To solve the problem of determining the volume of Ba(OH)₂ solution required to reach the equivalent point when titrating with benzoic acid, we can follow these steps:
### Step 1: Calculate the number of moles of benzoic acid (C₆H₅COOH)
Given:
- Mass of benzoic acid = 0.2 g
- Molecular mass of benzoic acid (C₆H₅COOH) = 122 g/mol
Using the formula for moles:
\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}
\]
\[
\text{Number of moles of C₆H₅COOH} = \frac{0.2 \, \text{g}}{122 \, \text{g/mol}} \approx 0.00164 \, \text{mol}
\]
### Step 2: Determine the number of equivalents of benzoic acid
Benzoic acid (C₆H₅COOH) is a monoprotic acid, meaning it donates one proton (H⁺) per molecule. Therefore, the number of equivalents is equal to the number of moles:
\[
\text{Number of equivalents of C₆H₅COOH} = 0.00164 \, \text{eq}
\]
### Step 3: Relate the equivalents of benzoic acid to Ba(OH)₂
Ba(OH)₂ is a diprotic base, meaning it can donate two hydroxide ions (OH⁻) per molecule. Therefore, the number of equivalents of Ba(OH)₂ will be twice the number of moles:
\[
\text{Number of equivalents of Ba(OH)₂} = 2 \times \text{Number of moles of Ba(OH)₂}
\]
### Step 4: Set up the equation for the titration
At the equivalence point, the number of equivalents of benzoic acid will equal the number of equivalents of Ba(OH)₂:
\[
\text{Number of equivalents of C₆H₅COOH} = \text{Number of equivalents of Ba(OH)₂}
\]
\[
0.00164 \, \text{eq} = 2 \times \text{Number of moles of Ba(OH)₂}
\]
### Step 5: Calculate the number of moles of Ba(OH)₂
Using the relationship from the previous step:
\[
\text{Number of moles of Ba(OH)₂} = \frac{0.00164 \, \text{eq}}{2} = 0.00082 \, \text{mol}
\]
### Step 6: Calculate the volume of Ba(OH)₂ solution required
Given the molarity of Ba(OH)₂ is 0.12 M, we can use the formula:
\[
\text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}}
\]
Rearranging gives:
\[
\text{Volume in liters} = \frac{\text{Number of moles}}{\text{Molarity}} = \frac{0.00082 \, \text{mol}}{0.12 \, \text{mol/L}} \approx 0.00683 \, \text{L}
\]
### Step 7: Convert volume to milliliters
\[
\text{Volume in mL} = 0.00683 \, \text{L} \times 1000 \approx 6.83 \, \text{mL}
\]
### Final Answer
The volume of Ba(OH)₂ solution required to reach the equivalence point is approximately **6.83 mL**.
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