About

Miscalculating pH by even 0.5 units represents a tenfold error in hydrogen ion concentration. In pharmaceutical compounding, wastewater treatment, or analytical chemistry, that magnitude of error causes batch rejection, regulatory violation, or equipment corrosion. This calculator solves the equilibrium expressions for strong acids, strong bases, weak acids (via the quadratic form of the K_a expression), weak bases, polyprotic systems with sequential dissociation constants, and buffer solutions using the Henderson-Hasselbalch equation. Temperature dependence is handled through the van't Hoff relationship applied to K_w, which shifts from 1.01 × 10⁻¹⁴ at 25°C to 2.92 × 10⁻¹⁴ at 37°C. The tool assumes ideal dilute solutions and does not correct for ionic strength above 0.1 M. Results should be cross-checked against experimental measurement for critical applications.

Formulas

For a strong acid with concentration C, complete dissociation yields:

pH = −log₁₀(C)

For a weak acid with acid dissociation constant K_a, the equilibrium expression K_a = x² ÷ (C − x) is solved via the quadratic formula:

x = −K_a + √K_a² + 4K_aC2

Where x = [H⁺], and pH = −log₁₀(x).

The Henderson-Hasselbalch equation for buffer solutions:

pH = pK_a + log₁₀([A⁻][HA])

Where pK_a = −log₁₀(K_a), [A⁻] is conjugate base concentration, [HA] is weak acid concentration.

The relationship between pH and pOH depends on temperature through the ion product of water:

pH + pOH = pK_w

Where K_w at temperature T is computed from K_w(25°C) = 1.01 × 10⁻¹⁴ using the van't Hoff approximation with ΔH = 55.8 kJ/mol.

Reference Data

Substance	Formula	Type	K_a or K_b	pK_a or pK_b
Hydrochloric Acid	HCl	Strong Acid	~10⁷	−7
Sulfuric Acid	H₂SO₄	Strong Acid (1st)	~10³	−3
Nitric Acid	HNO₃	Strong Acid	~10¹	−1.4
Acetic Acid	CH₃COOH	Weak Acid	1.76 × 10⁻⁵	4.754
Formic Acid	HCOOH	Weak Acid	1.77 × 10⁻⁴	3.752
Hydrofluoric Acid	HF	Weak Acid	6.76 × 10⁻⁴	3.17
Benzoic Acid	C₆H₅COOH	Weak Acid	6.46 × 10⁻⁵	4.19
Carbonic Acid (1st)	H₂CO₃	Weak Polyprotic	4.3 × 10⁻⁷	6.37
Carbonic Acid (2nd)	H₂CO₃	Weak Polyprotic	4.7 × 10⁻¹¹	10.33
Phosphoric Acid (1st)	H₃PO₄	Weak Polyprotic	7.11 × 10⁻³	2.148
Phosphoric Acid (2nd)	H₃PO₄	Weak Polyprotic	6.32 × 10⁻⁸	7.199
Phosphoric Acid (3rd)	H₃PO₄	Weak Polyprotic	4.49 × 10⁻¹³	12.35
Citric Acid (1st)	C₆H₈O₇	Weak Polyprotic	7.4 × 10⁻⁴	3.13
Citric Acid (2nd)	C₆H₈O₇	Weak Polyprotic	1.7 × 10⁻⁵	4.76
Citric Acid (3rd)	C₆H₈O₇	Weak Polyprotic	4.0 × 10⁻⁷	6.40
Oxalic Acid (1st)	H₂C₂O₄	Weak Polyprotic	5.9 × 10⁻²	1.23
Oxalic Acid (2nd)	H₂C₂O₄	Weak Polyprotic	6.4 × 10⁻⁵	4.19
Ascorbic Acid (1st)	C₆H₈O₆	Weak Acid	7.9 × 10⁻⁵	4.10
Hypochlorous Acid	HOCl	Weak Acid	2.9 × 10⁻⁸	7.54
Boric Acid	H₃BO₃	Weak Acid	5.8 × 10⁻¹⁰	9.24
Sodium Hydroxide	NaOH	Strong Base	~10¹⁴	−14
Potassium Hydroxide	KOH	Strong Base	~10¹⁴	−14
Calcium Hydroxide	Ca(OH)₂	Strong Base	~10¹⁴	−14
Barium Hydroxide	Ba(OH)₂	Strong Base	~10¹⁴	−14
Ammonia	NH₃	Weak Base	1.76 × 10⁻⁵	4.754
Methylamine	CH₃NH₂	Weak Base	4.38 × 10⁻⁴	3.358
Ethylamine	C₂H₅NH₂	Weak Base	5.6 × 10⁻⁴	3.25
Dimethylamine	(CH₃)₂NH	Weak Base	5.4 × 10⁻⁴	3.27
Pyridine	C₅H₅N	Weak Base	1.7 × 10⁻⁹	8.77
Aniline	C₆H₅NH₂	Weak Base	4.3 × 10⁻¹⁰	9.37

Frequently Asked Questions

The autoionization constant of water (K_w) is temperature-dependent. At 25°C, K_w = 1.01 × 10⁻¹⁴, giving neutral pH = 7.0. At 37°C (body temperature), K_w ≈ 2.4 × 10⁻¹⁴, so neutral pH shifts to about 6.81. This calculator adjusts K_w using the van't Hoff equation with an enthalpy of ionization of 55.8 kJ/mol.

The approximation x = √K_a ⋅ C assumes x << C. The conventional threshold is K_a ÷ C < 0.05. For a 0.001 M solution of acetic acid (K_a = 1.76 × 10⁻⁵), the ratio is 0.018, which is acceptable. But for HF at the same concentration (K_a = 6.76 × 10⁻⁴), the ratio is 0.68, requiring the full quadratic. This calculator always solves the full quadratic to avoid silent errors.

The Henderson-Hasselbalch equation pH = pK_a + log₁₀([A⁻] ÷ [HA]) is most accurate when the ratio [A⁻] ÷ [HA] falls between 0.1 and 10, corresponding to pH within ±1 of pK_a. Outside this range, buffer capacity drops sharply and the solution no longer resists pH change effectively. Maximum buffer capacity occurs when [A⁻] = [HA], i.e., pH = pK_a.

The acid dissociation constant K_a quantifies an acid's tendency to donate a proton. The base dissociation constant K_b quantifies a base's tendency to accept a proton. For a conjugate acid-base pair at a given temperature, K_a ⋅ K_b = K_w. At 25°C, this means pK_a + pK_b = 14. The calculator uses this relationship to convert between K_a and K_b when computing weak base pH.

Yes. Polyprotic acids dissociate in stages, each with its own K_a. For phosphoric acid: K_a1 = 7.11 × 10⁻³, K_a2 = 6.32 × 10⁻⁸, K_a3 = 4.49 × 10⁻¹³. Since successive K_a values differ by roughly 10⁵, the first dissociation dominates and subsequent steps contribute negligibly to [H⁺]. The calculator solves each stage sequentially and sums contributions, which is valid when K_a1 >> K_a2.

Above approximately 0.1 M, ion-ion interactions become significant and activities diverge from concentrations. The Debye-Hückel limiting law estimates activity coefficients as log₁₀(γ) = −0.509 ⋅ z² ⋅ √I, where I is ionic strength and z is ion charge. This calculator assumes ideal behavior (activity coefficients of 1). For concentrated solutions, expect deviations of 0.1 to 0.5 pH units.