50 mL of 2N acetic acid mixed with 10 mL of 1N sodium acetate solution will have an approximate pH of `(K_(a)=10^(-5))`:

Options

A. 4
B. 5
C. 6
D. 7

Explanation

To find the approximate pH of the solution formed by mixing 50 mL of 2N acetic acid with 10 mL of 1N sodium acetate, we can follow these steps:

### Step 1: Calculate the equivalents of acetic acid and sodium acetate.

1. **Calculate equivalents of acetic acid (HA)**:
- Volume of acetic acid = 50 mL
- Normality of acetic acid = 2N
- Equivalents of acetic acid = Volume (L) × Normality (N)
- Convert mL to L: 50 mL = 0.050 L
- Equivalents of acetic acid = 0.050 L × 2N = 0.1 equivalents

2. **Calculate equivalents of sodium acetate (A-)**:
- Volume of sodium acetate = 10 mL
- Normality of sodium acetate = 1N
- Equivalents of sodium acetate = Volume (L) × Normality (N)
- Convert mL to L: 10 mL = 0.010 L
- Equivalents of sodium acetate = 0.010 L × 1N = 0.01 equivalents

### Step 2: Determine the total volume of the solution.

- Total volume = Volume of acetic acid + Volume of sodium acetate
- Total volume = 50 mL + 10 mL = 60 mL = 0.060 L

### Step 3: Use the Henderson-Hasselbalch equation to calculate pH.

The Henderson-Hasselbalch equation is given by:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]

Where:
- \( \text{pK}_a = -\log(K_a) \)
- Given \( K_a = 10^{-5} \), therefore \( \text{pK}_a = 5 \).

### Step 4: Calculate the concentrations of acetic acid and sodium acetate.

1. **Concentration of acetic acid (HA)**:
- Concentration (M) = Equivalents / Total Volume (L)
- Concentration of acetic acid = 0.1 equivalents / 0.060 L = 1.67 N

2. **Concentration of sodium acetate (A-)**:
- Concentration of sodium acetate = 0.01 equivalents / 0.060 L = 0.167 N

### Step 5: Substitute values into the Henderson-Hasselbalch equation.

\[ \text{pH} = 5 + \log\left(\frac{0.167}{1.67}\right) \]

### Step 6: Calculate the log term.

- Calculate the ratio:
\[ \frac{0.167}{1.67} = 0.1 \]

- Now, calculate the log:
\[ \log(0.1) = -1 \]

### Step 7: Final calculation of pH.

\[ \text{pH} = 5 - 1 = 4 \]

### Conclusion:

The approximate pH of the solution is **4**.

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