1.575 g of a dibasic acid is neutralised by 25 mL 1 M NaOH solution. Hence, molar mass of dibasic acid is -

Options

A. `126g mol^(_1)`
B. `63 g mol^(-1)`
C. `12.6 g mol^(-1)`
D. none

Answer

To find the molar mass of the dibasic acid that is neutralized by a sodium hydroxide solution, we will follow these steps:

### Step 1: Understand the given information
- Mass of dibasic acid (m) = 1.575 g
- Volume of NaOH solution (V) = 25 mL = 0.025 L (conversion from mL to L)
- Concentration of NaOH (C) = 1 M

### Step 2: Calculate the number of moles of NaOH
Using the formula:
\[ \text{Number of moles} = \text{Concentration} \times \text{Volume} \]
\[ \text{Number of moles of NaOH} = 1 \, \text{mol/L} \times 0.025 \, \text{L} = 0.025 \, \text{mol} \]

### Step 3: Determine the number of equivalents of NaOH
Since NaOH is a monobasic base (it can donate one OH⁻ ion), the number of equivalents of NaOH is equal to the number of moles:
\[ \text{Equivalents of NaOH} = 0.025 \, \text{eq} \]

### Step 4: Relate the equivalents of the dibasic acid to NaOH
A dibasic acid can donate 2 protons (H⁺ ions), so:
\[ \text{Equivalents of dibasic acid} = \frac{\text{Number of moles of dibasic acid} \times n}{2} \]
Where \( n \) is the number of replaceable hydrogen ions (2 for dibasic acid).

### Step 5: Set up the equation for neutralization
Since the equivalents of the dibasic acid will equal the equivalents of NaOH:
\[ \text{Equivalents of dibasic acid} = \text{Equivalents of NaOH} \]
\[ \frac{\text{Number of moles of dibasic acid} \times 2}{2} = 0.025 \]
This simplifies to:
\[ \text{Number of moles of dibasic acid} = 0.025 \, \text{mol} \]

### Step 6: Calculate the molar mass of the dibasic acid
Using the formula:
\[ \text{Molar mass} = \frac{\text{Mass}}{\text{Number of moles}} \]
Substituting the values:
\[ \text{Molar mass} = \frac{1.575 \, \text{g}}{0.025 \, \text{mol}} = 63 \, \text{g/mol} \]

### Step 7: Correct the calculation for dibasic acid
Since we have a dibasic acid, we need to account for the factor of 2 in the equivalents:
\[ \text{Molar mass} = \frac{1.575 \, \text{g} \times 2}{0.025 \, \text{mol}} = \frac{3.15 \, \text{g}}{0.025 \, \text{mol}} = 126 \, \text{g/mol} \]

### Final Answer:
The molar mass of the dibasic acid is **126 g/mol**.

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