50 mL of 0.1 M solution of sodium acetate and 50 mL of 0.01 M acetic acid mixed. The `pK_(a)` of acetic acid is 4.76. The `P^(H)` of the buffer solution is

Answer

To solve the problem of finding the pH of the buffer solution formed by mixing sodium acetate and acetic acid, we can follow these steps:

### Step 1: Identify the components of the buffer solution
We have:
- Sodium acetate (the salt) with a concentration of 0.1 M
- Acetic acid (the weak acid) with a concentration of 0.01 M
- Both solutions have a volume of 50 mL.

### Step 2: Calculate the moles of each component
First, we need to calculate the number of moles of sodium acetate and acetic acid in the solution.

- Moles of sodium acetate:
\[ \text{Moles of sodium acetate} = \text{Concentration} \times \text{Volume} = 0.1 \, \text{M} \times 0.050 \, \text{L} = 0.005 \, \text{moles} \]

- Moles of acetic acid:
\[ \text{Moles of acetic acid} = \text{Concentration} \times \text{Volume} = 0.01 \, \text{M} \times 0.050 \, \text{L} = 0.0005 \, \text{moles} \]

### Step 3: Calculate the total volume of the solution
The total volume after mixing the two solutions is:
\[ \text{Total Volume} = 50 \, \text{mL} + 50 \, \text{mL} = 100 \, \text{mL} = 0.1 \, \text{L} \]

### Step 4: Calculate the concentrations of the components in the mixed solution
Now we can find the concentrations of sodium acetate and acetic acid in the total volume.

- Concentration of sodium acetate:
\[ \text{Concentration of sodium acetate} = \frac{\text{Moles}}{\text{Total Volume}} = \frac{0.005 \, \text{moles}}{0.1 \, \text{L}} = 0.05 \, \text{M} \]

- Concentration of acetic acid:
\[ \text{Concentration of acetic acid} = \frac{\text{Moles}}{\text{Total Volume}} = \frac{0.0005 \, \text{moles}}{0.1 \, \text{L}} = 0.005 \, \text{M} \]

### Step 5: Use the Henderson-Hasselbalch equation to find the pH
The Henderson-Hasselbalch equation is given by:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

Substituting the values we have:
- \( \text{pK}_a = 4.76 \)
- \( [\text{Salt}] = 0.05 \, \text{M} \)
- \( [\text{Acid}] = 0.005 \, \text{M} \)

\[ \text{pH} = 4.76 + \log\left(\frac{0.05}{0.005}\right) \]

### Step 6: Calculate the logarithm
\[ \frac{0.05}{0.005} = 10 \quad \Rightarrow \quad \log(10) = 1 \]

### Step 7: Final calculation of pH
\[ \text{pH} = 4.76 + 1 = 5.76 \]

### Final Answer
The pH of the buffer solution is **5.76**.

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