The hydrogen ion concentration of 0.1 M solution of acetic acid, which is 20% dissociated, is

Options

A. 0.02 M
B. 2 M
C. 0.2 M
D. 0.002 M

Answer

To find the hydrogen ion concentration of a 0.1 M solution of acetic acid that is 20% dissociated, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Concentration of acetic acid (C) = 0.1 M
- Degree of dissociation (α) = 20% = 20/100 = 0.2

2. **Write the Dissociation Reaction:**
- The dissociation of acetic acid (CH₃COOH) can be represented as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]

3. **Set Up the Initial and Equilibrium Concentrations:**
- Initially (before dissociation):
- [CH₃COOH] = C = 0.1 M
- [CH₃COO⁻] = 0
- [H⁺] = 0
- At equilibrium (after dissociation):
- [CH₃COOH] = C(1 - α) = 0.1(1 - 0.2) = 0.1 × 0.8 = 0.08 M
- [CH₃COO⁻] = Cα = 0.1 × 0.2 = 0.02 M
- [H⁺] = Cα = 0.1 × 0.2 = 0.02 M

4. **Calculate the Hydrogen Ion Concentration:**
- From the equilibrium expression, the concentration of hydrogen ions [H⁺] is given by:
\[ [H^+] = Cα = 0.1 \times 0.2 = 0.02 \text{ M} \]

5. **Final Answer:**
- The hydrogen ion concentration of the solution is **0.02 M**.