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Acids, Bases & Buffers

pKa Calculation Examples: Formulas and Worked Answers

Calculator No. 06-0131 · Updated · Formula and assumptions shown below

pKa 5.000
Acid dissociation constant Ka
0.00001
Set in the form below
You enter
Acid dissociation constant Ka
You get
pKa
Rounding
3 dp

For study and lab planning. The result follows from the numbers you enter and the formula shown. Check it against your method before you weigh, mix or dilute anything, follow the safety data sheet and your supervisor, and do not use it for clinical, dosing or medication work.

pKa calculations use the relationship pKa = −log10(Ka) to convert between an acid’s dissociation constant and its pKa. Enter either Ka or pKa to calculate the other; the examples below also show how pKa predicts the ratio of a weak acid to its conjugate base.

Formula

The calculator uses pKa = −log10(Ka). Ka is the acid dissociation constant, and pKa is its negative base-10 logarithm. In the reverse direction, Ka = 10−pKa. The calculator accepts a positive Ka and returns pKa; zero is excluded because its logarithm is undefined. Ka is conventionally dimensionless when expressed using activities relative to standard states. Introductory calculations often use concentration-based values and omit units.

Worked Example

For the calculator’s default Ka of 0.00001:

  1. Write the formula: pKa = −log10(Ka).
  2. Substitute the input: pKa = −log10(0.00001).
  3. Since 0.00001 = 10−5, pKa = −(−5) = 5.000.

This result is the pKa, rounded to three decimal places, as displayed by the calculator.

Assumptions

  • Ka is positive and is supplied for the acid and conditions of interest.
  • The logarithm is base 10, as in the standard pKa definition.
  • The simple conversion does not estimate Ka from measured concentrations or correct for non-ideal solution behavior.

Examples of Converting Ka and pKa

The sign is a frequent source of mistakes: pKa is the negative logarithm of Ka. For Ka = 1.0 × 10−5, pKa = 5. A smaller Ka gives a larger pKa and indicates a weaker acid, all else equal. Conversely, a larger Ka gives a smaller pKa and indicates a stronger acid.

  • Ka to pKa: if Ka = 1.8 × 10−5, then pKa = −log10(1.8 × 10−5) ≈ 4.745.
  • pKa to Ka: if pKa = 4.76, then Ka = 10−4.76 ≈ 1.74 × 10−5.
  • Very small Ka: if Ka = 3.2 × 10−8, pKa = −log10(3.2 × 10−8) ≈ 7.495.

These conversions do not identify which acid a value belongs to. The constant must come from a reliable reference or from an appropriate measurement, and it can depend on temperature, solvent, and the convention used to report it.

Using pKa to Estimate Acid–Base Ratios

For a weak acid written HA ⇌ H+ + A−, the Henderson–Hasselbalch equation relates pH, pKa, and the conjugate-base-to-acid ratio:

pH = pKa + log10([A−]/[HA])

Rearranging gives [A−]/[HA] = 10pH − pKa. For example, if pH is 6.00 and pKa is 5.00, the ratio is 101 = 10:1. Under the equation’s usual approximation, the conjugate base is ten times as abundant as the acid. At pH = pKa, the ratio is 1:1. One pH unit above pKa corresponds to a 10:1 ratio; one unit below corresponds to 1:10.

This ratio is not automatically the fraction of the total acid in either form. For a simple pair, the conjugate-base fraction is ratio/(1 + ratio). Thus a 10:1 ratio corresponds to 10/11, or about 90.9%, in the conjugate-base form. The Henderson–Hasselbalch relation is most useful for dilute solutions where activities can reasonably be approximated by concentrations; it may be less accurate in concentrated or strongly non-ideal mixtures.

Choosing the Right pKa and Reading the Result

Use the pKa for the particular ionization step and conditions relevant to the question. A molecule with several acidic or basic sites can have several pKa values; the value for one site should not be substituted for another. Reference values may differ slightly because of temperature, solvent, ionic strength, or measurement and rounding conventions. When comparing sources, check that they describe the same species and conditions.

For a polyprotic acid, successive protons have separate dissociation constants and pKa values. For example, the first and second ionizations of a diprotic acid are not represented by a single pKa. To calculate the distribution of all species, more information and the appropriate equilibrium equations are needed; the one-step ratio above applies to a conjugate acid–base pair.

pH and pKa are related but are not interchangeable. pKa characterizes an equilibrium under specified conditions; pH describes the hydrogen-ion activity of a particular solution. Knowing pKa alone does not tell you the solution’s pH, because concentrations and other chemical equilibria matter. For laboratory work, follow your lab method, the safety data sheet (SDS) and your supervisor. For pH or buffer work, a meter reading is the real check: temperature and ionic strength can shift pH.

Common Calculation Mistakes and Limits

  • Dropping the minus sign: for Ka = 10−5, the pKa is +5, not −5.
  • Using the wrong logarithm: pKa uses log base 10, not the natural logarithm ln.
  • Entering a pKa as though it were Ka: the two are related by a logarithm, not by a change of units.
  • Rounding too early: retain the original Ka or pKa through intermediate steps, then round the final result to a precision justified by the input.
  • Assuming a universal value: pKa is not perfectly condition-independent. Use a cited value appropriate to the solvent and temperature rather than treating a familiar textbook number as exact in every setting.

The basic calculator performs only the mathematical conversion. It cannot determine whether an input is experimentally reliable, select the correct dissociation step, or predict a real solution’s pH without composition and equilibrium information.

Frequently Asked Questions

How do I calculate pKa from Ka?
Take the base-10 logarithm of Ka and change its sign: pKa = −log10(Ka). For Ka = 1 × 10−6, pKa = 6.

How do I calculate Ka from pKa?
Use Ka = 10−pKa. If pKa is 4, then Ka = 10−4 = 0.0001.

Does a higher pKa mean a stronger acid?
No. For comparable acids under the same conditions, a lower pKa generally means a stronger acid because it corresponds to a larger Ka.

What does pH = pKa mean?
For a weak acid and its conjugate base in the Henderson–Hasselbalch relationship, pH = pKa means their concentrations are equal, so their ratio is 1:1.

Can pKa be negative?
Yes. If Ka is greater than 1 in the convention being used, −log10(Ka) is negative. A negative pKa does not mean the calculation is invalid.

Related

Formula used
in ka | Acid dissociation constant Ka | - | 0.00001 | 0
out pka | pKa | - | -log10(ka) | 3

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.

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