The degree of dissociation of acetic acid in a 0.1 M solution is `1.0xx10^(-2)`. The `pK_(a)` of acetic acid value.

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the \( pK_a \) of acetic acid given its degree of dissociation and concentration, we can follow these steps:

### Step 1: Understand the given data
- The concentration of acetic acid (\( C \)) = 0.1 M
- The degree of dissociation (\( \alpha \)) = \( 1.0 \times 10^{-2} \) = 0.01

### Step 2: Calculate the concentration of dissociated acetic acid
The concentration of dissociated acetic acid can be calculated using the formula:
\[ \text{Concentration of dissociated acid} = C \times \alpha \]
Substituting the values:
\[ \text{Concentration of dissociated acid} = 0.1 \, \text{M} \times 0.01 = 0.001 \, \text{M} \]

### Step 3: Calculate the concentration of undissociated acetic acid
The concentration of undissociated acetic acid is given by:
\[ \text{Concentration of undissociated acid} = C - \text{Concentration of dissociated acid} \]
Substituting the values:
\[ \text{Concentration of undissociated acid} = 0.1 \, \text{M} - 0.001 \, \text{M} = 0.099 \, \text{M} \]

### Step 4: Write the expression for \( K_a \)
The dissociation of acetic acid can be represented as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]
The expression for the acid dissociation constant \( K_a \) is given by:
\[ K_a = \frac{[\text{CH}_3\text{COO}^-][\text{H}^+]}{[\text{CH}_3\text{COOH}]} \]
Substituting the concentrations:
\[ K_a = \frac{(0.001)(0.001)}{0.099} \]
Calculating \( K_a \):
\[ K_a = \frac{0.000001}{0.099} \approx 0.0000101 \approx 1.01 \times 10^{-5} \]

### Step 5: Calculate \( pK_a \)
The \( pK_a \) is calculated using the formula:
\[ pK_a = -\log(K_a) \]
Substituting the value of \( K_a \):
\[ pK_a = -\log(1.01 \times 10^{-5}) \]
Using logarithm properties:
\[ pK_a \approx 5 \]

### Final Answer
The \( pK_a \) of acetic acid is approximately **5**.

---