10 g impure NaOH is completely neutralised by 1000 ml of `(1)/(10)N HCl`. Calculate the percentage purity of the impure NaOH.

Answer

To solve the problem of calculating the percentage purity of impure NaOH, we can follow these steps:

### Step 1: Understand the given data
We have:
- Mass of impure NaOH = 10 g
- Volume of HCl solution = 1000 ml = 1 L
- Normality of HCl = \( \frac{1}{10} \) N

### Step 2: Calculate the number of equivalents of HCl
Using the formula for normality:
\[ \text{Normality (N)} = \frac{\text{Number of equivalents}}{\text{Volume in L}} \]
We can rearrange this to find the number of equivalents of HCl:
\[ \text{Number of equivalents of HCl} = \text{Normality} \times \text{Volume in L} \]
Substituting the values:
\[ \text{Number of equivalents of HCl} = \frac{1}{10} \times 1 = \frac{1}{10} \text{ equivalents} \]

### Step 3: Relate the equivalents of NaOH to HCl
Since NaOH reacts with HCl in a 1:1 ratio, the number of equivalents of NaOH will also be \( \frac{1}{10} \) equivalents.

### Step 4: Calculate the mass of pure NaOH
The number of equivalents of NaOH can be calculated using the formula:
\[ \text{Number of equivalents} = \frac{\text{Mass}}{\text{Equivalent weight}} \]
The equivalent weight of NaOH is the molar mass divided by the number of replaceable hydroxide ions (which is 1 for NaOH):
\[ \text{Equivalent weight of NaOH} = 40 \text{ g/mol} \]
Let \( W \) be the mass of pure NaOH. Thus:
\[ \frac{W}{40} = \frac{1}{10} \]
Now, solving for \( W \):
\[ W = 40 \times \frac{1}{10} = 4 \text{ g} \]

### Step 5: Calculate the percentage purity of NaOH
The percentage purity can be calculated using the formula:
\[ \text{Percentage purity} = \left( \frac{\text{Mass of pure NaOH}}{\text{Total mass of impure NaOH}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage purity} = \left( \frac{4 \text{ g}}{10 \text{ g}} \right) \times 100 = 40\% \]

### Final Answer
The percentage purity of the impure NaOH is **40%**.

---