pH Calculator

pH of common solutions at 25 degrees C

pH Calculator: Complete Guide

pH = -log10([H+]) is the measure of hydrogen ion concentration in solution. This calculator handles four common pH calculation scenarios: strong acids and bases (complete dissociation), weak acids using the full quadratic equation, weak bases via Kb, and buffer solutions using the Henderson-Hasselbalch equation.

Strong acids and bases: complete dissociation

Strong acids (HCl, HNO3, HBr, HI, H2SO4 first proton, HClO4) dissociate completely: [H+] = c. pH = -log10(c). For 0.01 M HCl: pH = -log10(0.01) = 2.00. For strong bases: [OH-] = c; pOH = -log10(c); pH = 14 - pOH. For 0.001 M NaOH: pOH = 3.00; pH = 11.00. For very dilute strong acids (below 10^-6 M), the water contribution to [H+] becomes significant -- the pH approaches 7 but never exceeds it.

Weak acids: quadratic equation solution

For weak acid HA at concentration C with Ka: Ka = [H+][A-]/[HA]. Setting x = [H+]: x^2 + Ka*x - Ka*C = 0. Exact solution: x = (-Ka + sqrt(Ka^2 + 4*Ka*C)) / 2. Simplified (if x less than 5% of C): x = sqrt(Ka*C). This calculator always uses the full quadratic for accuracy. For 0.1 M acetic acid (Ka = 1.8 x 10^-5): x = 1.34 x 10^-3 M; pH = 2.87; dissociation = 1.34%. The 5% rule check: 1.34/100 = 1.34% -- simplification valid here but the quadratic is used regardless.

Weak bases: using Kb

For weak base B at concentration C with Kb: Kb = [BH+][OH-]/[B]. By analogy with the weak acid quadratic: [OH-] = (-Kb + sqrt(Kb^2 + 4*Kb*C)) / 2. Then pOH = -log10([OH-]); pH = 14 - pOH. For 0.1 M ammonia (Kb = 1.8 x 10^-5): [OH-] = 1.34 x 10^-3; pOH = 2.87; pH = 11.13. Relationship between Ka and Kb for a conjugate pair: Ka x Kb = Kw = 1.0 x 10^-14 at 25 degrees C. So pKa + pKb = 14.

Henderson-Hasselbalch equation for buffers

For a buffer containing weak acid HA and its conjugate base A-: pH = pKa + log10([A-]/[HA]). When [A-] = [HA]: pH = pKa (the half-equivalence point). Buffer capacity is greatest within +/-1 pH unit of pKa. For an acetate buffer (pKa = 4.74) with 0.1 M acetic acid and 0.1 M sodium acetate: pH = 4.74 + log(0.1/0.1) = 4.74 + 0 = 4.74. For a 2:1 ratio of base to acid: pH = 4.74 + log(2) = 4.74 + 0.301 = 5.04.

pH of salt solutions: hydrolysis

Salts of weak acids and strong bases produce basic solutions: for sodium acetate (CH3COONa), the acetate ion hydrolyses: CH3COO- + H2O = CH3COOH + OH-. Kb(acetate) = Kw/Ka = 10^-14 / 1.8 x 10^-5 = 5.6 x 10^-10. For 0.1 M sodium acetate: [OH-] = sqrt(5.6 x 10^-10 x 0.1) = 7.48 x 10^-6; pOH = 5.13; pH = 8.87. Salts of strong acids and weak bases (e.g. NH4Cl) produce acidic solutions. Salts of strong acids and strong bases (NaCl, KBr) are neutral: pH = 7 at 25 degrees C.

Using this calculator in lab and coursework

All LazyTools chemistry calculators run entirely in your browser with no data sent to any server. Results copy with one click for lab reports and assignments. The formula is always shown for verification and citation. The mixtures and solutions suite covers all major concentration, dilution and buffer calculations -- see the related tools section for the calculators used most often alongside this one.

Solutions chemistry: key formulas at a glance

The most used solution chemistry relationships: c = n/V (molarity); w% = m_solute/m_solution x 100 (mass percent); C1V1 = C2V2 (dilution); pH = -log[H+]; pH = pKa + log([A-]/[HA]) (Henderson-Hasselbalch); osmotic pressure pi = iMRT; colligative property delta-T = K x b x i. These eight formulas connect all the concentration and equilibrium calculations in solution chemistry and appear throughout A-level, IB, AP Chemistry and undergraduate analytical chemistry courses.

pH measurement methods in the laboratory

pH is measured using a calibrated pH meter with a glass electrode, litmus paper, or universal indicator solution. Glass electrode pH meters are accurate to 0.01 pH units when calibrated with standard buffer solutions (pH 4.00, 7.00 and 10.00 at 25 degrees C). Calibration must be performed at the temperature of measurement because the Nernst equation governing electrode response is temperature-dependent. Two-point calibration using pH 7 and pH 4 (for acidic samples) or pH 7 and pH 10 (for basic samples) is standard practice. The glass membrane generates a potential difference proportional to the difference in hydrogen ion activity between the sample and the internal reference solution inside the electrode.

