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=pxT`
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 solve the question, we need to analyze the relationships provided in the context of adsorption, specifically physical adsorption. We will evaluate each option to determine which one does not relate to the adsorption process.

### Step-by-Step Solution:

1. **Understanding Adsorption**:
- Adsorption is a surface phenomenon where molecules (adsorbate) adhere to the surface of a solid (adsorbent). The amount of adsorbate (X) per unit mass of adsorbent (M) gives us the extent of adsorption, represented as \( \frac{X}{M} \).

2. **Langmuir Adsorption Isotherm**:
- According to the Langmuir adsorption isotherm, at constant temperature, the relationship can be expressed as:
\[ \frac{X}{M} \propto P^{\frac{1}{n}} \]
- This indicates that \( \frac{X}{M} \) is a function of pressure (P) at constant temperature.

3. **Effect of Temperature**:
- For physical adsorption, \( \frac{X}{M} \) is inversely related to temperature (T). As temperature increases, the extent of adsorption decreases, which can be represented graphically as:
\[ \frac{X}{M} \propto \frac{1}{T} \]

4. **Pressure as a Function of Temperature**:
- For an ideal gas, the relationship between pressure and temperature is given by the ideal gas law \( PV = nRT \). Keeping \( \frac{X}{M} \) constant, we can say that pressure is a function of temperature.

5. **Identifying the Incorrect Relation**:
- The question asks for the relation that is not related to the adsorption process. The options provided include:
- \( \frac{X}{M} = P^x \cdot T \)
- This expression does not correspond to any known adsorption isotherm (like Langmuir or Freundlich) and does not represent a valid relationship in the context of adsorption.

6. **Conclusion**:
- Therefore, the relation that is not related to the adsorption process is:
\[ \frac{X}{M} = P^x \cdot T \]

### Final Answer:
The relation that is not related to the adsorption process is \( \frac{X}{M} = P^x \cdot T \).

---