Calculation of pH of a 0.1M Solution of Acetic Acid

Acetic acid (CH3COOH) is a weak acid that partially dissociates in water. To calculate the pH of a 0.1M solution of acetic acid, we need to determine the concentration of H+ ions, which is related to the degree of dissociation, α.

Step 1: Write the Dissociation Equation
The dissociation equation for acetic acid is as follows:
CH3COOH ⇌ CH3COO- + H+

Step 2: Write the Equilibrium Expression
The equilibrium expression for the dissociation of acetic acid is:
K = [CH3COO-][H+] / [CH3COOH]

where K is the equilibrium constant.

Step 3: Calculate the Degree of Dissociation (α)
The degree of dissociation is given as 0.0132, which means that 0.0132 moles of acetic acid dissociate per mole of acetic acid initially present.

Step 4: Calculate the Concentrations of the Species
Since the initial concentration of acetic acid is 0.1M, the concentration of acetic acid that has dissociated is:
[CH3COOH] dissociated = α × [CH3COOH] = 0.0132 × 0.1M = 0.00132M

The concentration of acetic acid that remains undissociated is:
[CH3COOH] undissociated = [CH3COOH] initial - [CH3COOH] dissociated = 0.1M - 0.00132M = 0.09868M

The concentration of acetate ions is equal to the concentration of the dissociated acetic acid:
[CH3COO-] = [CH3COOH] dissociated = 0.00132M

Step 5: Calculate the Concentration of H+ Ions
According to the dissociation equation, the concentration of H+ ions is equal to the concentration of the dissociated acetic acid:
[H+] = [CH3COOH] dissociated = 0.00132M

Step 6: Calculate the pH
The pH is calculated using the equation:
pH = -log10[H+]

where [H+] is the concentration of H+ ions.

Plugging in the value, we get:
pH = -log10(0.00132) ≈ 2.88

Conclusion
The pH of a 0.1M solution of acetic acid, with a degree of dissociation of 0.0132, is approximately 2.88. This indicates that the solution is acidic, as the pH is less than 7. Acetic acid is a weak acid, and its pH is lower than that of a strong acid with the same concentration due to its partial dissociation.