Derivation of General Formula

Starting from rate = k[A]^n:

$\frac{\text{mol}}{\text{L} \cdot \text{s}} = k \times \left(\frac{\text{mol}}{\text{L}}\right)^n$

Solving for k:

$k = \frac{\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1}}{(\text{mol} \cdot \text{L}^{-1})^n} = \frac{\text{mol}^1 \cdot \text{L}^{-1} \cdot \text{s}^{-1}}{\text{mol}^n \cdot \text{L}^{-n}}$

$\boxed{k = \text{mol}^{1-n} \cdot \text{L}^{n-1} \cdot \text{s}^{-1} = \left(\frac{\text{mol}}{\text{L}}\right)^{1-n} \cdot \text{s}^{-1}}$

Applying the Formula

NEET Trap: Fractional Individual Orders

For rate = k[A]^(1/2)[B]^(3/2):

• Do NOT use 1/2 or 3/2 individually in the unit formula
• Overall order = 1/2 + 3/2 = 2
• Units = L $mol^{-1}$ $s^{-1}$ (standard second-order units)

Alternative Unit Forms

L $mol^{-1}$ $s^{-1}$ = d$m^{3}$ $mol^{-1}$ $s^{-1}$ = $M^{-1}$ $s^{-1}$ (all equivalent for second order)