Activity vs concentration in pH calculations

Strictly, pH = -log10(a_H+) where a_H+ is hydrogen ion activity, not just concentration. Activity = concentration x activity coefficient (gamma). At low ionic strength below 0.01 mol/kg, gamma is approximately 1 and concentration approximates activity well. At higher ionic strengths, activity coefficients drop below 1 following the Debye-Huckel equation, so the measured pH deviates from concentration-based calculation. For physiological saline (0.15 M NaCl), gamma_H+ is approximately 0.76. For most academic and routine purposes, concentration substitutes for activity. This calculator uses concentration throughout, which is correct for dilute solutions and a good approximation up to approximately 0.1 M ionic strength.

Polyprotic acids: H2SO4, H3PO4 and H2CO3

Polyprotic acids donate more than one proton. Sulfuric acid H2SO4 has a complete first dissociation (strong acid) and Ka2 = 0.012 for the second. For 0.01 M H2SO4, the second dissociation adds approximately 0.00093 M H+, giving total [H+] approximately 0.01093 M and pH approximately 1.96 rather than exactly 2.00. Phosphoric acid H3PO4 has pKa1 = 2.12, pKa2 = 7.20 and pKa3 = 12.37. The pKa2 = 7.20 is the basis of the physiological phosphate buffer (pH 7.2). Carbonic acid has pKa1 = 6.35 and pKa2 = 10.33. The bicarbonate buffer system (CO2/HCO3-, pKa = 6.1 for the physiological system including CO2 equilibrium) maintains blood pH 7.35 to 7.45 in concert with lung regulation of CO2 partial pressure.

pH in biological and industrial systems

Blood is maintained at pH 7.35 to 7.45 by bicarbonate, plasma proteins and haemoglobin buffers. Gastric acid: pH 1.5 to 3.5 (approximately 0.1 M HCl). Lysosomes: pH 4.5 to 5.0 for acid hydrolase activity. Urine: pH 4.5 to 8.5. Enzyme activity is strongly pH-dependent: pepsin optimal at pH 1.5 to 2.0; amylase at 6.7 to 7.0; trypsin at 7.0 to 8.0; alkaline phosphatase at 8.0 to 10.0. In fermentation, pH is monitored and controlled throughout the process; lactic acid bacteria optimally produce lactic acid at pH 5.5 to 6.5. In electroplating, water treatment and food manufacture, pH control is a critical process parameter affecting product quality, regulatory compliance and equipment corrosion rates.

Calculating pH in mixed solutions and neutralisation reactions

When a strong acid and strong base are mixed, the pH depends on which is in excess. If acid is in excess: [H+]_excess = (n_acid - n_base) / V_total; pH = -log10([H+]_excess). If base is in excess: [OH-]_excess = (n_base - n_acid) / V_total; pOH = -log10([OH-]_excess); pH = 14 - pOH. At the equivalence point (equal moles of acid and base): pH = 7.00 for strong acid-strong base titrations at 25 degrees C. Example: mix 25 mL of 0.1 M HCl with 20 mL of 0.1 M NaOH. Moles HCl = 0.0025; moles NaOH = 0.0020. Excess HCl = 0.0005 mol in total volume 45 mL. [H+] = 0.0005/0.045 = 0.0111 M. pH = -log10(0.0111) = 1.95. For weak acid-strong base mixtures: before the equivalence point, a buffer region exists and pH = pKa + log([A-]/[HA]) using the Henderson-Hasselbalch equation. At the equivalence point: all acid converted to conjugate base; pH determined by hydrolysis of the salt (basic for weak acid salt).

pH and enzyme kinetics: practical implications

Every enzyme has a characteristic pH optimum at which activity is maximal. Departure from this optimum by as little as 0.5 pH units can reduce activity by 50% or more. The pH affects the ionisation state of amino acid residues in the active site (particularly histidine with pKa approximately 6, aspartate and glutamate with pKa approximately 4, lysine and arginine with pKa approximately 10) as well as the ionisation of the substrate itself. Pepsin (optimum pH 1.5-2.0) is active in gastric acid but irreversibly denatured above pH 6. Trypsin (optimum pH 7.5-8.0) is activated in the small intestine after secretion from the pancreas. Alkaline phosphatase (optimum pH 8.0-10.0) is measured in clinical blood tests as a marker of liver and bone disease. In industrial fermentation, maintaining the correct pH throughout the fermentation process (typically controlled within 0.1 pH units by automated addition of acid or base) is critical for yield and product quality. These considerations make accurate pH calculation and measurement a central skill in biochemistry, biotechnology and clinical science.

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