0.2 gm sample of benzoic acid `C_(6)H_(5)` COOH is titrated with 0.12 M `Ba(OH)_(2)` solution, what volume of `Ba(OH)_(2)` solution is required to reach the equivalent point ?

Options

A. 6.83 ml
B. 13.2 ml
C. 17.6 ml
D. 35.2 ml

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the moles of benzoic acid (C₆H₅COOH)
Given:
- Mass of benzoic acid = 0.2 g
- Molar mass of benzoic acid (C₆H₅COOH) = 122.1 g/mol

Using the formula for moles:
\[ \text{Moles of benzoic acid} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{0.2 \, \text{g}}{122.1 \, \text{g/mol}} \approx 0.00163 \, \text{mol} \]

### Step 2: Write the balanced chemical equation for the reaction
The balanced equation for the reaction between benzoic acid and barium hydroxide is:
\[ 2 \, \text{C}_6\text{H}_5\text{COOH} + \text{Ba(OH)}_2 \rightarrow 2 \, \text{H}_2\text{O} + \text{Ba(C}_6\text{H}_5\text{COO)}_2 \]

From the equation, we can see that:
- 2 moles of benzoic acid react with 1 mole of barium hydroxide.

### Step 3: Calculate the moles of barium hydroxide required
From the stoichiometry of the reaction:
\[ \text{Moles of Ba(OH)}_2 = \frac{\text{Moles of benzoic acid}}{2} = \frac{0.00163 \, \text{mol}}{2} \approx 0.000815 \, \text{mol} \]

### Step 4: Use the molarity of barium hydroxide to find the volume required
Given:
- Molarity of Ba(OH)₂ = 0.12 M

Using the formula for molarity:
\[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume (L)}} \]
Rearranging to find volume:
\[ \text{Volume (L)} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.000815 \, \text{mol}}{0.12 \, \text{mol/L}} \approx 0.00679 \, \text{L} \]

Converting liters to milliliters:
\[ \text{Volume (mL)} = 0.00679 \, \text{L} \times 1000 \approx 6.79 \, \text{mL} \]

### Step 5: Final answer
The volume of Ba(OH)₂ solution required to reach the equivalent point is approximately **6.79 mL**.

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