Match List-I with List-II.
| List-I | List-II |
| (A) Average rate of reaction | (p) Rate = k[A]x[B]y |
| (B) Instantaneous rate of reaction | (q) t1/2 = 0.693/k |
| (C) Half-life of a first-order reaction | (r) −d[R]/dt |
| (D) Rate law | (s) −Δ[R]/Δt |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-s, B-r, C-q, D-p
(A) Average rate of reaction — This matches (s) −Δ[R]/Δt. The average rate is the change in reactant concentration over a finite time interval Δt, with a minus sign because [R] decreases.
(B) Instantaneous rate of reaction — This matches (r) −d[R]/dt. It is the average rate taken over an infinitesimally small interval (Δt → 0), that is, the slope of the tangent to the concentration–time curve.
(C) Half-life of a first-order reaction — This matches (q) t1/2 = 0.693/k. Putting [R] = [R]0/2 in the first-order integrated equation gives t1/2 = 2.303 log 2/k = 0.693/k, independent of the initial concentration.
(D) Rate law — This matches (p) Rate = k[A]x[B]y. A rate law gives the rate in terms of the molar concentrations of the reactants, each raised to a power found by experiment.
NCERT (2026-27 edition):
3.1 Rate of a Chemical Reaction – “… So, to express the rate at a particular moment of time we determine the instantaneous rate. It is obtained when we consider the average rate at the smallest time interval say dt ( i.e. when Δt approaches zero). Hence, mathematically for an infinitesimally small dt instantaneous rate is given by
\( \displaystyle r_{av}=\frac{-\Delta[R]}{\Delta t}=\frac{\Delta[P]}{\Delta t} \qquad (3.3) \)
As Δt → 0 or
\( \displaystyle r_{inst}=\frac{-d[R]}{dt}=\frac{d[P]}{dt} \)”
3.3.3 Half-Life of a Reaction – “The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as t1/2. … For the first order reaction, …
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)”
3.2.2 Rate Expression and Rate Constant – “… Thus, rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.”