For a strong electrolyte, a plot of molar conductivity against (concentration)$$^{1/2}$$ is a straight line, with a negative slope, the correct unit for the slope is:

Find the unit of the slope in the Debye-Huckel-Onsager equation plot.

$$\Lambda_m = \Lambda_m^0 - A\sqrt{c}$$

where $$\Lambda_m$$ is molar conductivity, $$\Lambda_m^0$$ is limiting molar conductivity, $$A$$ is the slope, and $$c$$ is concentration.

The plot is $$\Lambda_m$$ (y-axis) vs $$\sqrt{c}$$ (x-axis).

$$[\Lambda_m] = \text{S cm}^2 \text{ mol}^{-1}$$ and $$[\sqrt{c}] = (\text{mol L}^{-1})^{1/2} = \text{mol}^{1/2} \text{ L}^{-1/2}$$.

$$[A] = \frac{[\Lambda_m]}{[\sqrt{c}]} = \frac{\text{S cm}^2 \text{ mol}^{-1}}{\text{mol}^{1/2} \text{ L}^{-1/2}} = \text{S cm}^2 \text{ mol}^{-1} \cdot \text{mol}^{-1/2} \cdot \text{L}^{1/2}$$

$$= \text{S cm}^2 \text{ mol}^{-3/2} \text{ L}^{1/2}$$

The correct answer is Option (2): S cm$$^2$$ mol$$^{-3/2}$$ L$$^{1/2}$$.