Predict the total number of intensive properties:
(i) Free energy , (ii) Critical density , (iii) Viscosity , (iv) Specific heat capacity
(v) molar heat capacity , (vi) Kinetic energy , (vii) Specific gravity , (viii) Dielectric constant
(ix) `pH`

Options

A. `9`
B. `8`
C. `7`
D. `6`

Answer

To determine the total number of intensive properties from the given list, we need to understand what intensive properties are. Intensive properties are those that do not depend on the amount of substance present. Let's analyze each property one by one:

1. **Free Energy**:
- Free energy (Gibbs free energy or Helmholtz free energy) is a thermodynamic potential that depends on the state of the system. It is not an intensive property because it depends on the amount of substance.
- **Conclusion**: Not an intensive property.

2. **Critical Density**:
- Critical density is defined as the density of a substance at its critical point. Density is an intensive property because it does not depend on the quantity of the substance.
- **Conclusion**: Intensive property.

3. **Viscosity**:
- Viscosity is a measure of a fluid's resistance to flow. It is considered an intensive property because it does not depend on the amount of fluid present.
- **Conclusion**: Intensive property.

4. **Specific Heat Capacity**:
- Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is an intensive property since it is defined per unit mass.
- **Conclusion**: Intensive property.

5. **Molar Heat Capacity**:
- Molar heat capacity is the heat capacity per mole of a substance. It is not an intensive property because it depends on the amount of substance (moles).
- **Conclusion**: Not an intensive property.

6. **Kinetic Energy**:
- Kinetic energy is given by the formula \( KE = \frac{1}{2} mv^2 \). Since it depends on mass (m), it is not an intensive property.
- **Conclusion**: Not an intensive property.

7. **Specific Gravity**:
- Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). It is an intensive property because it is a ratio and does not depend on the amount of substance.
- **Conclusion**: Intensive property.

8. **Dielectric Constant**:
- The dielectric constant is a measure of a material's ability to store electrical energy in an electric field. It is an intensive property as it does not depend on the amount of material.
- **Conclusion**: Intensive property.

9. **pH**:
- pH is a measure of the acidity or basicity of a solution. It is an intensive property because it does not depend on the volume of the solution.
- **Conclusion**: Intensive property.

Now, let's summarize the intensive properties identified:

- Critical Density (Intensive)
- Viscosity (Intensive)
- Specific Heat Capacity (Intensive)
- Specific Gravity (Intensive)
- Dielectric Constant (Intensive)
- pH (Intensive)

**Total Intensive Properties**: 6

### Final Answer:
The total number of intensive properties is **6**.