pH and Hydrogen Ion Concentration Calculator

pH and Acid-Base Chemistry Guide

What's the key thing to understand about The pH Scale?

pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. The scale runs 0–14 at 25°C: pH < 7 is acidic, pH = 7 is neutral (pure water at 25°C), pH > 7 is alkaline. Each unit change represents a 10-fold change in [H⁺]: pH 3 has 10× more H⁺ than pH 4, and 100× more than pH 5. Lemon juice ≈ pH 2. Black coffee ≈ pH 5. Pure water pH 7. Baking soda pH 9. Bleach pH 12. Human blood is maintained at pH 7.35–7.45 — outside this range is life-threatening.

What's the key thing to understand about Converting pH and [H⁺]?

From pH to [H⁺]: [H⁺] = 10^(−pH). pH 3 → [H⁺] = 10⁻³ = 0.001 mol/L. pH 7 → [H⁺] = 10⁻⁷ mol/L. From [H⁺] to pH: pH = −log₁₀[H⁺]. [H⁺] = 0.01 → pH = −log(0.01) = −(−2) = 2. The ionic product of water: Kw = [H⁺][OH⁻] = 1×10⁻¹⁴ at 25°C. This means pH + pOH = 14. If pH = 4, then pOH = 10, [OH⁻] = 10⁻¹⁰ mol/L. Strong acids fully dissociate: 0.01 mol/L HCl → [H⁺] = 0.01 mol/L → pH = 2.

What's the key thing to understand about Buffer Solutions?

A buffer resists pH change when small amounts of acid or alkali are added. Composed of a weak acid and its conjugate base (or weak base and conjugate acid). Example: ethanoic acid/sodium ethanoate buffer. Biological importance: blood is buffered at pH 7.4 by the carbonic acid/bicarbonate system. CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻. The Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]) — used to calculate buffer pH and design buffers for specific pH values in lab work.

What should I know about Indicators and pH Measurement?

Indicators are weak acids that change colour when they donate or accept a proton — the colour depends on the ratio of acid to conjugate base form. Litmus: red in acid (pH < 7), blue in alkali. Universal indicator: continuous colour spectrum from red (pH 1) through green (pH 7) to purple (pH 14). Phenolphthalein: colourless below pH 8.3, pink above — used in alkaline endpoint titrations. Methyl orange: red below pH 3.1, yellow above pH 4.4 — used in acid endpoint titrations. For precision measurement beyond what an indicator's colour change can offer, a calibrated pH meter with a glass electrode gives a direct numerical reading accurate to about ±0.01 pH units, and is the standard method wherever precise pH values (rather than just crossing a known threshold) are needed.

What's the difference between Strong and Weak Acid/Base pH Calculations?

For a strong acid or base, the stated concentration converts directly to [H+] or [OH-] because dissociation is essentially complete — 0.01 mol/L HCl gives [H+] = 0.01 mol/L exactly, so pH = 2. For a weak acid such as ethanoic acid (Ka = 1.8x10^-5), only a small fraction of molecules dissociate, so [H+] must be found from the equilibrium expression. The approximation [H+] is approx sqrt(Ka x C) applies when the acid is only weakly dissociated — for 0.1 mol/L ethanoic acid, [H+] = sqrt(1.8x10^-5 x 0.1) = 1.34x10^-3 mol/L, giving pH = 2.87, nearly two full pH units higher (less acidic) than a strong acid of the same concentration. The same distinction applies to bases: strong bases (NaOH, KOH) dissociate completely while weak bases (ammonia) require the equivalent Kb-based calculation — mixing up strong and weak treatment is the most common source of error in pH problems.

What should I know about Acid Rain and Environmental pH?

Unpolluted rainwater is naturally slightly acidic, around pH 5.6, because atmospheric CO2 dissolves to form a weak carbonic acid equilibrium. Acid rain refers to rainwater significantly more acidic than this baseline, typically pH 4-4.5 or lower in polluted regions, caused mainly by sulfur dioxide and nitrogen oxides from fossil fuel combustion forming sulfuric and nitric acid. Because the pH scale is logarithmic, rain at pH 4 has roughly 40 times more H+ than natural pH 5.6 rain. Ecological effects include leaching of aluminium from soils into waterways (toxic to fish), damage to tree foliage and roots, and gradual dissolution of calcium carbonate in limestone and in the shells of aquatic organisms. Ocean acidification is a related phenomenon: dissolved atmospheric CO2 has lowered average surface ocean pH by roughly 0.1 units since pre-industrial times, corresponding to about a 30% increase in H+ concentration.

