentration of reactants, raised to some powers, which may or may not be equal to the stoichiometric coefficients.Rate law is determined experimentally.

Factors affecting rate of reaction are:

(i) concentration

(ii) temperature

(iii) pressure

(iv) catalyst

(v) Surface area of reactant

(vi) Light in photochemical reactions.

Order of a reaction is the sum of powers of concentration terms in the rate law of a reaction. Order can be zero, integers or even fractional values.

**Note:**It is given in the question that the volume of the reaction vessel is reduced to half. If the volume of the reaction vessel is reduced to one-fourth, the volume of all the reactants is getting reduced to one fourth.