Match List-I with List-II.
| List-I | List-II |
| Order of a chemical reaction | Unit of rate constant |
| (A) -1/2 | (I) mol2 L-2 s-1 |
| (B) 3/2 | (II) s-1 |
| (C) 1 | (III) mol-1/2 L1/2 s-1 |
| (D) -1 | (IV) mol3/2 L-3/2 s-1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
The rate of any reaction has the unit mol L−1 s−1. For a reaction of order n, Rate = k[A]n, so the unit of k depends on n:
\( \displaystyle k=\frac{\text{Rate}}{[A]^n} \)
\( \displaystyle \text{Unit of }k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^n}=(\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \)
(A) -1/2 — This matches (IV) mol3/2 L-3/2 s-1. Here 1 − n = 1 + 1/2 = 3/2.
\( \displaystyle (\mathrm{mol\,L^{-1}})^{3/2}\,\mathrm{s^{-1}}=\mathrm{mol^{3/2}\,L^{-3/2}\,s^{-1}} \)
(B) 3/2 — This matches (III) mol-1/2 L1/2 s-1. Here 1 − n = 1 − 3/2 = −1/2.
\( \displaystyle (\mathrm{mol\,L^{-1}})^{-1/2}\,\mathrm{s^{-1}}=\mathrm{mol^{-1/2}\,L^{1/2}\,s^{-1}} \)
(C) 1 — This matches (II) s-1. Here 1 − n = 0, so the concentration unit cancels.
\( \displaystyle (\mathrm{mol\,L^{-1}})^{0}\,\mathrm{s^{-1}}=\mathrm{s^{-1}} \)
(D) -1 — This matches (I) mol2 L-2 s-1. Here 1 − n = 1 + 1 = 2.
\( \displaystyle (\mathrm{mol\,L^{-1}})^{2}\,\mathrm{s^{-1}}=\mathrm{mol^{2}\,L^{-2}\,s^{-1}} \)
Shortcut: The pair (C)–(II) appears in Options (1) and (2), and (A)–(IV) then leaves only Option (2).