Read the passage carefully and answer the Questions.

The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.

A reaction is first order in A and second order in B. If the concentration of B is doubled its initial concentration and A is reduced to 3/4th of its initial concentration, the new rate of the reaction is

triples

The correct answer is Option (3) → triples **

Core Concept:

Rate $\propto$ concentration raised to its order.

New rate factor $= (\text{change in A})^1 \times (\text{change in B})^2$

Explanation:

Rate law: $Rate \propto [A]^1 [B]^2$

Initial rate: $r_0 \propto [A][B]^2$

New concentrations:

$[A] \rightarrow \frac{3}{4} [A]$

$[B] \rightarrow 2[B]$

New rate:

$r \propto (\frac{3}{4} [A]) (2[B])^2$

$r \propto (\frac{3}{4}) [A] \times 4[B]^2$

$r \propto 3 [A][B]^2$

$r = 3r_0$

Hence, the rate becomes three times the original rate.

Hence, option (3) - Triples is the answer