2.0 g of polybasic organic acid (Molecular mass =600) required 100 mL of a `(M)/(6)` NaOH solution for complete neutralisation. Find the basicity of acid .

Answer

To find the basicity of the polybasic organic acid, we can follow these steps:

### Step 1: Understand the given information
- Weight of the organic acid = 2.0 g
- Molecular mass of the organic acid = 600 g/mol
- Volume of NaOH solution = 100 mL = 0.1 L
- Concentration of NaOH solution = \( \frac{1}{6} \) M

### Step 2: Calculate the number of moles of the organic acid
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molecular weight}} \]
Substituting the values:
\[ \text{Number of moles of acid} = \frac{2.0 \, \text{g}}{600 \, \text{g/mol}} = \frac{2.0}{600} = \frac{1}{300} \, \text{mol} \]

### Step 3: Calculate the number of equivalents of NaOH
First, we need to calculate the normality of the NaOH solution. Since normality (N) is related to molarity (M) and the number of equivalents (n), we can use:
\[ N = M \times n \]
For NaOH, which provides one OH⁻ ion, the n factor is 1. Thus:
\[ \text{Normality of NaOH} = \frac{1}{6} \, \text{N} \]
Now, we can find the number of equivalents of NaOH:
\[ \text{Number of equivalents of NaOH} = \text{Normality} \times \text{Volume in L} \]
Substituting the values:
\[ \text{Number of equivalents of NaOH} = \frac{1}{6} \times 0.1 = \frac{0.1}{6} = \frac{1}{60} \, \text{equivalents} \]

### Step 4: Set the number of equivalents of the acid equal to the number of equivalents of NaOH
In a neutralization reaction, the number of equivalents of acid equals the number of equivalents of base:
\[ \text{Number of equivalents of acid} = \text{Number of equivalents of NaOH} \]
Let \( n \) be the basicity of the acid. The number of equivalents of the acid can be expressed as:
\[ \text{Number of equivalents of acid} = \text{Number of moles of acid} \times n \]
Thus, we have:
\[ \frac{1}{300} \times n = \frac{1}{60} \]

### Step 5: Solve for the basicity \( n \)
To find \( n \), we can rearrange the equation:
\[ n = \frac{1}{60} \times 300 \]
Calculating this gives:
\[ n = 5 \]

### Conclusion
The basicity of the organic acid is 5, meaning it can donate 5 H⁺ ions.

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