pH of Weak Acid Calculator
Calculate the pH of weak acid solutions with step-by-step explanations, ICE table generation, and multiple input options. Perfect for chemistry students and lab work.
Weak Acid Parameters
pH Calculation Results
Error
Select an acid preset or enter Ka/pKa and concentration to calculate pH
What is pH of Weak Acids
Weak acids don't fully dissociate in water. Unlike strong acids that release all their hydrogen ions, weak acids establish an equilibrium between the undissociated acid (HA) and its ions (H⁺ and A⁻). This partial dissociation is what makes pH calculations for weak acids a bit more involved.
Vinegar is a common example—it contains acetic acid, which only about 1% dissociates in water. This is why vinegar has a pH around 2.9 rather than being extremely acidic. Understanding how weak acids behave helps in fields ranging from food science to pharmaceuticals.
Key Formulas for Weak Acid pH
Acid Dissociation Constant:
Ka = [H⁺][A⁻] / [HA]
Approximation Formula (Ka < 0.01 × C):
[H⁺] = √(Ka × C)
Quadratic Formula (when approximation fails):
x = (-Ka + √(Ka² + 4KaC)) / 2
pH Calculation:
pH = -log[H⁺]
The approximation formula works well when the acid is weak enough that its ionization doesn't significantly change the initial concentration. As a rule of thumb, if the percent ionization exceeds 5%, you should switch to the quadratic formula for accurate results.
Worked Example: Acetic Acid
Calculate the pH of a 0.10 M acetic acid solution (Ka = 1.8 × 10⁻⁵)
Step 1: Check if approximation is valid. Ka = 1.8 × 10⁻⁵, C = 0.10 M. Since Ka is much smaller than C, approximation should work.
Step 2: Apply [H⁺] = √(Ka × C) = √(1.8 × 10⁻⁵ × 0.10) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M
Step 3: Calculate pH = -log(1.34 × 10⁻³) = 2.87
Step 4: Check ionization: (1.34 × 10⁻³ / 0.10) × 100 = 1.34% ✓ (less than 5%, approximation valid)
pH Comparison Table
| Conc. (M) | Ka | [H⁺] (M) | pH | % Ion. |
|---|---|---|---|---|
| 0.10 | 1.8×10⁻⁵ | 1.34×10⁻³ | 2.87 | 1.34% |
| 0.050 | 1.8×10⁻⁵ | 9.5×10⁻⁴ | 3.02 | 1.90% |
| 0.010 | 1.8×10⁻⁵ | 4.2×10⁻⁴ | 3.38 | 4.20% |
| 0.20 | 1.8×10⁻⁵ | 1.90×10⁻³ | 2.72 | 0.95% |
| 0.001 | 1.8×10⁻⁵ | 1.34×10⁻⁴ | 3.87 | 13.4% |
| 0.15 | 1.8×10⁻⁵ | 1.64×10⁻³ | 2.78 | 1.10% |
| 0.025 | 1.8×10⁻⁵ | 6.7×10⁻⁴ | 3.17 | 2.68% |
| 0.30 | 1.8×10⁻⁵ | 2.32×10⁻³ | 2.63 | 0.77% |
| 0.40 | 1.8×10⁻⁵ | 2.68×10⁻³ | 2.57 | 0.67% |
| 0.50 | 1.8×10⁻⁵ | 3.0×10⁻³ | 2.52 | 0.60% |
| 0.005 | 1.8×10⁻⁵ | 3.0×10⁻⁴ | 3.52 | 6.00% |
| 0.002 | 1.8×10⁻⁵ | 1.9×10⁻⁴ | 3.72 | 9.49% |
| 0.10 | 6.8×10⁻⁴ | 8.25×10⁻³ | 2.08 | 8.25% |
| 0.050 | 6.8×10⁻⁴ | 5.66×10⁻³ | 2.25 | 11.3% |
| 0.10 | 1.77×10⁻⁴ | 4.21×10⁻³ | 2.38 | 4.21% |
| 0.020 | 1.77×10⁻⁴ | 1.88×10⁻³ | 2.73 | 9.41% |
| 0.10 | 6.5×10⁻⁵ | 2.55×10⁻³ | 2.59 | 2.55% |
| 0.050 | 6.5×10⁻⁵ | 1.80×10⁻³ | 2.74 | 3.61% |
| 0.10 | 4.3×10⁻⁷ | 2.07×10⁻⁴ | 3.68 | 0.21% |
| 0.010 | 4.3×10⁻⁷ | 6.56×10⁻⁵ | 4.18 | 0.66% |
| 0.10 | 4.9×10⁻¹⁰ | 7.0×10⁻⁶ | 5.15 | 0.007% |
| 0.001 | 4.9×10⁻¹⁰ | 7.0×10⁻⁷ | 6.15 | 0.07% |
| 0.10 | 1.0×10⁻³ | 9.51×10⁻³ | 2.02 | 9.51% |
Data includes: acetic acid (Ka=1.8×10⁻⁵), hydrofluoric acid (Ka=6.8×10⁻⁴), formic acid (Ka=1.77×10⁻⁴), benzoic acid (Ka=6.5×10⁻⁵), carbonic acid (Ka=4.3×10⁻⁷), hydrocyanic acid (Ka=4.9×10⁻¹⁰)
Notice how dilution affects both pH and percent ionization. As the acid becomes more dilute, pH increases (solution becomes less acidic), but the percent ionization also increases. This makes sense—there's less acid to begin with, so a larger fraction needs to dissociate to reach equilibrium.