`25cm^(3)` of oxalic acid completely neutralised 0.064g of soldium hydroxied. molarity of the oxalic acid solution is

Options

A. `0.064`
B. `0.045`
C. `0.015`
D. `0.032`

Explanation

To find the molarity of the oxalic acid solution, we will follow these steps:

### Step 1: Understand the relationship between oxalic acid and sodium hydroxide
Oxalic acid (H₂C₂O₄) is a diprotic acid, meaning it can donate two protons (H⁺ ions). When it reacts with sodium hydroxide (NaOH), it will neutralize two moles of NaOH for every mole of oxalic acid.

### Step 2: Calculate the moles of sodium hydroxide
We are given the mass of sodium hydroxide:
- Mass of NaOH = 0.064 g

Next, we need to calculate the number of moles of NaOH using the formula:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

The molar mass of NaOH is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Thus, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

Now, we can calculate the moles of NaOH:
\[ \text{Moles of NaOH} = \frac{0.064 \, \text{g}}{40 \, \text{g/mol}} = 0.0016 \, \text{mol} \]

### Step 3: Determine the moles of oxalic acid
Since oxalic acid neutralizes NaOH in a 1:2 ratio, the moles of oxalic acid will be half the moles of NaOH:
\[ \text{Moles of oxalic acid} = \frac{0.0016 \, \text{mol}}{2} = 0.0008 \, \text{mol} \]

### Step 4: Convert the volume of the oxalic acid solution to liters
The volume of the oxalic acid solution is given as 25 cm³. To convert this to liters:
\[ \text{Volume in liters} = \frac{25 \, \text{cm}^3}{1000} = 0.025 \, \text{L} \]

### Step 5: Calculate the molarity of the oxalic acid solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
\[ \text{Molarity} = \frac{0.0008 \, \text{mol}}{0.025 \, \text{L}} = 0.032 \, \text{M} \]

### Final Answer
The molarity of the oxalic acid solution is **0.032 M**.

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