Calculate the percentage ionization of 0.01 M acetic acid in 0.1 M HCI. `K_a` of acetic acid is `1.8 xx 10^(-5)`

Options

A. 0.0018
B. 0.0001
C. 0.018
D. 0.18

Answer

To calculate the percentage ionization of 0.01 M acetic acid in 0.1 M HCl, we will follow these steps:

### Step 1: Understand the Ionization of Acetic Acid
Acetic acid (CH₃COOH) is a weak acid, which means it does not completely ionize in solution. In the presence of a strong acid like HCl, which completely ionizes to give H⁺ ions, the ionization of acetic acid will be affected.

### Step 2: Write the Ionization Equation
The ionization of acetic acid can be represented as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]

### Step 3: Set Up Initial Concentrations
- Initial concentration of acetic acid, \([CH₃COOH] = 0.01 \, \text{M}\)
- Initial concentration of HCl, \([H^+] = 0.1 \, \text{M}\) (since HCl completely ionizes)

### Step 4: Define Changes in Concentration
Let \(x\) be the amount of acetic acid that ionizes. After ionization:
- Concentration of acetic acid: \([CH₃COOH] = 0.01 - x\)
- Concentration of acetate ion: \([CH₃COO^-] = x\)
- Total concentration of H⁺ ions: \([H^+] = x + 0.1\)

### Step 5: Apply the Acid Dissociation Constant (Kₐ)
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:
\[ K_a = \frac{x(x + 0.1)}{0.01 - x} \]

Given \(K_a = 1.8 \times 10^{-5}\).

### Step 6: Make Assumptions
Since acetic acid is a weak acid, we can assume \(x\) is very small compared to the initial concentration of acetic acid (0.01 M). Thus:
- \(0.01 - x \approx 0.01\)
- \(x + 0.1 \approx 0.1\)

### Step 7: Simplify the Equation
Substituting the approximations into the \(K_a\) expression:
\[ 1.8 \times 10^{-5} = \frac{x(0.1)}{0.01} \]

### Step 8: Solve for \(x\)
Rearranging gives:
\[ x = \frac{1.8 \times 10^{-5} \times 0.01}{0.1} \]
\[ x = 1.8 \times 10^{-6} \]

### Step 9: Calculate Percentage Ionization
The percentage ionization is calculated using the formula:
\[ \text{Percentage Ionization} = \left( \frac{x}{\text{Initial concentration of acetic acid}} \right) \times 100 \]
\[ \text{Percentage Ionization} = \left( \frac{1.8 \times 10^{-6}}{0.01} \right) \times 100 \]
\[ \text{Percentage Ionization} = 0.018\% \]

### Final Answer
The percentage ionization of 0.01 M acetic acid in 0.1 M HCl is **0.018%**.

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