The unit of rate constant of a reaction with the rate law, Rate = k[A…

The correct answer is Option (4) → \(mol^{1/2}\, L^{-1/2}\, s^{-1}\)

The unit of a rate constant follows from the rate law. The rate is in mol L⁻¹ s⁻¹ and each concentration in mol L⁻¹. The order is the sum of the powers, here including a negative power:

    \( \displaystyle n = \frac{3}{2} + (-1) = \frac{1}{2} \)

    \( \displaystyle k = \frac{\text{Rate}}{[\mathrm{A}]^{3/2}[\mathrm{B}]^{-1}} \)

    \( \displaystyle \text{unit of } k = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^{1/2}} = (\mathrm{mol\,L^{-1}})^{1/2}\,\mathrm{s^{-1}} \)

    \( \displaystyle = \mathrm{mol^{1/2}\,L^{-1/2}\,s^{-1}} \)

So the unit is mol^1/2 L^−1/2 s⁻¹.

Shortcut: For order n, the unit of k is \( (\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \); with \( n = 1/2 \) the power is \( +1/2 \).