Calculate approximate pH of the resultant solution formed by titration of 25 mL of 0.04 M `Na_(2)CO_(3)` with 50 mL of 0.025 M HCl. `[Given : pK_(a1)=6.4 and pK_(a2)=10.3 for H_(2)CO_(3)]`

Options

A. `5.92`
B. `6.88`
C. `6.4`
D. `5.88`

Answer

To calculate the approximate pH of the resultant solution formed by the titration of 25 mL of 0.04 M Na₂CO₃ with 50 mL of 0.025 M HCl, we can follow these steps:

### Step 1: Calculate the initial millimoles of Na₂CO₃ and HCl

1. **Calculate the millimoles of Na₂CO₃:**
\[ \text{Millimoles of Na}_2\text{CO}_3 = \text{Volume (mL)} \times \text{Concentration (M)} = 25 \, \text{mL} \times 0.04 \, \text{mol/L} = 1 \, \text{mmol} \]

2. **Calculate the millimoles of HCl:**
\[ \text{Millimoles of HCl} = \text{Volume (mL)} \times \text{Concentration (M)} = 50 \, \text{mL} \times 0.025 \, \text{mol/L} = 1.25 \, \text{mmol} \]

### Step 2: Determine the reaction between Na₂CO₃ and HCl

When Na₂CO₃ is titrated with HCl, the carbonate ions (CO₃²⁻) react with hydrogen ions (H⁺) to form bicarbonate ions (HCO₃⁻):
\[ \text{CO}_3^{2-} + \text{H}^+ \rightarrow \text{HCO}_3^{-} \]

### Step 3: Calculate the final amounts after the reaction

1. **Initial moles before reaction:**
- CO₃²⁻: 1 mmol
- H⁺: 1.25 mmol

2. **After the reaction:**
- 1 mmol of CO₃²⁻ will react with 1 mmol of H⁺, forming 1 mmol of HCO₃⁻.
- Remaining H⁺ after reaction:
\[ 1.25 \, \text{mmol} - 1 \, \text{mmol} = 0.25 \, \text{mmol} \]
- HCO₃⁻ produced: 1 mmol

### Step 4: Calculate the concentration of HCO₃⁻ and H₂CO₃

1. **Total volume of the solution after mixing:**
\[ \text{Total Volume} = 25 \, \text{mL} + 50 \, \text{mL} = 75 \, \text{mL} = 0.075 \, \text{L} \]

2. **Concentration of HCO₃⁻:**
\[ [\text{HCO}_3^-] = \frac{1 \, \text{mmol}}{0.075 \, \text{L}} = 0.01333 \, \text{M} \]

3. **Concentration of H₂CO₃:**
- H₂CO₃ is formed from the remaining H⁺ reacting with HCO₃⁻:
- H₂CO₃ produced = 0.25 mmol
\[ [\text{H}_2\text{CO}_3] = \frac{0.25 \, \text{mmol}}{0.075 \, \text{L}} = 0.00333 \, \text{M} \]

### Step 5: Use the Henderson-Hasselbalch equation to find pH

The pH of the buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{HCO}_3^-]}{[\text{H}_2\text{CO}_3]} \right) \]

1. **Substituting the values:**
- Given: pKₐ₁ = 6.4
- Concentration of HCO₃⁻ = 0.01333 M
- Concentration of H₂CO₃ = 0.00333 M

\[ \text{pH} = 6.4 + \log \left( \frac{0.01333}{0.00333} \right) \]

2. **Calculating the log term:**
\[ \frac{0.01333}{0.00333} \approx 4 \]
\[ \log(4) \approx 0.602 \]

3. **Final pH calculation:**
\[ \text{pH} = 6.4 + 0.602 = 7.002 \]

### Final Result:
The approximate pH of the resultant solution is **7.00**.