Q.For the Freundlich adsorption isotherm, a graph of $\log(x/m)$ is plotted against $\log p$. The slope of the line and its y-axis intercept respectively correspond to

An adsorption isotherm is a plot of the amount of adsorbate adsorbed against pressure (or, for solutions, concentration) at CONSTANT temperature. The Freundlich isotherm is the classical empirical equation used to fit this relationship: $\dfrac{x}{m} = kp^{1/n}$, where x is the mass of adsorbate held on mass m of adsorbent at pressure p, and k and n are empirical constants (n always greater than unity, so $1/n$ is a positive fraction). For adsorption from solution, pressure p is simply replaced by concentration c: $x/m = Kc^{1/n}$. The equation predicts that x/m keeps rising with pressure, but with diminishing returns, since raising p to a fractional exponent produces smaller and smaller proportional gains as p grows — and indeed real data show noticeable deviation from the equation at low pressure.

Because the raw equation is not linear, it is normally handled in its logarithmic form: $\log(x/m) = \log k + \dfrac{1}{n}\log p$. Plotting $\log(x/m)$ against $\log p$ gives a straight line whose SLOPE is $1/n$ and whose Y-INTERCEPT is $\log k$ — so both empirical constants can be read directly off a straight-line graph built from a handful of experimental (p, x/m) pairs. The Freundlich isotherm is purely empirical, however: it is valid only over a limited pressure range, its constants k and n are found to vary with temperature, and it offers no theoretical explanation for either the low-pressure deviations or the temperature dependence — these are simply accepted as limitations of an otherwise very useful practical tool for fitting adsorption data.