HA is a weak acid. The pH of 0.1 M HA solution is 2. What is the degree of dissociation `(alpha)` of HA ?

Options

A. 0.5
B. 0.2
C. 0.1
D. 0.301

Explanation

To find the degree of dissociation (α) of the weak acid HA, we can follow these steps:

### Step 1: Understand the relationship between pH and [H⁺]
The pH of a solution is related to the concentration of hydrogen ions [H⁺] by the formula:
\[ \text{pH} = -\log[H^+] \]

### Step 2: Calculate [H⁺] from the given pH
Given that the pH of the 0.1 M HA solution is 2, we can find [H⁺]:
\[ [H^+] = 10^{-\text{pH}} = 10^{-2} \, \text{M} \]

### Step 3: Set up the equation for degree of dissociation
For a weak acid HA that dissociates as follows:
\[ HA \rightleftharpoons H^+ + A^- \]
Let the initial concentration of HA be \( C = 0.1 \, \text{M} \).

At equilibrium, if α is the degree of dissociation, the concentration of H⁺ ions produced will be:
\[ [H^+] = C \cdot \alpha \]
Thus, we have:
\[ C \cdot \alpha = 10^{-2} \]

### Step 4: Substitute the value of C
Substituting \( C = 0.1 \, \text{M} \) into the equation:
\[ 0.1 \cdot \alpha = 10^{-2} \]

### Step 5: Solve for α
Now, we can solve for α:
\[ \alpha = \frac{10^{-2}}{0.1} \]
\[ \alpha = 10^{-2} \cdot 10^{1} \]
\[ \alpha = 10^{-1} \]
\[ \alpha = 0.1 \]

### Final Answer
The degree of dissociation (α) of the weak acid HA is:
\[ \alpha = 0.1 \]

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