Two bottles `A` and `B` contain `1`M and `1` m aqueous solution of sulphuric acid respectively

Options

A. `A` is more concentrated than `B`
B. `B` is more concentrated than `A`
C. Concentration of `A=` Concentration of `B`
D. It is not possible to compare the concentration

Explanation

To solve the problem of comparing the concentrations of 1M (molar) and 1m (molal) aqueous solutions of sulfuric acid, we will follow these steps:

### Step 1: Understand the Definitions
- **Molarity (M)**: It is defined as the number of moles of solute per liter of solution. The unit is moles per liter (mol/L).
- **Molality (m)**: It is defined as the number of moles of solute per kilogram of solvent. The unit is moles per kilogram (mol/kg).

### Step 2: Calculate the Molarity of the 1m Solution
1. **Given**: 1 molal solution of sulfuric acid (H₂SO₄) means there is 1 mole of H₂SO₄ in 1 kg of water (solvent).
2. **Mass of water (solvent)**: 1 kg = 1000 g.
3. **Mass of 1 mole of H₂SO₄**: The molar mass of H₂SO₄ is approximately 98 g/mol.
4. **Total mass of the solution**:
- Mass of solute (H₂SO₄) = 98 g.
- Mass of solvent (water) = 1000 g.
- Total mass of solution = 98 g + 1000 g = 1098 g.

### Step 3: Calculate the Volume of the Solution
- Since the density of the solution is approximately 1 g/mL (for dilute solutions), the volume of the solution can be calculated as:
\[ \text{Volume of solution} = \frac{\text{mass of solution}}{\text{density}} = \frac{1098 \text{ g}}{1 \text{ g/mL}} = 1098 \text{ mL} = 1.098 \text{ L} \]

### Step 4: Calculate the Molarity of the 1m Solution
- Using the definition of molarity:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in L}} = \frac{1 \text{ mol}}{1.098 \text{ L}} \approx 0.910 \text{ M} \]

### Step 5: Compare Molarity and Molality
- **Molarity of solution A**: 1 M (given).
- **Molarity of solution B (1m solution)**: Approximately 0.910 M (calculated).
- Since 1 M > 0.910 M, we conclude that the 1 M solution (solution A) is more concentrated than the 1 m solution (solution B).

### Conclusion
The correct statement is that solution A (1 M) is more concentrated than solution B (1 m).