If x is amount of adsorbate and m is amount of adsorbent which of the following relations is not related to adsorption process ?

Options

A. `(x)/(m) = pxxT`
B. x/m = f(P) at constant T
C. x/m = f(T) at constant P
D. p = f(T) at constant (x/m)

Answer

To determine which relation is not related to the adsorption process, let's analyze the given relations step by step.

### Step 1: Understanding Adsorption
Adsorption is the process where particles (adsorbate) accumulate on the surface of a solid (adsorbent). The amount of adsorbate is denoted by \( x \) and the amount of adsorbent is denoted by \( m \).

### Step 2: Degree of Adsorption
The degree of adsorption or extent of adsorption is given by the ratio \( \frac{x}{m} \). This ratio indicates how much adsorbate is present per unit mass of adsorbent.

### Step 3: Freundlich Isotherm
According to the Freundlich Isotherm, the relation can be expressed as:
\[ \frac{x}{m} \propto P^{\frac{1}{n}} \]
This indicates that the extent of adsorption (\( \frac{x}{m} \)) is proportional to the pressure (\( P \)) raised to the power of \( \frac{1}{n} \) at constant temperature.

### Step 4: Adsorption Isobar
At constant pressure, the extent of adsorption can be expressed as a function of temperature:
\[ \frac{x}{m} = f(T) \]
This indicates that the amount of adsorbate per unit mass of adsorbent changes with temperature at constant pressure.

### Step 5: Pressure-Temperature Relation
The relation that pressure is a function of temperature at constant \( \frac{x}{m} \) can be derived from the ideal gas law:
\[ PV = nRT \]
This implies that if the amount of gas is constant, pressure will change with temperature.

### Conclusion
The relations discussed above (degree of adsorption, Freundlich Isotherm, and adsorption isobar) are all related to the adsorption process. However, if we consider a relation that does not directly pertain to adsorption, it could be any relation that does not involve \( x \) or \( m \) or does not describe the adsorption phenomenon.

### Final Answer
The relation that is not related to the adsorption process is one that does not involve \( \frac{x}{m} \), \( P \), or \( T \) in the context of adsorption.