0.4 gm of polybasic acid `H_(n)A` (M.wt = 96) requires 0.5 gm NaOH for complete neutralisation. The number of replacable hydorgen atoms are (all the hydrogens are acidic)

Answer

To solve the problem, we need to determine the number of replaceable hydrogen atoms (N) in the polybasic acid \( H_nA \). Here’s the step-by-step solution:

### Step 1: Determine the Equivalent Mass of the Acid
The equivalent mass of the acid can be expressed as:
\[ \text{Equivalent Mass} = \frac{\text{Molar Mass}}{N} \]
Given that the molar mass of the acid \( H_nA \) is 96 g/mol, we can write:
\[ \text{Equivalent Mass} = \frac{96}{N} \]

### Step 2: Calculate the Number of Equivalents of the Acid
The number of equivalents of the acid can be calculated using the formula:
\[ \text{Number of Equivalents} = \frac{\text{Given Mass}}{\text{Equivalent Mass}} \]
The given mass of the acid is 0.4 g. Therefore:
\[ \text{Number of Equivalents of Acid} = \frac{0.4}{\frac{96}{N}} = \frac{0.4N}{96} \]

### Step 3: Determine the Equivalent Mass of Sodium Hydroxide (NaOH)
The molar mass of NaOH is calculated as follows:
\[ \text{Molar Mass of NaOH} = 23 \, (\text{Na}) + 16 \, (\text{O}) + 1 \, (\text{H}) = 40 \, \text{g/mol} \]
Since NaOH has one replaceable hydrogen, its equivalent mass is equal to its molar mass:
\[ \text{Equivalent Mass of NaOH} = 40 \, \text{g} \]

### Step 4: Calculate the Number of Equivalents of NaOH
Using the given mass of NaOH, which is 0.5 g:
\[ \text{Number of Equivalents of NaOH} = \frac{0.5}{40} = \frac{1}{80} \]

### Step 5: Set Up the Equation for Neutralization
For complete neutralization, the number of equivalents of the acid must equal the number of equivalents of the base:
\[ \frac{0.4N}{96} = \frac{1}{80} \]

### Step 6: Solve for N
Cross-multiplying gives:
\[ 0.4N \cdot 80 = 96 \cdot 1 \]
\[ 32N = 96 \]
\[ N = \frac{96}{32} = 3 \]

### Conclusion
The number of replaceable hydrogen atoms in the polybasic acid \( H_nA \) is:
\[ \boxed{3} \]