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

Options

A. `273K`
B. `298K`
C. `277K`
D. none of these

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 Molarity and Molality
- **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: Consider the Properties of Water
- At 4°C, the density of water is 1 g/cm³. This means that 1 liter of water has a mass of 1 kg (1000 g).

### Step 3: Set Up the Relationship
- At 4°C, if we take 1 liter of water (which is 1 kg), we can say:
- 1 liter of water = 1000 g of water = 1 kg of water.

### Step 4: Calculate Molarity and Molality
- If we assume we have 1 mole of solute dissolved in this 1 kg of water:
- **Molarity** = 1 mole / 1 L = 1 M
- **Molality** = 1 mole / 1 kg = 1 m

### Step 5: Conclusion
- At 4°C, the molarity of pure water is equal to its molality because both are calculated based on the same mass and volume of water.

### Final Result
- The temperature at which the molarity of pure water is equal to its molality is **4°C** or **277 K** (when converted to Kelvin).