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 solution containing 0.4 g of NaOH in 60 mL of solution, we can follow these steps:

### Step 1: Calculate the number of moles of NaOH
To find the number of moles, we use the formula:
\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of NaOH = 0.4 g
- Molar mass of NaOH = 40 g/mol

Substituting the values:
\[ \text{moles} = \frac{0.4 \, \text{g}}{40 \, \text{g/mol}} = 0.01 \, \text{moles} \]

### Step 2: Convert the volume from mL to L
To calculate molarity, we need the volume in liters.
Given:
- Volume = 60 mL

Convert mL to L:
\[ \text{Volume (L)} = \frac{60 \, \text{mL}}{1000} = 0.06 \, \text{L} \]

### Step 3: Calculate the molarity (M)
Using the formula for molarity:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in L}} \]
Substituting the values:
\[ M = \frac{0.01 \, \text{moles}}{0.06 \, \text{L}} \approx 0.167 \, \text{mol/L} \]

### Step 4: Calculate the normality (N)
Normality is calculated using the formula:
\[ N = M \times \text{valency factor} \]
For NaOH, the valency factor is 1 (since it can donate one hydroxide ion).
Substituting the values:
\[ N = 0.167 \, \text{mol/L} \times 1 = 0.167 \, \text{N} \]

### Final Answer
- Molarity (M) = 0.167 mol/L
- Normality (N) = 0.167 N