Explanation:

Adsorption is the process of attracting and binding molecules or particles of one substance onto the surface of another substance. The amount of adsorbate (F x) adsorbed by adsorbent (m) can be quantified using various relations, depending on the conditions of the process. However, one of the given relations is not related to the adsorption process. Let's analyze each option to understand why.

(a) x/m = f (p) at constant T: This relation is known as the adsorption isotherm, which describes the amount of adsorbate adsorbed by the adsorbent at different pressures (p) and constant temperature (T). It shows the extent of adsorption and helps to understand the adsorption mechanism and surface properties of the adsorbent.

(b) x/m = f (T) at constant p: This relation is known as the temperature adsorption isotherm, which describes the amount of adsorbate adsorbed by the adsorbent at different temperatures (T) and constant pressure (p). It helps to determine the thermodynamic parameters of adsorption, such as the heat of adsorption, entropy, and Gibbs free energy.

(c) p = f (T) at constant (x/m) continuously: This relation is known as the adsorption isobar, which describes the pressure required to adsorb a certain amount of adsorbate (x/m) by the adsorbent at different temperatures (T). It helps to determine the adsorption capacity and selectivity of the adsorbent.

(d) x/m = p×T: This relation is not related to the adsorption process but rather to the ideal gas law, which describes the behavior of gases under different conditions of temperature, pressure, and volume. It relates the amount of adsorbate (x/m) to the product of pressure (p) and temperature (T), which is not relevant to adsorption.

Therefore, the correct answer is (d) x/m = p×T, which is not related to the adsorption process.

Conclusion:

In summary, adsorption is an important process in various fields, such as chemistry, physics, engineering, and environmental science. The amount of adsorbate adsorbed by the adsorbent can be quantified using different relations, depending on the conditions of the process. It is crucial to understand the principles and applications of adsorption for designing efficient adsorbents and processes.