Adsorption isostere are

Options

A. Plot at constant pressure. Between `(x)/(m)` and temperature.
B. Plot at constant volume , between `(x)/(m)` and pressure.
C. Plot at constant `(x)/(m)` between pressure and temperature
D. A special type of adsorption isotherm

Answer

### Step-by-Step Text Solution:

**Step 1: Definition of Adsorption Isostere**
- Adsorption isostere refers to a specific type of plot that represents the relationship between temperature and pressure at a constant extent of adsorption (denoted as \( \frac{x}{m} \)). Here, \( x \) represents the amount of adsorbate, and \( m \) represents the mass of the adsorbent.

**Step 2: Understanding the Variables**
- In the context of adsorption isostere:
- \( \frac{x}{m} \) is the extent of adsorption, indicating how much of the adsorbate has been adsorbed onto the surface of the adsorbent.
- The plot typically shows how changes in temperature and pressure affect the extent of adsorption.

**Step 3: Relationship Between Temperature, Pressure, and Adsorption**
- As temperature increases, the kinetic energy of the molecules also increases, which can lead to a decrease in the rate of adsorption. This is because higher energy allows more molecules to escape from the surface of the adsorbent.

**Step 4: Maintaining Constant Adsorption Rate**
- To maintain a constant rate of adsorption despite the increase in temperature, the pressure must also be increased. This is because higher pressure can help to push more adsorbate molecules onto the adsorbent surface, compensating for the increased energy that allows molecules to escape.

**Step 5: Graphical Representation**
- The adsorption isostere can be represented graphically, where one axis represents temperature and the other represents pressure, with curves indicating constant \( \frac{x}{m} \) values. Each curve corresponds to a different level of adsorption under varying conditions.

**Step 6: Industrial Applications**
- Understanding adsorption isostere is crucial in various industrial applications, such as in the design of adsorption systems for purification processes, catalysis, and environmental remediation.