Animated Solution for Chemistry - Surface Chemistry: According to Freundlich adsorption isotherm which of the following is correct?

Imagine you have a piece of charcoal (the adsorbent) and you expose it to a gas (the adsorbate). As you increase the pressure of the gas, more and more gas molecules stick to the surface of the charcoal. But does this happen infinitely? Does the amount of gas adsorbed keep increasing linearly with pressure forever? This is exactly the question the Freundlich Adsorption Isotherm tries to answer.

To understand this, we plot a graph of the extent of adsorption, denoted by $\frac{x}{m}$ (where $x$ is the mass of the gas adsorbed and $m$ is the mass of the adsorbent), against the pressure $p$.

Freundlich proposed an empirical equation to describe this curve:

Here, $k$ and $n$ are constants that depend on the nature of the adsorbate and adsorbent at a particular temperature. The value of $n$ is generally greater than 1. This single equation beautifully captures the behavior of adsorption across different pressure ranges, but we need to break it down to truly appreciate it.

1. At Low Pressure: When the pressure is very low, there are plenty of empty sites on the surface of the adsorbent. Every new gas molecule easily finds a spot to stick. In this regime, the graph is almost a straight line passing through the origin. Mathematically, this corresponds to $n=1$. Therefore, the extent of adsorption is directly proportional to the pressure:

2. At Moderate Pressure: As the pressure increases, the surface starts getting crowded. It becomes harder for new gas molecules to find an empty spot. The rate at which adsorption increases starts to slow down, and the graph begins to curve. This is the regime where the general Freundlich equation holds true, with $n>1$:

3. At High Pressure: Eventually, if you keep increasing the pressure, the entire surface of the adsorbent gets completely covered with a monolayer of gas molecules. There are simply no more sites left for adsorption. At this point, increasing the pressure further has absolutely no effect on the extent of adsorption. The graph becomes a horizontal line, parallel to the pressure axis. Mathematically, this means the extent of adsorption is independent of pressure:

Looking at the options provided in the question, we can see that $\frac{x}{m}\propto p^0$, $\frac{x}{m}\propto p^1$, and $\frac{x}{m}\propto p^{1/n}$ are all correct descriptions of the adsorption process, but each applies to a different range of pressure.

Therefore, the most accurate and comprehensive answer is that all of the above are correct for different ranges of pressure. It is crucial to remember that the Freundlich isotherm is an empirical model. Its failure to theoretically explain the saturation at high pressures paved the way for the more rigorous Langmuir Adsorption Isotherm.