Acetic acid has a dissociation constant of `1.8xx10^(-5)`. Calculate the pH value of the decinormal solution of acetic acid.

Answer

To calculate the pH of a decinormal (0.1 M) solution of acetic acid (CH₃COOH) with a dissociation constant (Kₐ) of 1.8 x 10^(-5), we can follow these steps:

### Step 1: Write the dissociation equation of acetic acid
Acetic acid dissociates in water as follows:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]

### Step 2: Set up the expression for the dissociation constant (Kₐ)
The expression for the dissociation constant (Kₐ) is given by:
\[ K_a = \frac{[\text{CH}_3\text{COO}^-][\text{H}^+]}{[\text{CH}_3\text{COOH}]} \]

### Step 3: Define initial concentrations and changes
Let the initial concentration of acetic acid be 0.1 M. At equilibrium, if \( x \) is the concentration of \( \text{H}^+ \) ions produced, we can write:
- Initial concentration of CH₃COOH = 0.1 M
- Change in concentration of CH₃COOH = -x
- Change in concentration of CH₃COO⁻ = +x
- Change in concentration of H⁺ = +x

At equilibrium:
- [CH₃COOH] = 0.1 - x
- [CH₃COO⁻] = x
- [H⁺] = x

### Step 4: Substitute into the Kₐ expression
Substituting these values into the Kₐ expression gives:
\[ K_a = \frac{x \cdot x}{0.1 - x} = \frac{x^2}{0.1 - x} \]

### Step 5: Assume x is small compared to 0.1 M
Since Kₐ is small, we can assume that \( x \) is negligible compared to 0.1 M, thus:
\[ K_a \approx \frac{x^2}{0.1} \]

### Step 6: Solve for x
Substituting the value of Kₐ:
\[ 1.8 \times 10^{-5} = \frac{x^2}{0.1} \]
\[ x^2 = 1.8 \times 10^{-5} \times 0.1 \]
\[ x^2 = 1.8 \times 10^{-6} \]
\[ x = \sqrt{1.8 \times 10^{-6}} \]
\[ x \approx 1.34 \times 10^{-3} \, \text{M} \]

### Step 7: Calculate the pH
The concentration of H⁺ ions is approximately \( 1.34 \times 10^{-3} \, \text{M} \). The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
\[ \text{pH} = -\log(1.34 \times 10^{-3}) \]
\[ \text{pH} \approx 2.87 \]

### Final Answer
The pH of the decinormal solution of acetic acid is approximately **2.87**.

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