A Brief summary of pH calculations:
1. pH = -log[H3O+]
pK = -logK
pOH = -log[OH-]
pKw = logKw = 14
lower case p means -log
2. H2O + H2O ⇆ H3O+ + OHKw = 1 x 10-14 = [H3O+][OH-]
pKw = 14
= pH + pOH
3. Common strong acids:
Common strong bases:
HCl, HBr, HI, HNO3, H2SO4, HClO4
LiOH, NaOH, KOH, Ba(OH)2, NaNH2, CH3ONa
What’s the pH of 0.1 M HCl? -log(0.1) = 1
What’s the pH of 0,1 M H2SO4? -log(0.1 x 2) = 0.7
What’s the pH of 0.1 M Ba(OH)2? pOH = -log(0.1 x 2) = 0.7. pH = 14 – 0.7 = 13.3
4. For any weak acid HA and its conjugate weak base AHA + H2O ⇆ A- + H3O+
Ka = [A- ][H3O+]/[HA] << 1
pKa = -logKa
A- + H2O ⇆ HA + OH-
Kb = [HA][OH-]/[A-] << 1
pKb = -logKb
pKa + pKb = pKw
FOR A PURE WEAK ACID IN AQUEOUS SOLUTION:
pH ≅ pKa + p[HA]
2
FOR A PURE WEAK BASE IN AQUEOUS SOLUTION:
pOH ≅ pKb + p[A-]
. .
2
remember to convert pKa to pKb and pOH to pH if that’s
what the question asks for!
FOR A MIXTURE OF A WEAK ACID AND ITS CONJUGATE BASE:
pH = pKa + log[A-]/[HA]
FOR A MIXTURE OF A WEAK ACID AND A CONJUGATE BASE
pOH = pKb + log[HA]/[A-]
pH calculations: Find the pH of any weak acid, HA, anywhere along the titration curve.
1. A pure weak acid, HA:
HA + H2O ⇄ A- + H3O+
H2O + H2O ⇄ H3O+
+
OH-
pH ≈ pKa + p[HA]
2
2. Somewhere along the curve: A mixture of HA and AHA + OH- ⇄ A- + H2O
HA + H2O ⇄ A- + H3O+
H2O + H2O ⇄ H3O+
+
OH-
Moles HAeq = moles HAstart - moles OH- added
Moles A-eq = moles OH- added
pH = pKa + log[A-]/[HA] In this case, pH = pKa + log (0.25/0.75)
3. Half-way through the titration: Equal concentrations of HA and AHA + OH- ⇄ A- + H2O
HA + H2O ⇄ A- + H3O+
H2O + H2O ⇄ H3O+
+
OH-
Moles HAeq = Moles A-eq
pH = pKa + log[A-]/[HA] = pKa + log(1) = pKa
4. Somewhere along the curve: A mixture of HA and AHA + OH- ⇄ A- + H2O
HA + H2O ⇄ A- + H3O+
H2O + H2O ⇄ H3O+
+
OH-
Moles HAeq = moles HAstart - moles OH- added
Moles A-eq = moles OH- added
pH = pKa + log[A-]/[HA] In this case, pH = pKa + log (0.75/0.25)
5. At the endpoint.
A- + H2O
PURE A-
⇄ HA + OH-
H2O + H2O ⇄ H3O+
+
OH-
Ka x Kb = Kw
pKa + pKb = pKw = 14.0
pOH = pKb + p[A-]
2
pH = pKw – pOH
[H3O+] = 10-pH
For a mixture of weak base and weak acid:
A- + H2O
⇄ HA + OH-
H2O + H2O ⇄ H3O+
+
OH-
pOH = pKb + log[HA]/[A-]
How can you spot weak acids or weak bases?
1. Weak acids/bases are not in the short list of strong acids (HCl, HBr, HI,
HNO3, HClO4, H2SO4) or strong bases (LiOH, NaOH, KOH, Ba(OH)2, CH3ONa)
2. Weak acids/bases will usually have the pKa listed. Since the Ka of a strong
acid is >> 1, (and pKa is a negative number ) it is assumed that strong acids
dissociate virtually 100% in water.