CalcAgent

pH from Concentration Calculator

For a weak monoprotic acid HA with concentration c_Mol, Ka is defined by Ka = [H⁺][A‑]/[HA]. Assuming negligible protonation of the solvent, let x be the amount dissociated so that [H⁺] = [A‑] = x and [HA] = c_Mol–x. Substituting gives Kl = x²/(c_Mol–x), which rearranges to a quadratic: x²+Ka·x–Ka·c_Mol = 0. The physically meaningful root is x = (‑Ka + √(Ka² + 4·Ka·c_Mol))/2, yielding the hydrogen ion concentration and pH = ‑log₁₀(x). For a weak base B it follows analogous steps using Kb and solving for OH⁻; pOH is obtained from x = (‑Kb + √(Kb² + 4·Kb·c_Mol))/2, with subsequent conversion to pH via pH+pOH = 14 at 25 °C.

Select whether the solution contains a weak acid or weak base.
Enter the molar concentration of the weak acid or base in the solution. E.g., 0.01 for 10 mM.
Enter the acid dissociation constant Ka (for acids) or base dissociation constant Kb (for bases). Use the value as a dimensionless number, e.g., 1.8e-5.

What it is

The calculator determines the pH (and complementary pOH) of an aqueous solution containing a single weak acid or weak base at a known molar concentration. It does this by applying the equilibrium expression Ka = [H⁺][A‑]/[HA] for acids and Kb = [BH⁺][OH‑]/[B] for bases, then solving the quadratic equation that arises from assuming the total acid or base is split between undissociated and dissociated species. This gives an accurate estimate of [H⁺] or [OH⁻], which can be converted to pH or pOH. The result is immediately useful when designing buffers, predicting reaction rates, assessing corrosiveness or toxicity, and teaching equilibrium concepts in the laboratory.

How to use it

Enter the species type by selecting ‘Weak Acid’ or ‘Weak Base’. Input the molar concentration of your solution, then provide its acid or base dissociation constant (Ka for acids, Kb for bases). After pressing calculate, the tool will display two values: pH and pOH. For buffer design compare the desired pH to the calculated value and adjust concentrations accordingly; always verify that Ka/Kb values correspond to the temperature of your experiment.

Worked example

In this routine, we calculate the pH of a 0.010 M solution of a weak acid with Ka = 1.80×10⁻⁵. The concentration of dissociated hydrogen ions, [H⁺], is found as x = (‑Ka + √(Ka² + 4·Ka·c)) / 2. Plugging in the numbers gives x ≈ 4.153 × 10⁻⁴ M. Taking –log₁₀(x) yields pH ≈ 3.382. The corresponding hydroxide concentration is derived from Kw = [H⁺][OH⁻] ⇒ [OH⁻] = 1.0×10⁻¹⁴ / x ≈ 2.41 × 10⁻¹¹ M, giving pOH ≈ 10.618. The calculator presents these two metrics for further buffer design or reporting.

Inputs

  • Species type: 0
  • Concentration (M): 0.01
  • Concentration constant (Ka or Kb): 1.8e-05

Result

  • pH: 3.382
  • pOH: 10.618

Frequently asked questions

I get a ‘NaN’ result—what went wrong?

A negative or zero Ka/Kb was entered, which is physically impossible for a weak acid or base. Ensure you input positive values and that the units are correct.

Can I calculate pH of a mixed solution (acid + base)?

This calculator handles only single-species solutions. For mixtures you must consider each component’s contribution or use a dedicated buffer calculator.

Why does my calculated pH differ from the textbook value?

The discrepancy often arises from ignoring activity coefficients or temperature dependence of Ka/Kb. The calculator uses ideal activity (dimensionless constants), so deviations may appear in concentrated or non‑aqueous systems.

How do I use this for buffer preparation?

Determine the desired pH, choose a conjugate acid/base pair and obtain its Ka. Use the Henderson–Hasselbalch equation with your calculator’s concentration to find the ratio of base to acid that meets the target pH; then adjust concentrations accordingly.