The temperature at which molarity of pure water is equal to its molality is `:`

Options

A. `273K`
B. `298K`
C. `277K`
D. None

Explanation

To find the temperature at which the molarity of pure water is equal to its molality, we can follow these steps:

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

### Step 2: Determine the Conditions
For pure water:
- The density of water at 4°C (or 277 K) is approximately 1 g/mL. This means that 1 liter of water weighs about 1 kg.

### Step 3: Calculate Molarity and Molality
1. **Calculate the number of moles of water**:
- The molecular weight of water (H₂O) is approximately 18.015 g/mol.
- For 1 liter of water (which weighs approximately 997.07 g), the number of moles can be calculated as:
\[ \text{Number of moles} = \frac{\text{Weight of water}}{\text{Molecular weight}} = \frac{997.07 \text{ g}}{18.015 \text{ g/mol}} \approx 55.348 \text{ moles} \]

2. **Calculate Molarity**:
- Molarity is calculated as:
\[ M = \frac{\text{Number of moles}}{\text{Volume of solution in liters}} = \frac{55.348 \text{ moles}}{1 \text{ L}} = 55.348 \text{ M} \]

3. **Calculate Molality**:
- Since we are considering 1 liter of water, the weight of the solvent (water) is approximately 1 kg (or 0.99707 kg for more accuracy).
- Molality is calculated as:
\[ m = \frac{\text{Number of moles}}{\text{Weight of solvent in kg}} = \frac{55.348 \text{ moles}}{1 \text{ kg}} \approx 55.348 \text{ m} \]

### Step 4: Conclusion
At 4°C (or 277 K), the molarity and molality of pure water are equal, both being approximately 55.348.

### Final Answer
The temperature at which the molarity of pure water is equal to its molality is **4°C** or **277 K**.

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