4.76
1
4.76
50
%
50
%
4.76
1
4.76
50
%
50
%
The Henderson-Hasselbalch Calculator applies the most important equation in acid-base chemistry and buffer science: pH = pKa + log₁₀([A⁻]/[HA]). This equation relates the pH of a buffer solution to the pKa of the weak acid and the ratio of its conjugate base to acid concentrations. Named after Lawrence Joseph Henderson and Karl Albert Hasselbalch, this equation is indispensable in biochemistry, pharmacology, clinical medicine, and environmental science. This calculator operates in three modes: calculate pH from pKa and concentrations, find the required [A⁻]/[HA] ratio for a target pH, or determine pKa from measured pH and known concentrations. It also computes the percent dissociation, showing what fraction of the acid exists in deprotonated form.
The Henderson-Hasselbalch equation is derived from the Ka equilibrium expression:
Ka = [H⁺][A⁻] / [HA]
Taking -log₁₀ of both sides:
pH = pKa + log₁₀([A⁻] / [HA])
This equation has three key implications:
1. When [A⁻] = [HA] (ratio = 1), pH = pKa. This is the half-equivalence point in a titration and the point of maximum buffer capacity.
2. When [A⁻] > [HA] (ratio > 1), pH > pKa — the solution is more basic than the pKa.
3. When [A⁻] < [HA] (ratio < 1), pH < pKa — the solution is more acidic than the pKa.
The percent dissociation is calculated as: % = [A⁻] / ([A⁻] + [HA]) × 100 = ratio / (1 + ratio) × 100. At pH = pKa, this is exactly 50%. The equation assumes that equilibrium concentrations approximate initial concentrations (valid for buffers where Ka is small relative to the concentrations) and that activity coefficients are approximately 1 (valid at low ionic strength).
The pH output gives the expected solution pH based on the buffer composition. If the calculated pH differs significantly from pKa (by more than ±1), the buffer is near the edge of its effective range. The [A⁻]/[HA] ratio quantifies the balance between conjugate base and acid — ratios between 0.1 and 10 (pH within ±1 of pKa) define the effective buffer range. The percent dissociated indicates the acid-base balance: 50% at the pKa, approaching 100% at pH >> pKa, and approaching 0% at pH << pKa.
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With pKa = 4.76, a [acetate]/[acetic acid] ratio of 1.74 gives pH ≈ 5.0. About 63.5% of the total acetic acid is in the dissociated acetate form.
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To make a phosphate buffer at pH 7.4 (pKa₂ = 7.2), the [HPO₄²⁻]/[H₂PO₄⁻] ratio must be ~1.58. Use about 1.58 parts dibasic to 1 part monobasic phosphate.
The equation is approximate and fails when: (1) the acid or base is strong (pKa < 1 or > 13), (2) concentrations are very dilute (< 10⁻³ M) where water autoionization matters, (3) the solution has high ionic strength affecting activity coefficients, or (4) the ratio is extreme (> 100 or < 0.01). In these cases, exact equilibrium calculations are needed.
A buffer works effectively within pH = pKa ± 1, corresponding to [A⁻]/[HA] ratios between 0.1 and 10. Outside this range, one component is nearly depleted, and the buffer cannot resist pH changes effectively. Maximum buffer capacity occurs at pH = pKa.
Yes. For a base B and its conjugate acid BH⁺: pOH = pKb + log₁₀([B]/[BH⁺]), or equivalently pH = 14 - pKb - log₁₀([B]/[BH⁺]). Alternatively, use pKa of BH⁺ directly: pH = pKa(BH⁺) + log₁₀([B]/[BH⁺]).
The Henderson-Hasselbalch equation predicts drug ionization at different body pH values. Un-ionized drugs cross cell membranes more easily. For a weak acid drug in the stomach (pH 1.5), most of the drug is un-ionized and readily absorbed. In blood (pH 7.4), the same drug may be mostly ionized and unable to cross into tissues.
In a titration, the half-equivalence point is reached when exactly half the acid has been neutralized: [A⁻] = [HA]. At this point, log₁₀(1) = 0, so pH = pKa. This provides a simple experimental method to determine pKa — just titrate to halfway and read the pH.
Choose a weak acid with pKa within 1 unit of your target pH. Calculate the required ratio: [A⁻]/[HA] = 10^(pH - pKa). Then prepare solutions with that concentration ratio. For example, for pH 7.4 using phosphate (pKa₂ = 7.2): ratio = 10^(0.2) ≈ 1.58.
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