500 ml of a solution contain 12.6 grams of oxalic acid [Mol. Mass = 126 g/mole]. 10 ml of this solution is diluted to 100 ml in a flask. What is the molarity of the resultant solution?

Options

A. 0.1
B. 0.2
C. 0.01
D. 0.02

Answer

To find the molarity of the resultant solution after dilution, we can follow these steps:

### Step 1: Calculate the number of moles of oxalic acid in the original solution.
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mole)}} \]

Given:
- Mass of oxalic acid = 12.6 g
- Molar mass of oxalic acid = 126 g/mole

Calculating the number of moles:
\[ n = \frac{12.6 \, \text{g}}{126 \, \text{g/mole}} = 0.1 \, \text{moles} \]

### Step 2: Calculate the molarity of the original solution.
Molarity (M) is defined as the number of moles of solute per liter of solution.
\[ M = \frac{n}{V} \]

Where:
- \( n = 0.1 \, \text{moles} \)
- \( V = 500 \, \text{ml} = 0.5 \, \text{L} \)

Calculating the molarity:
\[ M = \frac{0.1 \, \text{moles}}{0.5 \, \text{L}} = 0.2 \, \text{M} \]

### Step 3: Use the dilution formula to find the molarity of the diluted solution.
The dilution formula is given by:
\[ C_1V_1 = C_2V_2 \]

Where:
- \( C_1 \) = initial concentration (molarity of original solution) = 0.2 M
- \( V_1 \) = volume of the original solution taken for dilution = 10 ml = 0.01 L
- \( C_2 \) = final concentration (molarity of diluted solution) = ?
- \( V_2 \) = final volume after dilution = 100 ml = 0.1 L

Substituting the values into the dilution formula:
\[ 0.2 \, \text{M} \times 0.01 \, \text{L} = C_2 \times 0.1 \, \text{L} \]

### Step 4: Solve for \( C_2 \).
Rearranging the equation:
\[ C_2 = \frac{0.2 \times 0.01}{0.1} \]

Calculating:
\[ C_2 = \frac{0.002}{0.1} = 0.02 \, \text{M} \]

### Final Answer:
The molarity of the resultant solution after dilution is **0.02 M**.

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