When the volume of the solution is doubled, the following becomes exactly half

Options

A. Molality
B. Mole - fraction
C. Molarity
D. Weight - percent

Explanation

To solve the problem, we need to analyze how different concentration terms change when the volume of a solution is doubled. We will evaluate each option one by one.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine which concentration term becomes half when the volume of the solution is doubled.

2. **Checking Molality**:
- **Formula**: Molality (m) is defined as the number of moles of solute (n) divided by the mass of the solvent (in kg).
- **Mathematical Expression**: \( m = \frac{n}{\text{mass of solvent (kg)}} \)
- **Analysis**: Since molality depends only on the amount of solute and the mass of the solvent, it is independent of the volume of the solution. Therefore, if the volume is doubled, molality remains unchanged.
- **Conclusion**: Molality does not become half.

3. **Checking Mole Fraction**:
- **Formula**: The mole fraction of a component is the number of moles of that component divided by the total number of moles in the solution.
- **Mathematical Expression**: \( x_A = \frac{n_A}{n_A + n_B} \)
- **Analysis**: Mole fraction is also independent of the volume of the solution as it depends on the number of moles of solute and solvent. Doubling the volume does not affect the mole fraction.
- **Conclusion**: Mole fraction does not become half.

4. **Checking Weight Percentage**:
- **Formula**: Weight percentage is calculated as the weight of the solute divided by the total weight of the solution, multiplied by 100.
- **Mathematical Expression**: \( \text{Weight \%} = \frac{W_A}{W_A + W_B} \times 100 \)
- **Analysis**: Similar to molality and mole fraction, weight percentage depends on the mass of solute and solvent, not on the volume of the solution. Thus, doubling the volume does not change the weight percentage.
- **Conclusion**: Weight percentage does not become half.

5. **Checking Molarity**:
- **Formula**: Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters.
- **Mathematical Expression**: \( M = \frac{n}{V} \)
- **Analysis**: Molarity is directly dependent on the volume of the solution. If the volume is doubled (i.e., \( V_2 = 2V_1 \)), then:
\[ M_2 = \frac{n}{V_2} = \frac{n}{2V_1} = \frac{M_1}{2} \]
- **Conclusion**: Molarity becomes half when the volume is doubled.

6. **Final Answer**:
Based on the analysis, the concentration term that becomes exactly half when the volume of the solution is doubled is **Molarity**. Therefore, the answer is option 3, Molarity.