Accumulation of lactic acid `(HC_(3)H_(5)O_(3))`, a monobasic acid in tissues leads to pain and a feeling of fatigue. In a 0.10 M aqueous solution, lactic acid is `3.7%` dissociates. The value of dissociation constant Ka, for this acid will be

Options

A. `1.4 xx 10^(-5)`
B. `1.4 xx 10^(-4)`
C. `3.7 xx 10^(-4)`
D. `2.8 xx 10^(-4)`

Explanation

To find the dissociation constant \( K_a \) for lactic acid (HC\(_3\)H\(_5\)O\(_3\)), we can follow these steps:

### Step 1: Determine the concentration of the dissociated species
Given that lactic acid is a monobasic acid, it dissociates according to the following equation:

\[ HC_3H_5O_3 \rightleftharpoons H^+ + C_3H_5O_3^- \]

In a 0.10 M solution, if 3.7% of the acid dissociates, we can calculate the concentration of the dissociated species.

\[ \text{Dissociation percentage} = 3.7\% \]
\[ \text{Concentration of dissociated acid} = 0.10 \, \text{M} \times \frac{3.7}{100} = 0.0037 \, \text{M} \]

### Step 2: Calculate the concentrations at equilibrium
At equilibrium, the concentrations will be:

- Concentration of \( H^+ \) = 0.0037 M
- Concentration of \( C_3H_5O_3^- \) = 0.0037 M
- Concentration of undissociated \( HC_3H_5O_3 \) = Initial concentration - Concentration dissociated

\[ \text{Concentration of } HC_3H_5O_3 = 0.10 \, \text{M} - 0.0037 \, \text{M} = 0.0963 \, \text{M} \]

### Step 3: Write the expression for the dissociation constant \( K_a \)
The expression for the dissociation constant \( K_a \) is given by:

\[ K_a = \frac{[H^+][C_3H_5O_3^-]}{[HC_3H_5O_3]} \]

Substituting the equilibrium concentrations into the expression:

\[ K_a = \frac{(0.0037)(0.0037)}{0.0963} \]

### Step 4: Calculate \( K_a \)
Now, we can calculate \( K_a \):

\[ K_a = \frac{0.00001369}{0.0963} \approx 0.000142 \]

### Step 5: Express \( K_a \) in scientific notation
Converting the result into scientific notation:

\[ K_a \approx 1.42 \times 10^{-4} \]

### Final Answer
The value of the dissociation constant \( K_a \) for lactic acid is approximately:

\[ K_a \approx 1.4 \times 10^{-4} \]

---