If `0.4gm` of `NaOH` is present in 60 ml of solution. What is the molarity and normality `[M. wt`. Of `NaOH = 40]`

Options

A. `0.250 M` & `0.250 N`
B. `0.250 M` & `0.125 N`
C. `0.125 M` & `0.250 N`
D. `0.125 M` & `0.125 N`

Explanation

To solve the problem of finding the molarity and normality of a NaOH solution, we will follow these steps:

### Step 1: Identify the given values
- Weight of NaOH (w) = 0.4 g
- Volume of solution (V) = 60 mL
- Molecular weight of NaOH (M) = 40 g/mol

### Step 2: Convert the volume from mL to L
To calculate molarity, we need the volume in liters.
\[ V = 60 \text{ mL} = \frac{60}{1000} = 0.06 \text{ L} \]

### Step 3: Calculate the number of moles of NaOH
Using the formula:
\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molecular weight}} = \frac{0.4 \text{ g}}{40 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 4: Calculate the molarity (M)
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
\[ M = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.01 \text{ moles}}{0.06 \text{ L}} \approx 0.167 \text{ M} \]

### Step 5: Calculate the equivalent weight of NaOH
The equivalent weight of NaOH can be calculated as:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{Number of replaceable OH}^- \text{ ions}} = \frac{40 \text{ g/mol}}{1} = 40 \text{ g/equiv} \]

### Step 6: Calculate the normality (N)
Normality (N) is defined as the number of equivalents of solute per liter of solution. The formula for normality is:
\[ N = \frac{\text{Weight}}{\text{Equivalent weight} \times \text{Volume in L}} = \frac{0.4 \text{ g}}{40 \text{ g/equiv} \times 0.06 \text{ L}} = \frac{0.4}{2.4} \approx 0.167 \text{ N} \]

### Final Results
- Molarity (M) = 0.167 M
- Normality (N) = 0.167 N