What is the % dissociation of `CH_(3)COOH`, if equivalent conductivity at this dilution and at infinite dilution are 148 and 398 S `cm^(2)//mol` respectively

Options

A. `37.18%`
B. `47%`
C. `48.78%`
D. `10.8%`

Explanation

To find the percentage dissociation of acetic acid (CH₃COOH), we can use the formula relating equivalent conductivity at a given dilution and at infinite dilution. The steps to solve the problem are as follows:

### Step 1: Understand the relationship between equivalent conductivity and dissociation
The equivalent conductivity (Λ) of a weak electrolyte can be expressed in terms of its degree of dissociation (α) and its concentration (C). The formula is:
\[ \Lambda = \alpha \Lambda_0 \]
where:
- \( \Lambda \) is the equivalent conductivity at a given dilution (148 S cm²/mol in this case),
- \( \Lambda_0 \) is the equivalent conductivity at infinite dilution (398 S cm²/mol).

### Step 2: Set up the equation
From the relationship, we can express the degree of dissociation (α) as:
\[ \alpha = \frac{\Lambda}{\Lambda_0} \]

### Step 3: Substitute the values
Now, substitute the given values into the equation:
\[ \alpha = \frac{148}{398} \]

### Step 4: Calculate α
Now, perform the division:
\[ \alpha = 0.3718 \]

### Step 5: Convert α to percentage
To find the percentage dissociation, multiply α by 100:
\[ \text{Percentage dissociation} = \alpha \times 100 = 0.3718 \times 100 \]

### Step 6: Final calculation
Calculating this gives:
\[ \text{Percentage dissociation} = 37.18\% \]

Thus, the percentage dissociation of CH₃COOH is approximately **37.18%**.