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 will analyze each property one by one, identifying whether it is intensive or extensive.

### Step-by-Step Solution:

1. **Free Energy**:
- Free energy is dependent on the amount of substance present. Therefore, it is an **extensive property**.

2. **Critical Density**:
- Density is defined as mass per unit volume. Since both mass and volume are extensive properties, the ratio (density) is an **intensive property**.

3. **Viscosity**:
- Viscosity does not depend on the amount of liquid; it remains the same regardless of the quantity. Thus, viscosity is an **intensive property**.

4. **Specific Heat Capacity**:
- Specific heat capacity is defined as the heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is independent of the amount of substance, making it an **intensive property**.

5. **Molar Heat Capacity**:
- Molar heat capacity is the heat capacity per mole of a substance. It is also independent of the quantity of substance, hence it is an **intensive property**.

6. **Kinetic Energy**:
- Kinetic energy is given by the formula \( KE = \frac{1}{2} mv^2 \), which clearly shows that it depends on mass. Therefore, kinetic energy is an **extensive property**.

7. **Specific Gravity**:
- Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Since it is a ratio of two densities, it is an **intensive property**.

8. **Dielectric Constant**:
- The dielectric constant is a measure of a substance's ability to insulate charges from each other and does not depend on the amount of substance. Thus, it is an **intensive property**.

9. **pH**:
- pH is a measure of the hydrogen ion concentration in a solution and is independent of the amount of solution present. Therefore, pH is an **intensive property**.

### Summary of Properties:
- **Intensive Properties**: Critical Density, Viscosity, Specific Heat Capacity, Molar Heat Capacity, Specific Gravity, Dielectric Constant, pH.
- **Extensive Properties**: Free Energy, Kinetic Energy.

### Total Number of Intensive Properties:
From the analysis, we find that there are **7 intensive properties** out of the 9 listed.