The density of 3 molal solution of NaOH is 1.110g `mL^(-1)`. Calculate the molarity of the solution.

Options

A. 2.69 M
B. 2.97 M
C. 4.57 M
D. 6.70 M

Explanation

To calculate the molarity of a 3 molal solution of NaOH with a density of 1.110 g/mL, we can follow these steps:

### Step 1: Understand the given data
- The solution is 3 molal, which means there are 3 moles of NaOH in 1000 grams of water.
- The density of the solution is given as 1.110 g/mL.

### Step 2: Calculate the mass of the solute (NaOH)
- The molar mass of NaOH is approximately 40 g/mol.
- For 3 moles of NaOH:
\[ \text{Mass of NaOH} = 3 \, \text{moles} \times 40 \, \text{g/mol} = 120 \, \text{g} \]

### Step 3: Calculate the mass of the solution
- The mass of the solvent (water) is 1000 g.
- Therefore, the total mass of the solution is:
\[ \text{Mass of solution} = \text{mass of water} + \text{mass of NaOH} = 1000 \, \text{g} + 120 \, \text{g} = 1120 \, \text{g} \]

### Step 4: Calculate the volume of the solution
- Using the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), we can rearrange it to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1120 \, \text{g}}{1.110 \, \text{g/mL}} \approx 1009.01 \, \text{mL} \]
- To convert this volume into liters:
\[ \text{Volume in liters} = \frac{1009.01 \, \text{mL}}{1000} \approx 1.009 \, \text{L} \]

### Step 5: Calculate the molarity of the solution
- Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{moles of NaOH}}{\text{volume of solution in liters}} = \frac{3 \, \text{moles}}{1.009 \, \text{L}} \approx 2.97 \, \text{M} \]

### Final Answer
The molarity of the solution is approximately **2.97 M**.

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