OpenSpecEngineering

Finds the pH of a buffer made of a weak acid and its conjugate base, or of a weak monoprotic acid or base on its own in water. Chemists, lab technicians and water treatment staff use it to design a buffer recipe or to predict the pH of a dilute acid or base.

Equations

For a buffer, the page uses the Henderson–Hasselbalch equation [1], [2]:

pH = pK_a + log₁₀([A⁻]/[HA])

[A⁻] and [HA] are the concentrations of the conjugate base and the weak acid as made up, in mol/L. pK_a = −log₁₀K_a, where K_a is the acid dissociation constant.

For a weak acid alone, the page solves the charge balance for x = [H⁺]:

x = K_a·C/(K_a + x) + K_w/x

C is the analytical concentration, the total acid added per liter. K_w = 10⁻¹⁴ is the ion product of water at 25 °C. The last term keeps water’s own ions, so a very dilute acid never comes out basic. For a weak base the page uses the same equation with x = [OH⁻] and K_b = K_w/K_a in place of K_a. The fraction dissociated is K_a/(K_a + x).

Inputs

• Acid / Buffer Pair fills pK_a at 25 °C and zero ionic strength from Harris, App. G [1]. Choose Custom to type it.
• pK_a is always for the acid form. For a weak base such as ammonia, enter the pK_a of its conjugate acid, ammonium (9.245).

Limits and common mistakes

• A buffer works best within one pH unit of its pK_a. The Buffer note flags a ratio outside that band.
• Henderson–Hasselbalch uses the concentrations as made up. Below about 0.001 mol/L, or at a ratio far from 1, the acid’s own dissociation shifts them and the equation drifts.
• The page uses concentrations, not activities. At real ionic strengths a measured pH can differ by about 0.1, so adjust a buffer with a pH meter.
• For a polyprotic acid, choose the pK_a of the pair you actually have. A phosphate buffer near pH 7 uses pK_a2.
• K_w and the listed pK_a values are for 25 °C. Both change with temperature.

Worked example

A lab needs an acetate buffer for an assay. The recipe has 0.15 mol/L sodium acetate and 0.05 mol/L acetic acid. What pH will it give?

1. Choose System Buffer (weak acid + conjugate base).
2. Choose Acid / Buffer Pair Acetic acid / acetate: 4.756. The pKa field fills in 4.756.
3. Enter [A⁻] conjugate base 0.15 and [HA] weak acid 0.05.
4. Press Solve. The Solution shows: Ka: 1.75388e-5
   Ratio [A⁻]/[HA]: 3
   pH: 5.23312
   pOH: 8.76688
   Buffer note: Within ±1 pH of pKa — effective buffering

Check by hand: log₁₀3 = 0.477, so pH = 4.756 + 0.477 = 5.233. A 3:1 ratio of base to acid should put the pH about half a unit above pK_a, and it does.