pKa Calculator for Bases: Find the pKa of a Conjugate Acid

A pKa calculator for bases estimates the pKa of a base’s conjugate acid from the base’s pKb, using pKa + pKb = pKw. Enter the base’s pKb and the temperature-dependent pKw; the calculator returns the conjugate-acid pKa, a key measure of how strongly the base accepts protons in water.

Formula

For a base B and its conjugate acid BH⁺, pKa(BH⁺) + pKb(B) = pKw. Rearranged for the calculator:

pKa(BH⁺) = pKw − pKb(B)

• pKa(BH⁺) is the conjugate acid’s pKa, dimensionless.
• pKb(B) is the base’s pKb, dimensionless.
• pKw is −log₁₀(K_w), where K_w is water’s ion-product constant; pKw is dimensionless and depends on temperature and solution conditions.

The default pKw of 14 is the conventional approximation for dilute aqueous solutions at 25 °C. The relationship follows from K_aK_b = K_w: taking negative base-10 logarithms gives pKa + pKb = pKw. The dash units indicate logarithmic quantities rather than physical units.

Worked Example

For the default inputs, the base has pKb = 4.75 and the selected aqueous pKw is 14:

pKa = pKw − pKb

pKa = 14 − 4.75 = 9.25

The calculator displays the conjugate acid’s pKa to two decimal places. This result is meaningful only for the stated pKw and the conditions under which the pKb applies.

Assumptions

• The calculation concerns a conjugate acid–base pair in water.
• The entered pKb and pKw use compatible conditions, especially temperature and solution medium.
• pKw = 14 is used as a 25 °C dilute-water approximation, not as a universal constant.
• This is a relationship between equilibrium constants; it does not calculate a sample’s pH or account for concentrations, activity coefficients, or other chemical reactions.

What pKa and pKb Mean for Bases

A base accepts a proton. In water, a simple base equilibrium can be written B + H₂O ⇌ BH⁺ + OH⁻. Its base-dissociation constant is K_b = [BH⁺][OH⁻]/[B] at equilibrium, with activities used for rigorous thermodynamic definitions. pKb is −log₁₀(K_b).

The pKa belongs to BH⁺, not directly to B: it describes how readily the conjugate acid donates a proton. A higher pKa means BH⁺ is a weaker acid and, for a paired system under the same conditions, B is a stronger base. A lower pKb also indicates a stronger base. These scales describe equilibria; they do not mean that every base with a particular pKa produces the same pH in every solution.

How to Use the Calculator

1. Find a reliable pKb for the specific base and its conjugate-acid pair. Check that the source identifies the solvent and temperature.
2. Enter that pKb in the first field. Do not enter a pH or a pKa there.
3. Enter the appropriate pKw in the second field. For a standard aqueous estimate at 25 °C, 14 is commonly used.
4. Read the displayed result as the pKa of the conjugate acid. Use it to compare acid–base equilibria under compatible conditions.

For example, ammonia’s conjugate acid is ammonium, NH₄⁺. Using a commonly tabulated pKb of about 4.75 for ammonia and pKw = 14 gives pKa ≈ 9.25 for ammonium. Published values may differ slightly with data source, temperature, and conventions. The example is an illustration of the arithmetic, not a substitute for checking a source appropriate to a particular experiment.

Choosing Values and Reading the Result

Use pKb and pKw values that refer to the same solvent and temperature. A table value measured or calculated under one set of conditions may not transfer exactly to another. In particular, pKw changes with temperature; 14 is a convenient rounded value for dilute water around 25 °C, not an exact value at all temperatures.

pKa is logarithmic. A difference of one pKa unit corresponds to a factor of ten in K_a, not a small linear change. Because pKa and pKb have no units, the result should not be labeled in mol/L. Reporting extra decimal places does not make uncertain input data more precise: round the answer in line with the reliability of the source values.

Some references report pKa directly for a conjugate acid, while others list pKb for its base. If a trustworthy pKa is already available, use it rather than converting back and forth. This calculator is most useful when the source supplies pKb and you need the corresponding conjugate-acid pKa.

Common Errors and Limits

• Confusing the species: pKa is for the conjugate acid BH⁺; pKb is for the base B. The calculator returns the former.
• Using the wrong operation: subtract pKb from pKw. Adding the numbers or calculating pKw − pKa when pKb is the input answers a different question.
• Treating pKw as always 14: this is an approximation tied to ordinary dilute water near 25 °C. Use a suitable value for other temperatures or conditions.
• Mixing media: aqueous values should not be combined casually with values measured in another solvent. Solvent effects can substantially alter acid–base equilibria.
• Interpreting pKa as pH: pKa is an equilibrium property; pH depends on the composition and concentration of a particular solution.

The simple relation assumes a matching conjugate pair and a consistent equilibrium convention. At appreciable ionic strength, activities differ from concentrations, and tabulated conditional values can depend on the measurement medium. Polyprotic substances have multiple acid–base steps and therefore multiple pKa values; identify the specific protonation step before using a value. The calculator does not determine which form predominates at a given pH or model a full buffer system.

Frequently Asked Questions

How do you calculate pKa from pKb for a base?
Subtract the base’s pKb from pKw: pKa of the conjugate acid = pKw − pKb. For dilute water near 25 °C, pKw is commonly approximated as 14.

Is pKa the same as pKb?
No. pKa describes an acid’s proton-donating equilibrium, while pKb describes a base’s proton-accepting equilibrium. For a conjugate acid–base pair in water, their sum is pKw.

Does a stronger base have a higher pKa?
A stronger base generally has a conjugate acid with a higher pKa and has a lower pKb. This comparison is valid only when the values refer to compatible conditions and the corresponding conjugate pair.

Is pKw always 14?
No. Fourteen is a useful approximate value for dilute water at about 25 °C. Water’s ion product varies with temperature, and solution conditions can affect reported equilibrium values.

Can I use pH as the pKb input?
No. pH describes the hydrogen-ion activity of a solution, whereas pKb is an equilibrium constant expressed on a logarithmic scale. Enter a pKb value from an appropriate reference.

Can the calculator find a base’s pKa directly?
Strictly, pKa refers to an acid, so this calculation returns the pKa of the base’s conjugate acid. It does not calculate solution pH, and the base itself may have several protonation equilibria.

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in pb | Base pKb | - | 4.75 | -
in pw | Water pKw | - | 14 | 0
out pa | Conjugate-acid pKa | - | pw - pb | 2