Adsorption of a gas follows Freundlich adsorption isotherm. If x is the mass of the gas adsorbed on

Q: Why does the curve flatten out at high pressures instead of going up forever?

At high pressures, the surface of the solid adsorbent becomes completely covered with a unimolecular layer of gas molecules. Once all the 'parking spots' are taken, increasing the pressure further cannot force more gas to be adsorbed. The adsorption becomes independent of pressure.

Q: Why is physical adsorption always considered an exothermic process?

When a gas is adsorbed on a solid surface, its molecules lose their freedom of movement, leading to a decrease in entropy ($\Delta S < 0$). For the process to happen spontaneously ($\Delta G < 0$), the enthalpy change ($\Delta H$) must be negative to compensate. This means heat must be released.

Q: Does the Freundlich isotherm work perfectly at all pressure ranges?

No, the Freundlich isotherm is an empirical formula. It works very well at low and moderate pressures but fails to accurately describe adsorption at very high pressures where the curve becomes completely flat (saturation pressure).

Q: What exactly does the constant $1/n$ represent in the equation?

The constant $1/n$ represents the intensity of adsorption or how strongly the adsorption depends on pressure. Its value generally lies between 0 and 1. When $1/n = 0$, adsorption is independent of pressure. When $1/n = 1$, adsorption varies linearly with pressure.

Q: Why are the straight-line graphs in the options incorrect?

The Freundlich equation $\frac{x}{m} = k p^{1/n}$ (where $n>1$) mathematically represents a curve, not a straight line, when plotted directly as $\frac{x}{m}$ versus $p$. You would only get a straight line if you plotted $\log(\frac{x}{m})$ versus $\log p$.

Question

Adsorption of a gas follows Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent, the correct plot of $\frac{x}{m}$ versus $p$ is

Sigma Percentile · Accepted Answer

### The Freundlich Adsorption Isotherm

Welcome to the fascinating world of Surface Chemistry! When a gas comes into contact with a solid surface, the gas molecules tend to accumulate on the surface. This phenomenon is known as **adsorption**. To quantify this, we use the Freundlich adsorption isotherm, which provides an empirical relationship between the quantity of gas adsorbed by a unit mass of solid adsorbent and pressure at a particular temperature.

The mathematical expression for the Freundlich isotherm is:

$$ \frac{x}{m} = k \cdot p^{1/n} $$

Here, $x$ is the mass of the gas adsorbed, $m$ is the mass of the adsorbent, $p$ is the pressure, and $k$ and $n$ are constants that depend on the nature of the adsorbent and the gas at a given temperature.

### Analyzing the Shape of the Curve

If we plot $\frac{x}{m}$ against pressure $p$, we don't get a simple straight line. The behavior changes depending on the pressure range:

1. **At low pressures:** The value of $\frac{1}{n}$ is approximately $1$. The equation becomes $\frac{x}{m} \propto p^1$. This means adsorption increases linearly with pressure, which corresponds to the initial steep part of the curve.
2. **At high pressures:** The surface of the adsorbent becomes completely covered with a unimolecular layer of gas. Further increase in pressure does not increase adsorption. Here, $\frac{1}{n} \approx 0$, making $\frac{x}{m} \propto p^0$. The curve flattens out and becomes parallel to the pressure axis.

Because the graph must be a curve that eventually flattens, we can immediately eliminate any options that show straight lines.

### The Role of Temperature

Now, let's introduce temperature into the mix. What happens to the extent of adsorption when we heat the system?

To answer this, we must look at the thermodynamics of the process. When gas molecules (which are moving freely and randomly) get adsorbed onto a solid surface, their freedom of movement is restricted. This decrease in randomness means the entropy change ($\Delta S$) is negative. For the adsorption process to be spontaneous, the Gibbs free energy change ($\Delta G = \Delta H - T\Delta S$) must be negative. This is only possible if the enthalpy change ($\Delta H$) is highly negative.

Therefore, **physical adsorption is an exothermic process**:

$$ 	ext{Gas} + 	ext{Solid} ightleftharpoons 	ext{Gas adsorbed} + 	ext{Heat} $$

According to **Le Chatelier's Principle**, if we increase the temperature of an exothermic equilibrium system, the system will shift in the reverse direction to absorb the added heat. In our case, the reverse process is desorption.

As we increase the temperature, the adsorbed gas molecules gain kinetic energy, overcome the weak van der Waals forces holding them to the surface, and escape back into the gaseous phase. Consequently, **the extent of adsorption ($\frac{x}{m}$) decreases with an increase in temperature**.

### Final Conclusion

Armed with this knowledge, let's evaluate the curves. For any given pressure, the curve representing the highest temperature must show the lowest amount of adsorption (it should be the bottom-most curve). Conversely, the curve for the lowest temperature will show the highest adsorption (the top-most curve).

Looking at the correct option, we see three curves:
- The top curve is at **$200	ext{ K}$** (Lowest temperature, highest adsorption).
- The middle curve is at **$250	ext{ K}$**.
- The bottom curve is at **$270	ext{ K}$** (Highest temperature, lowest adsorption).

This perfectly aligns with the principles of thermodynamics and Le Chatelier's principle, making it the correct graphical representation of the Freundlich adsorption isotherm at varying temperatures.

Animated Solution for Chemistry - Surface Chemistry: Adsorption of a gas follows Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent, the correct plot of $\frac{x}{m}$ versus $p$ is

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Visualized Solution

\text{Freundlich Adsorption Isotherm}

\text{Dependence on Pressure}

\text{Effect of Temperature}

\text{Le Chatelier's Principle}

\text{Conclusion}

The Sigma Insight: Adsorption

The Freundlich Adsorption Isotherm

Analyzing the Shape of the Curve

The Role of Temperature

Final Conclusion

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