Acids, Bases and pH: Definitions, Calculations and Buffers

The three definitions

Ammonia shows why the broader definitions matter: NH₃ has no OH⁻, so Arrhenius cannot call it a base, but it accepts a proton, so Brønsted–Lowry can. BF₃ has no proton to donate at all, yet accepts an electron pair — a Lewis acid.

Conjugate pairs

• •An acid becomes its conjugate base when it loses a proton; a base becomes its conjugate acid when it gains one.
• •The pair differs by exactly one H⁺: HCl / Cl⁻, H₂O / OH⁻, NH₄⁺ / NH₃.
• •The stronger the acid, the weaker its conjugate base. Cl⁻ is a negligible base because HCl is a strong acid.
• •Amphoteric species act as either: water is the standard example, and HCO₃⁻ is the one exams prefer.

The calculations

• •pH = −log[H⁺] and [H⁺] = 10^(−pH).
• •pOH = −log[OH⁻], and at 25 °C, pH + pOH = 14.
• •Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.
• •Weak acid: Ka = [H⁺][A⁻] / [HA]; pKa = −log Ka. A larger Ka (smaller pKa) means a stronger acid.
• •For a weak acid of concentration c, [H⁺] ≈ √(Ka·c) when dissociation is under about 5%.
• •Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]).

Strong vs weak — and why it is not concentration

Strength is how completely an acid dissociates; concentration is how much of it is dissolved. A dilute solution of a strong acid and a concentrated solution of a weak acid can have the same pH.

• •Strong acids to know: HCl, HBr, HI, HNO₃, H₂SO₄ (first proton), HClO₄.
• •Strong bases: the group 1 hydroxides, plus Ca(OH)₂, Sr(OH)₂ and Ba(OH)₂.
• •Everything else is weak: acetic acid, carbonic acid, ammonia, most organic acids and bases.

Buffers

A buffer resists pH change because it holds a weak acid and its conjugate base in the same solution: added H⁺ is mopped up by the base, added OH⁻ by the acid.

Buffering is most effective when pH is within about one unit of the pKa, and best of all when [A⁻] = [HA], where pH equals pKa exactly.

Blood is buffered by the carbonic acid / bicarbonate pair and is held near pH 7.4.

Titration in one paragraph

At the equivalence point the moles of acid and base are equal — which does not mean pH 7. Strong acid with strong base gives pH 7; weak acid with strong base gives a basic equivalence point (the conjugate base remains); strong acid with weak base gives an acidic one. The half-equivalence point is the useful one to recognise: there pH = pKa.

Flashcards

Tap a card to reveal the answer.

• Brønsted–Lowry acid?⌄

  A proton (H⁺) donor.

• Lewis base?⌄

  An electron-pair donor.

• What is the conjugate base of H₂SO₄?⌄

  HSO₄⁻ — the acid minus one proton.

• pH formula⌄

  pH = −log[H⁺]; equivalently [H⁺] = 10^(−pH).

• Value of Kw at 25 °C⌄

  1.0 × 10⁻¹⁴ = [H⁺][OH⁻].

• Henderson–Hasselbalch equation⌄

  pH = pKa + log([A⁻]/[HA]).

• pH of 0.01 M HCl⌄

  2 — HCl is strong, so [H⁺] = 0.01 M and pH = −log(10⁻²).

• Difference between strong and concentrated⌄

  Strong describes complete dissociation; concentrated describes how much solute is present.

• When does a buffer work best?⌄

  Within roughly one pH unit of the pKa; ideally at equal concentrations of acid and conjugate base.

• pH at the half-equivalence point⌄

  pH = pKa, because [HA] = [A⁻] there.

• Name an amphoteric species⌄

  Water, or HCO₃⁻ — each can donate or accept a proton.

• Which is the stronger acid: pKa 3.2 or pKa 4.8?⌄

  pKa 3.2 — a lower pKa means a larger Ka and more dissociation.

Practice quiz

Answer first, then open the explanation.

1. 1. What is the pH of a 0.001 M solution of HCl?

   • A. 1
   • B. 2
   • C. 3
   • D. 11
   Show answer

   C. 3
   HCl dissociates completely, so [H⁺] = 10⁻³ M and pH = 3.

2. 2. The conjugate acid of NH₃ is:

   • A. NH₂⁻
   • B. NH₄⁺
   • C. N₂H₄
   • D. NH₃OH
   Show answer

   B. NH₄⁺
   Gaining one proton turns ammonia into the ammonium ion.

3. 3. A solution has pOH = 4.5 at 25 °C. Its pH is:

   • A. 4.5
   • B. 7
   • C. 9.5
   • D. 14
   Show answer

   C. 9.5
   pH = 14 − pOH at 25 °C.

4. 4. Which definition is needed to classify BF₃ as an acid?

   • A. Arrhenius
   • B. Brønsted–Lowry
   • C. Lewis
   • D. None — it is a base
   Show answer

   C. Lewis
   BF₃ has no proton to donate but accepts an electron pair, which is the Lewis definition.

5. 5. Titrating acetic acid with NaOH gives an equivalence point that is:

   • A. Acidic
   • B. Neutral
   • C. Basic
   • D. Impossible to predict
   Show answer

   C. Basic
   The solution at equivalence contains acetate, a weak base, so the pH is above 7.

6. 6. A buffer is made with equal concentrations of an acid (pKa 4.76) and its conjugate base. Its pH is:

   • A. 4.76
   • B. 7.00
   • C. 9.24
   • D. Depends on the concentrations
   Show answer

   A. 4.76
   Henderson–Hasselbalch: log(1) = 0, so pH = pKa.

7. 7. Which statement is true?

   • A. A concentrated weak acid always has a lower pH than a dilute strong acid
   • B. Strength and concentration are independent properties
   • C. All strong acids have pH 1
   • D. Weak acids do not dissociate at all
   Show answer

   B. Strength and concentration are independent properties
   Strength is the degree of dissociation; concentration is how much is dissolved. Either can dominate the resulting pH.