How many of the following quantities show increase in their value of increasing temperature?
a. Extent of physisorption of gases on solids.
b. Electrical conductivity of an electrolyte solution.
c. Electrical conductivity of an electrolyte solution.
d. Ionic product of water.
e. Vapour pressure of a pure and liquid.
f. Vapour pressure of an ideal solution which follows Rault's law, (keeping composition same)
g. Solubility of gases in liquids.
h. Reducing power of carbon monoxide for extraction of metals
Correct answer:

Options

A. `5`
B. `4`
C. `6`
D. `3`

Explanation

To determine how many of the given quantities show an increase in their value with increasing temperature, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Extent of physisorption of gases on solids**:
- As temperature increases, the kinetic energy of gas molecules increases, leading to a greater tendency for them to escape from the surface of the solid. Therefore, the extent of physisorption decreases with increasing temperature.
- **Conclusion**: Does not increase.

2. **Electrical conductivity of an electrolyte solution**:
- With an increase in temperature, the degree of dissociation of the electrolyte increases, leading to more ions in solution. The mobility of these ions also increases, resulting in higher electrical conductivity.
- **Conclusion**: Increases.

3. **Electrical conductivity of an electrolyte solution** (duplicate):
- This is the same as the previous point, so the conclusion remains the same.
- **Conclusion**: Increases.

4. **Ionic product of water**:
- The ionic product of water increases with temperature because more water molecules dissociate into H⁺ and OH⁻ ions at higher temperatures.
- **Conclusion**: Increases.

5. **Vapor pressure of a pure liquid**:
- As temperature increases, more liquid molecules gain enough energy to escape into the vapor phase, resulting in an increase in vapor pressure.
- **Conclusion**: Increases.

6. **Vapor pressure of an ideal solution which follows Raoult's law (keeping composition same)**:
- Raoult's law states that the vapor pressure of a solvent in a solution is dependent on the temperature. However, if the composition is kept the same, the vapor pressure does not inherently increase just because of temperature alone; it is dependent on the mole fraction. Thus, it does not show a direct increase in value with temperature.
- **Conclusion**: Does not increase.

7. **Solubility of gases in liquids**:
- Generally, the solubility of gases in liquids decreases with increasing temperature due to decreased gas solubility at higher temperatures.
- **Conclusion**: Does not increase.

8. **Reducing power of carbon monoxide for extraction of metals**:
- The reducing power of carbon monoxide decreases with increasing temperature because higher temperatures favor the oxidation of CO, making it a weaker reducing agent.
- **Conclusion**: Does not increase.

### Summary of Results:
- Increases:
- Electrical conductivity of an electrolyte solution (2 instances)
- Ionic product of water
- Vapor pressure of a pure liquid

- Does not increase:
- Extent of physisorption of gases on solids
- Vapor pressure of an ideal solution (Raoult's law)
- Solubility of gases in liquids
- Reducing power of carbon monoxide

### Total Count of Quantities that Increase:
- Total = 4 (Electrical conductivity (2), Ionic product of water, Vapor pressure of a pure liquid)

### Final Answer:
The correct answer is **4** quantities show an increase in their value with increasing temperature.

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