pH of a Weak Acid Solution
Calculate the pH of a weak acid solution using the Ka value and equilibrium expressions. Essential for understanding acid-base chemistry.
Problem Scenario
Calculate the pH of a 0.15 M solution of acetic acid (CH3COOH). The Ka of acetic acid is 1.8 x 10^-5.
Given Data
Requirements
- Write the dissociation equation
- Set up the ICE table
- Write the Ka expression
- Solve for [H+]
- Calculate pH
Solution
Step 1:
Write the dissociation equation: CH3COOH ⇌ H+ + CH3COO-
Step 2:
Set up ICE table: Initial: [CH3COOH] = 0.15 M, [H+] = 0, [CH3COO-] = 0. Change: -x, +x, +x. Equilibrium: (0.15 - x), x, x
Step 3:
Write Ka expression: Ka = [H+][CH3COO-]/[CH3COOH] = (x)(x)/(0.15 - x) = 1.8 x 10^-5
Step 4:
Check if approximation is valid: Since Ka << 0.15 (specifically, 0.15/Ka = 8333 > 100), we can assume x << 0.15, so (0.15 - x) ≈ 0.15. Then x^2/0.15 = 1.8 x 10^-5, so x^2 = 2.7 x 10^-6
Step 5:
Solve for x: x = sqrt(2.7 x 10^-6) = 1.64 x 10^-3 M = [H+]
Step 6:
Verify approximation: x/0.15 = 1.64 x 10^-3 / 0.15 = 0.011 = 1.1%, which is < 5%, so approximation is valid.
Step 7:
Calculate pH: pH = -log[H+] = -log(1.64 x 10^-3) = 2.79
Final Answer
The pH of the 0.15 M acetic acid solution is 2.79. This is acidic but much less so than a strong acid at the same concentration (which would have pH = 0.82) because acetic acid only partially dissociates.
Key Takeaways
- ✓Weak acids partially dissociate, requiring equilibrium calculations
- ✓The 5% rule determines if approximations are valid
- ✓Ka values indicate acid strength - smaller Ka means weaker acid
- ✓Always verify approximations after solving
Common Errors to Avoid
- ✗Treating weak acids like strong acids ([H+] ≠ initial concentration)
- ✗Forgetting to check if the approximation is valid
- ✗Taking the log of x instead of -log
- ✗Using Kb instead of Ka for acids
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Common questions about this problem type
When x is more than 5% of the initial concentration, the approximation fails and you need the quadratic formula. This happens when the acid is stronger (larger Ka) or more dilute.
Strong acids completely dissociate, so [H+] equals the initial acid concentration. Weak acids only partially dissociate, so we must use equilibrium calculations.