The unit of rate constant for -2.5 order reaction is:

The correct answer is Option (2) → \( (\text{mol}\ \text{L}^{-1})^{7/2}\ \text{s}^{-1} \)

The unit of a rate constant follows from the rate law. For a reaction of order n, rate \( = k[\mathrm{A}]^{n} \), so

    \( \displaystyle k = \frac{\text{rate}}{[\mathrm{A}]^{n}} \)

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

This general form gives the familiar units: mol L⁻¹ s⁻¹ for zero order (n = 0), s⁻¹ for first order (n = 1) and mol⁻¹ L s⁻¹ for second order (n = 2). It holds for any value of n, including a negative one.

For n = −2.5:

    \( \displaystyle 1 - n = 1 - (-2.5) = 3.5 = \frac{7}{2} \)

    \( \displaystyle \text{unit of } k = (\mathrm{mol\,L^{-1}})^{7/2}\,\mathrm{s^{-1}} \)

So the unit is (mol L⁻¹)^7/2 s⁻¹.