The pH of a solution obtained by mixing 100 ml of 0.2 M `CH_3COOH` with 100 ml of 0.2 N NaOH will be
`(pK_a "for " CH_3COOH=4.74 and log 2 =0.301)`

Options

A. 4.74
B. 8.87
C. 9.1
D. 8.57

Answer

To find the pH of the solution obtained by mixing 100 ml of 0.2 M acetic acid (CH₃COOH) with 100 ml of 0.2 N NaOH, we can follow these steps:

### Step 1: Calculate the moles of acetic acid and sodium hydroxide
- Moles of CH₃COOH = Molarity × Volume (in liters)
\[ \text{Moles of CH}_3\text{COOH} = 0.2 \, \text{M} \times 0.1 \, \text{L} = 0.02 \, \text{moles} \]

- Moles of NaOH = Normality × Volume (in liters)
\[ \text{Moles of NaOH} = 0.2 \, \text{N} \times 0.1 \, \text{L} = 0.02 \, \text{moles} \]

### Step 2: Determine the reaction between acetic acid and sodium hydroxide
The reaction between acetic acid (weak acid) and sodium hydroxide (strong base) is:
\[ \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{H}_2\text{O} \]
Since both reactants are present in equal moles (0.02 moles), they will completely neutralize each other.

### Step 3: Calculate the concentration of the resulting solution
After the reaction, we will have a solution of sodium acetate (CH₃COONa) in a total volume of:
\[ \text{Total Volume} = 100 \, \text{ml} + 100 \, \text{ml} = 200 \, \text{ml} = 0.2 \, \text{L} \]

The concentration of the resulting sodium acetate can be calculated as:
\[ \text{Concentration of CH}_3\text{COONa} = \frac{\text{Moles of CH}_3\text{COONa}}{\text{Total Volume}} = \frac{0.02 \, \text{moles}}{0.2 \, \text{L}} = 0.1 \, \text{M} \]

### Step 4: Use the Henderson-Hasselbalch equation
Since we have a weak acid (acetic acid) and its conjugate base (sodium acetate), we can use the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
Where:
- \([\text{A}^-]\) = concentration of the conjugate base (sodium acetate) = 0.1 M
- \([\text{HA}]\) = concentration of the weak acid (acetic acid) = 0 M (since it has been completely neutralized)

Since the concentration of acetic acid is 0 after complete neutralization, we need to consider the pH of the resulting solution as a basic solution due to the presence of the acetate ion.

### Step 5: Calculate the pH
Using the given pKₐ for acetic acid:
\[ \text{pK}_a = 4.74 \]
Since we have only the conjugate base:
\[ \text{pH} = 7 + \frac{1}{2} \text{pK}_a + \frac{1}{2} \log C \]
Where \(C = 0.1\):
\[ \text{pH} = 7 + \frac{1}{2} \times 4.74 + \frac{1}{2} \times \log(0.1) \]
Using \(\log(0.1) = -1\):
\[ \text{pH} = 7 + 2.37 - 0.5 = 8.87 \]

### Final Answer
The pH of the solution is **8.87**.

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