pKa Calculator

Q: How do I calculate the pH of a weak acid solution?

For weak acid HA at concentration C, set up the equilibrium: Ka = [H+][A-]/[HA]. If C/Ka > 100, the approximation [H+] = sqrt(Ka x C) is accurate to within 5%. Otherwise, solve the exact quadratic: [H+] = (-Ka + sqrt(Ka^2 + 4 x Ka x C)) / 2. Then pH = -log10([H+]).

Frequently Asked Questions

What is pKa and what does it measure?

pKa = -log10(Ka), where Ka is the acid dissociation constant. It measures the strength of a weak acid: lower pKa = stronger acid (more dissociated at a given pH). Strong acids like HCl have pKa < 0; weak acids range from 2 (strong weak acid) to 12 (very weak acid). At pH = pKa, exactly half of the acid is dissociated.

How do I calculate the pH of a weak acid solution?

For weak acid HA at concentration C, set up the equilibrium: Ka = [H+][A-]/[HA]. If C/Ka > 100, the approximation [H+] = sqrt(Ka x C) is accurate to within 5%. Otherwise, solve the exact quadratic: [H+] = (-Ka + sqrt(Ka^2 + 4 x Ka x C)) / 2. Then pH = -log10([H+]).

What is the relationship between pKa and pKb?

For a conjugate acid-base pair: pKa + pKb = pKw = 14.00 at 25 degrees C. So if acetic acid has pKa = 4.76, its conjugate base (acetate ion) has pKb = 14.00 - 4.76 = 9.24. This means acetate is a weak base. The stronger the acid (low pKa), the weaker its conjugate base (high pKb), and vice versa.

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How This Calculator Works

This calculator converts between Ka and pKa, finds the pH of a weak acid solution from pKa and initial concentration, and reports percent dissociation. It uses the exact quadratic solution for [H+] rather than just the square-root approximation, and it tells you whether the 5% approximation rule is satisfied.

Choose a mode from the dropdown or load a preset common acid. For pH calculation, enter both the pKa and the initial molar concentration of the undissociated acid.

Ka and pKa Explained

Ka is the acid dissociation constant for the equilibrium HA = H+ + A-. It equals [H+][A-] / [HA] at equilibrium. A larger Ka means stronger acid dissociation. pKa = -log10(Ka) is the negative logarithm, so a lower pKa means a stronger acid (just as lower pH means more acidic). Strong acids have pKa below about 0; common weak acids fall between pKa 2 and 12.

Strong vs. Weak Acids

Strong acids (HCl, HBr, HI, HNO3, HClO4, H2SO4 first proton) dissociate essentially completely - Ka is very large and pKa is negative or very small. Weak acids dissociate only partially. The distinction matters for pH calculations: for strong acids, [H+] equals the initial concentration; for weak acids, you must solve the equilibrium expression.

pH of a Weak Acid Solution

The equilibrium expression x^2 + Ka*x - Ka*C0 = 0 (where x = [H+]) solves exactly to:

x = (-Ka + sqrt(Ka^2 + 4*Ka*C0)) / 2

pH = -log10(x)

The approximation assumes x is small compared to C0, giving x = sqrt(Ka * C0). This is valid when C0/Ka is greater than 100 (error less than about 0.5%). For dilute weak acid solutions or strong weak acids, use the exact quadratic result.

The 5% Rule for the Approximation

If percent dissociation ([H+] / C0 x 100) is less than 5%, the approximation is considered acceptable and x can be treated as much smaller than C0. When dissociation exceeds 5%, the quadratic solution is needed for accurate results. The 5% threshold corresponds roughly to C0/Ka greater than 400, though textbooks vary on the exact cutoff.

Conjugate Acid-Base Pairs

Every weak acid has a conjugate base (A-) with pKb = 14 - pKa (at 25 degrees C, where Kw = 1e-14). A strong acid (low pKa) has a weak conjugate base (high pKb, close to inert). A weak acid (high pKa) has a relatively strong conjugate base. This relationship governs buffer selection, hydrolysis reactions, and the behavior of salts in water. For example, sodium acetate dissolves to give acetate ion, which hydrolyzes to raise the pH because acetic acid is a weak acid (pKa 4.76, so pKb of acetate = 9.24).

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