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
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → triples
The order with respect to a reactant is the power of its concentration in the rate law. When a concentration is multiplied by a factor, the rate is multiplied by that factor raised to the order.
First order in A and second order in B gives:
\( \displaystyle r_1 = k[\mathrm{A}][\mathrm{B}]^2 \)
Now \( [\mathrm{A}] \) becomes \( \frac{3}{4}[\mathrm{A}] \) and \( [\mathrm{B}] \) becomes \( 2[\mathrm{B}] \):
\( \displaystyle r_2 = k\left(\frac{3}{4}[\mathrm{A}]\right)(2[\mathrm{B}])^2 \)
\( \displaystyle r_2 = \frac{3}{4} \times 4 \times k[\mathrm{A}][\mathrm{B}]^2 = 3\,r_1 \)
So the new rate is three times the initial rate: the rate triples. Doubling B alone would have made it four times, because B enters the rate law squared.
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27 edition):
Exercises – “A reaction is first order in A and second order in B.
(i) Write the differential rate equation.
(ii) How is the rate affected on increasing the concentration of B three times?
(iii) How is the rate affected when the concentrations of both A and B are doubled?”