Match the LIST-I with LIST-II.
| LIST-I Expression / unit | LIST-II Explanation |
| (A) \( \displaystyle \frac{0.693}{k} \) | (I) Half-life time of zero order reaction |
| (B) mol L−1 s−1 | (II) Units of activation energy |
| (C) \( \displaystyle \frac{[A]_0}{2k} \) | (III) Half-life time of first order reaction |
| (D) J mol−1 | (IV) Unit of rate constant for zero order reaction |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
The half-life (t1/2) is the time in which the reactant concentration falls to half its initial value. It follows from the integrated rate equation of each order, and the units of k follow from the rate law, Rate = k[A]n.
(A) \( \displaystyle \frac{0.693}{k} \) — This matches (III) Half-life time of first order reaction. Putting [R] = [R]0/2 in the first order equation gives a half-life that is independent of the initial concentration:
\( \displaystyle t_{1/2}=\frac{2.303}{k}\log\frac{[R]_0}{[R]_0/2}=\frac{2.303\times0.3010}{k}=\frac{0.693}{k} \)
(B) mol L−1 s−1 — This matches (IV) Unit of rate constant for zero order reaction. For n = 0, Rate = k[A]0 = k, so k has the same unit as the rate:
\( \displaystyle k=\frac{\text{Rate}}{[A]^0}=\mathrm{mol\,L^{-1}\,s^{-1}} \)
(C) \( \displaystyle \frac{[A]_0}{2k} \) — This matches (I) Half-life time of zero order reaction. Putting [R] = [R]0/2 in the zero order equation gives a half-life that is directly proportional to the initial concentration:
\( \displaystyle k=\frac{[R]_0-[R]}{t}\quad\Rightarrow\quad t_{1/2}=\frac{[R]_0-[R]_0/2}{k}=\frac{[R]_0}{2k} \)
(D) J mol−1 — This matches (II) Units of activation energy. Ea is an energy per mole, as in the Arrhenius equation, where Ea/RT must be dimensionless (R in J K−1 mol−1, T in K):
\( \displaystyle k=A\,e^{-E_a/RT} \)
Shortcut: (B)–(IV) and (C)–(I) together appear only in Option (1).