If \(\alpha\) is the amount of gas adsorbed per unit mass of adsorbent, k and n are constants that depend on the nature of adsorbent and adsorbate, Freundlich adsorption isotherm is

The Freundlich isotherm is the empirical power law $x/m = kC^{1/n}$; in the notation of the question, $\alpha = kC^n$ (with a fractional exponent). The form $k = \alpha C^n$ is not an adsorption law, $1/\alpha = kC^n$ gives $\alpha$ decreasing with C, and $\alpha = kC/(1 + nC)$ is the Langmuir-type (saturation) form.