The units of rate constant of four reactions are given below. Arrange them in the increasing order of reaction.
(A) \( s^{-1} \)
(B) \( mol\, L^{-1}\, s^{-1} \)
(C) \( mol^{1/2}\, L^{-1/2}\, s^{-1} \)
(D) \( L^{1/2}\, mol^{-1/2}\, s^{-1} \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B), (C), (A), (D)
The unit of a rate constant depends on the order of the reaction. For a reaction of order n, Rate \( = k[\mathrm{A}]^{n} \), so
\( \displaystyle k = \frac{\text{Rate}}{[\mathrm{A}]^{n}} = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^{n}} = \mathrm{mol^{1-n}\,L^{n-1}\,s^{-1}} \)
So the power of mol is 1 − n. Reading it from each unit:
(A) \( \mathrm{s^{-1}} \): power of mol = 0, so 1 − n = 0 and n = 1.
(B) \( \mathrm{mol\,L^{-1}\,s^{-1}} \): 1 − n = 1, so n = 0.
(C) \( \mathrm{mol^{1/2}\,L^{-1/2}\,s^{-1}} \): 1 − n = 1/2, so n = 1/2.
(D) \( \mathrm{L^{1/2}\,mol^{-1/2}\,s^{-1}} \): 1 − n = −1/2, so n = 3/2.
In increasing order of reaction:
\( \displaystyle 0\,(\mathrm{B}) \lt 1/2\,(\mathrm{C}) \lt 1\,(\mathrm{A}) \lt 3/2\,(\mathrm{D}) \)
Shortcut: (B) is the zero order unit and (D), with mol in the denominator, has the highest order. Only Option (4) starts with (B) and ends with (D).