Molarity of 1m aqueous NaOH solution [density of the solution is 1.02 g/ml]

Options

A. 1 M
B. 1.02 M
C. 1.2 M
D. 0.98 M

Explanation

To find the molarity of a 1m aqueous NaOH solution with a density of 1.02 g/ml, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Molality**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent.
- Given that the molality of the NaOH solution is 1m, this means there is 1 mole of NaOH in 1 kg of water (solvent).

2. **Calculating the Weight of Solvent**:
- Since the molality is 1m, the weight of the solvent (water) is 1 kg, which is equivalent to 1000 grams.

3. **Calculating the Weight of Solute (NaOH)**:
- The molecular weight of NaOH can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol
- Total molecular weight of NaOH = 23 + 16 + 1 = 40 g/mol.
- Since we have 1 mole of NaOH, the weight of the solute (NaOH) is:
- Weight of NaOH = 1 mole × 40 g/mol = 40 grams.

4. **Calculating the Total Weight of the Solution**:
- The total weight of the solution is the sum of the weight of the solvent and the weight of the solute:
- Total weight of solution = Weight of solvent + Weight of solute
- Total weight of solution = 1000 g + 40 g = 1040 grams.

5. **Using Density to Find Volume of Solution**:
- The density of the solution is given as 1.02 g/ml.
- We can use the formula for density (Density = Weight/Volume) to find the volume of the solution:
- Volume of solution = Total weight of solution / Density
- Volume of solution = 1040 g / 1.02 g/ml = 1020.59 ml.

6. **Converting Volume to Liters**:
- To convert the volume from milliliters to liters, we divide by 1000:
- Volume in liters = 1020.59 ml / 1000 = 1.02059 L.

7. **Calculating Molarity**:
- Molarity (M) is defined as the number of moles of solute per liter of solution:
- Molarity = Number of moles of solute / Volume of solution in liters
- Molarity = 1 mole / 1.02059 L ≈ 0.978 M.

8. **Final Result**:
- The molarity of the 1m aqueous NaOH solution is approximately 0.98 M.

### Final Answer:
The molarity of the 1m aqueous NaOH solution is **0.98 M**.