Titration Curves & Half-Equivalence Points (College Board AP® Chemistry)

Titration Curves & Half-Equivalence Points

Four Types of Acid-Base Titrations

• There are four combinations of acids and alkalis that you should know about:

  • strong acid + strong base

  • weak acid + strong base

  • weak base + strong acid

  • weak acid + weak base

Strong Acid + Strong Base

• In this example, sodium hydroxide, NaOH (aq), is being added to hydrochloric acid, HCl (aq)

HCl (aq) + NaOH (aq) → NaCl (aq) + H₂O (l)

• The pH intercept on the y-axis starts at a low pH, roughly 1, due to the relative strength of the hydrochloric acid

• As the NaOH (aq) is added, there is a gradual rise in pH until the titration approaches the equivalence point

• In this case, the pH at equivalence is 7

  • The equivalence point is in the middle of the vertical section of the pH curve

• Once all of the acid has been neutralised, the curve flattens out and continues to rise gradually

• At the end of the titration, the pH will be high due to the relative strength of the sodium hydroxide

Strong acid - strong base pH curve 

As an alkali is added the pH increases

Weak Acid + Strong Base

• In this example, strong sodium hydroxide, NaOH (aq), is being added to weak ethanoic acid, CH₃COOH (aq)

NaOH (aq) + CH₃COOH (aq) → CH₃COONa (aq) + H₂O (l)

• The pH on the intercept on the y axis starts at roughly 3 due to the relative strength of the ethanoic acid

• The initial rise in pH is steep as the neutralisation of the weak acid by the strong base is rapid

• Ethanoate ions (conjugate base to ethanoic acid) are formed which then creates a buffer

  • A buffer consists of a weak acid and its conjugate base or a weak base and its conjugate acid

• At this point, the buffer formed will resist changes in pH so the pH rises gradually as shown in the buffer region

• The half equivalence point is the stage of the titration at which exactly half the amount of weak acid has been neutralised

  • [CH₃COOH (aq)] = [CH₃COO^- (aq)]

  • At this point, it is important to note that the pK_a of the acid is equal to the pH

    • pK_a = pH at half equivalence 

• The equivalence point in a weak acid - strong base titration is above 7

Weak acid - strong base pH curve

As the alkali is added the pH increases

Weak Base + Strong Acid

• In this example, strong hydrochloric acid, HCl (aq), is being added to weak ammonia, NH₃ (aq)

NH₃ (aq) + HCl (aq) → NH₄Cl (aq)

• The pH on the intercept on the y axis starts at roughly 11 due to the relative strength of the ammonia

• The pH will fall as the ammonia begins to be neutralised and the conjugate acid, NH₄⁺ (aq), is produced

• This again creates a buffer region so the pH will only fall gradually

• The half equivalence point is the stage of the titration at which exactly half the amount of weak base has been neutralised

  • [NH₃ (aq)] = [NH₄⁺ (aq)]

  • At this point it is important to note that the pK_b of the base is equal to the pOH

    • pK_b = pOH at half equivalence 

• The pH at equivalence for a weak base-strong acid is below 7

Weak base - strong acid pH curve

As the acid is added the pH decreases

Weak Acid + Weak Base

• In this example, weak ethanoic acid, CH₃COOH (aq), is being added to weak ammonia, NH₃ (aq)

NH₃ (aq) + CH₃COOH (aq)→ CH₃COONH₄ (aq)

• The starting pH of roughly 11 for the weak base will fall as it begins to neutralise

• The change in pH for this titration is very gradual

  • Note the that the vertical section of this pH curve is not steep as with other three so the equivalence point is difficult to determine

  • Therefore this titration is not performed

• The pH at equivalence for a weak acid -weak base is roughly 7 but is difficult to determine

Weak acid - weak base pH curve

As the acid is added the pH decreases