Select the dimensionless quantity (ies) :

Options

A. vapour density
B. molality
C. specific gravity
D. mass fraction

Answer

To solve the question of selecting dimensionless quantities, we will analyze each of the given options step by step.

### Step-by-Step Solution:

1. **Understanding Dimensionless Quantities**:
- A dimensionless quantity is a ratio of two quantities that have the same dimension, resulting in the cancellation of units.

2. **Analyzing Vapor Density**:
- **Definition**: Vapor density is defined as the ratio of the density of a substance to the density of a reference substance (usually air).
- **Formula**: Vapor Density = Density of substance / Density of reference substance.
- **Units**: Since both densities are measured in the same units (e.g., g/cm³), the units cancel out.
- **Conclusion**: Vapor density is a dimensionless quantity.

3. **Analyzing Morality**:
- **Definition**: Morality (or molarity) is defined as the number of moles of solute per unit mass of solution.
- **Formula**: Morality = (Number of moles of solute) / (Mass of solution in kg).
- **Units**: The units are moles/kg, which means it has dimensions.
- **Conclusion**: Morality is not a dimensionless quantity.

4. **Analyzing Specific Gravity**:
- **Definition**: Specific gravity is the ratio of the density of a substance to the density of water.
- **Formula**: Specific Gravity = Density of substance / Density of water.
- **Units**: Similar to vapor density, both densities have the same units, which cancel out.
- **Conclusion**: Specific gravity is a dimensionless quantity.

5. **Analyzing Mass Fraction**:
- **Definition**: Mass fraction is the ratio of the mass of a component (solute) to the total mass of the solution.
- **Formula**: Mass Fraction = (Mass of solute) / (Total mass of solution).
- **Units**: Both masses are measured in the same units (e.g., grams), which cancel out.
- **Conclusion**: Mass fraction is a dimensionless quantity.

### Final Conclusion:
The dimensionless quantities among the options provided are:
- Vapor Density
- Specific Gravity
- Mass Fraction