# Freundlich Equation's dimensions

So, we have the Freundlich's Isotherm equation as $\frac{x}{m} = kp^{\frac{1}n}$, where the LHS measures the extent of adsorption with the corresponding pressure $p$ in the RHS with the two constants, $k$ and $n > 1$. But, I got a little confused with the dimensions on both the sides. Since $\frac{x}{m}$ is dimensionless, so should be the RHS. Therefore, I reasoned that the constant $k$ having units should cancel out the units of $p^{\frac{1}n}$. But yet I'm confused, and I don't think its right. What is going on?

But, otherwise your intuition is correct and $$k$$ just needs units that will cancel with $$p^{\frac{1}{n}}$$ to give the units on the left hand side. So $$k$$ could have units of $$\left(\dfrac{\text{mg chemical}}{\text{g surface}}\right)\left(\mathrm{bar^{\frac{-1}{n}}}\right)$$.
We could also reformulate Freundlich's equation in terms of concentration (since we are dealing with an isotherm) as: $$q=KC^{\frac{1}{n}}$$ where $$q=m/x$$, $$C$$ is concentration of the chemical and $$K$$ is a new constant with units of $$\left(\dfrac{\text{mg chemical}}{\text{g surface}}\right)\left(\mathrm{{\dfrac{L}{\text{mg chemical}}}}\right)^{\frac{1}{n}}$$.