`0.63 g` of diabasic acid was dissolved in water. The volume of the solution was made `100 mL`. `20 mL` of this acid solution required `10 mL` of `N//5 NaOH` solution. The molecular mass of acid is:

Options

A. `63`
B. `126`
C. `252`
D. `128`

Explanation

To find the molecular mass of the di-basic acid, we can follow these steps:

### Step 1: Calculate the number of equivalents of NaOH used
Given that the normality of the NaOH solution is \( \frac{N}{5} \) (which is 0.2 N), we can calculate the number of equivalents of NaOH used in the reaction.

\[ \text{Normality (N)} = \text{Equivalents of solute} / \text{Volume of solution in liters} \]
\[ \text{Volume of NaOH solution} = 10 \, \text{mL} = 0.01 \, \text{L} \]
\[ \text{Equivalents of NaOH} = \text{Normality} \times \text{Volume in L} = 0.2 \, \text{N} \times 0.01 \, \text{L} = 0.002 \, \text{equivalents} \]

### Step 2: Determine the number of equivalents of the di-basic acid
Since the di-basic acid can donate two protons (H⁺ ions), the number of equivalents of the di-basic acid in 20 mL of the solution is equal to the number of equivalents of NaOH used.

\[ \text{Equivalents of di-basic acid} = 0.002 \, \text{equivalents} \]

### Step 3: Calculate the total number of equivalents in the 20 mL acid solution
The total volume of the acid solution is 100 mL, but we are only considering 20 mL for our calculations. The equivalents in 20 mL can be calculated as follows:

\[ \text{Equivalents of di-basic acid in 100 mL} = \text{Equivalents in 20 mL} \times \frac{100 \, \text{mL}}{20 \, \text{mL}} = 0.002 \, \text{equivalents} \times 5 = 0.01 \, \text{equivalents} \]

### Step 4: Calculate the molecular mass of the di-basic acid
The molecular mass can be calculated using the formula:

\[ \text{Molecular mass} = \frac{\text{mass of acid}}{\text{number of equivalents}} \]

Given that the mass of the di-basic acid is 0.63 g:

\[ \text{Molecular mass} = \frac{0.63 \, \text{g}}{0.01 \, \text{equivalents}} = 63 \, \text{g/equiv} \]

Since the di-basic acid can donate 2 equivalents of H⁺, we need to multiply the equivalent mass by 2 to find the molecular mass:

\[ \text{Molecular mass of di-basic acid} = 63 \, \text{g/equiv} \times 2 = 126 \, \text{g/mol} \]

### Final Answer:
The molecular mass of the di-basic acid is **126 g/mol**.

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