What should I know about pH of Polyprotic Acids?

Polyprotic acids like carbonic acid (H₂CO₃) or sulfuric acid (H₂SO₄) donate more than one proton, each with its own dissociation constant (Ka₁, Ka₂, …), and Ka₁ is always much larger than Ka₂. In practice, this means the solution's pH is almost always determined by the first dissociation step alone, since so little of the acid proceeds to the much weaker second ionisation that its contribution to [H⁺] is usually negligible by comparison. Only in specialised calculations — finding the concentration of the fully deprotonated species, for instance — does the second (or third) Ka value actually need to be used.

Worked Example: pH Change on Serial Dilution

For a strong acid like HCl, each 10-fold dilution lowers [H+] by exactly a factor of 10, which raises pH by exactly 1 unit, since pH = −log10[H+] and strong acids dissociate completely. Starting from 0.1M HCl (pH 1.00), diluting 10x gives 0.01M (pH 2.00), then 0.001M (pH 3.00), and so on — a clean, linear relationship. Weak acids don't behave the same way, because dilution shifts their dissociation equilibrium. For acetic acid (Ka = 1.8×10⁻⁵), using [H+] ≈ √(Ka × C): at 0.1M, [H+] = √(1.8×10⁻⁵ × 0.1) = 1.34×10⁻³, pH ≈ 2.87. Diluting 10x to 0.01M gives [H+] = √(1.8×10⁻⁶) = 4.24×10⁻⁴, pH ≈ 3.37 — a rise of only 0.5 pH units, not 1.

pH Change With Serial Dilution: Strong vs Weak Acid

The weak acid's pH rises more slowly because dilution pushes the equilibrium toward further dissociation, partially replenishing some of the H+ that simple dilution would otherwise remove — this approximation holds while the concentration stays well above Ka, and becomes less accurate at extreme dilution.

Worked Example: Finding [H+] and [OH-] From a Given pH

A solution has a measured pH of 4.0. The hydrogen ion concentration is [H+] = 10^-pH = 10^-4.0 = 0.0001 mol/L, or 1.0 × 10^-4 M. At 25°C, the ion product of water requires [H+][OH-] = 1.0 × 10^-14, so [OH-] = (1.0×10^-14) / (1.0×10^-4) = 1.0×10^-10 M. As a check, pOH = 14 - pH = 14 - 4.0 = 10.0, and indeed -log(1.0×10^-10) = 10.0, confirming the result. This solution is acidic (pH below 7), and the hydrogen ion concentration (10^-4 M) is a full ten thousand times (10^4) larger than the hydroxide ion concentration (10^-10 M) -- a ten-thousand-to-one imbalance that is typical of a moderately strong acidic solution, and a useful intuition-builder for how dramatically the two ion concentrations diverge as pH moves away from the neutral value of 7.

Molar Concentration Needed for Common pH Targets

For a strong acid or strong base that dissociates essentially completely, the required molar concentration to hit a target pH can be read directly from the [H+] = 10^-pH relationship, without needing an equilibrium constant.

This table only applies directly to strong acids and strong bases (such as HCl or NaOH), which dissociate fully in water; weak acids and bases require the equilibrium (Ka or Kb) treatment covered in the buffer-focused calculator, since only a fraction of a weak acid's molecules actually release a hydrogen ion at any given concentration.

pH Shift From Mixing Two Solutions of Different Concentration

When two acidic solutions of different concentration are mixed, the resulting [H+] is a volume-weighted average of the individual hydrogen ion concentrations, not of the pH values directly, because pH is a logarithmic scale. For example, mixing 100 mL of pH 2.0 solution ([H+] = 0.01 M) with 100 mL of pH 4.0 solution ([H+] = 0.0001 M) gives a combined [H+] of (100×0.01 + 100×0.0001) / 200 = (1.0 + 0.01)/200 = 1.01/200 ≈ 0.00505 M, so the mixed pH = -log(0.00505) ≈ 2.30. Note the result is much closer to the more concentrated solution's pH of 2.0 than to the average of 2.0 and 4.0 (which would naively suggest 3.0) -- a direct consequence of the logarithmic scale, where the more concentrated solution dominates the mixture's final [H+] far more than a simple pH average would imply.