A sample of NaOH weighing 0.40 is dissolved in water and the solution is made to 50.0 `cm^(3)` in volumetric flask. What is the molarity of the resulting solution?

Answer

To find the molarity of the NaOH solution, we will follow these steps:

### Step 1: Determine the mass of NaOH
The mass of NaOH given is 0.40 grams.

### Step 2: Calculate the molar mass of NaOH
The molar mass of NaOH (sodium hydroxide) is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

So, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

### Step 3: Calculate the number of moles of NaOH
Using the formula for moles:
\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Moles of NaOH} = \frac{0.40 \text{ g}}{40 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 4: Convert the volume of the solution from cm³ to liters
The volume of the solution is given as 50.0 cm³. To convert this to liters:
\[ \text{Volume (L)} = \frac{50.0 \text{ cm}^3}{1000} = 0.0500 \text{ L} \]

### Step 5: Calculate the molarity of the solution
Using the formula for molarity:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
Substituting the values:
\[ \text{Molarity} = \frac{0.01 \text{ moles}}{0.0500 \text{ L}} = 0.20 \text{ M} \]

### Final Answer:
The molarity of the resulting NaOH solution is **0.20 M**.

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