1.12.3 - 1.12.5 Kw, Ka, pH curves

what is K_w ?

give the units

• ionic product of water

• K_w = [H⁺][OH^-]

  • units: mol² dm^-6

where is K_w derived from

• H₂O ⇌ H⁺ + OH^-

• K_c = [H⁺] [OH] / [H₂O]

• K_c [H₂O] = [H⁺] [OH]

• two constants multiplied together make one constant

• so K_c [H₂O] = K_w

why is [H₂O] not in the K_w expression?

• water is only slightly dissociated, so [H₂O] at start ≈ [H₂O] at equilibrium
  

• so [H₂O] is effectively constant, as [H₂O] is very large compared to [H⁺] and [OH^-]

what is K_w at 298 K?

10^-14

K_w in pure water

K_w = [H⁺]²

because in pure water [H⁺] = [OH^-]

why is pure water always considered neutral?

[H⁺] = [OH^-]

how does K_w and pH of water change when temperature is increased?

• water dissociation is endothermic, as bonds are broken

• increasing temperature shifts equilibrium to the RHS in the endothermic direction to oppose the temperature increase

• so [H⁺] and [OH^-] increases

• so K_w increases

• so pH decreases

  • although pH decreases, water still neutral as [H⁺] = [OH^-]

mole ratio of H₂SO₄ and H⁺

[H₂SO₄] : [H⁺] = 1 : 2

• H₂SO₄ → 2 H⁺ + SO₄^2-
  

mole ratio of Ba(OH)₂ and OH^-

[Ba(OH)₂] : [OH^-] = 1 : 2

• Ba(OH)₂ → Ba²⁺ + 2 OH^-

how does adding water to an acid affect pH?

more water = decreased [H⁺] = less acidic = pH increase

• adding water does NOT affect moles of H⁺; greater volume so lower conc

how does adding water to a base affect pH?

more water = decreased [OH^-] = less basic = pH decrease

• adding water does NOT affect moles of OH^-; greater volume so lower conc

dissociation of a weak acid in aqueous solution

HA ⇌ H⁺ + A^-
HA + H₂O ⇌ H₃O⁺ + A^-

HA = undissociated acid

A^- = conjugate base

K_a

the dissociation constant for a weak acid

• the weak acid is only slightly dissociated, so [HA] at start ≈ [HA] at equilibrium

• so [HA] is effectively constant, as [HA] is very large compared to [H⁺] and [A^-]

pK_a

-log₁₀(K_a)

pure weak acid (with nothing else reacted)

• [HA] is effectively constant, as [HA] is very large compared to [H⁺] and [A^-]

• [H⁺] = [A^-]

what does K_a tell us about the strength of a weak acid?

bigger K_a

= equilibirum on RHS

= HA dissociates more

= greater [H⁺]

= stronger acid

what does pK_a tell us about the strength of a weak acid?

smaller pK_a

= bigger K_a

= equilibirum on RHS

= HA dissociates more

= greater [H⁺]

= stronger acid

equivalence point vs end point

• equivalence point: the point in a titration when [H⁺] = [OH^-] as acid is neutralised by alkali

  • steep/vertical part of a pH titration curve

• end point: the point in a titration where we observe the indicator colour change

why do we need to calibrate the pH meter?

• over time / after storage the meter does not give accurate readings / reproducible readings

how to generate a pH titration curve

• measure and record pH of HA acid in conical flask, using a pH meter

• add alkali from the burette slowly in known small portions, e.g. 1cm³

• stir to ensure pH is uniform throughout mixture

• measure pH and volume of alkali added after each addition

• repeat

• add alkali in smaller amounts as the end point approaches, as there is a large pH change for addition of small amounts of alkali

  • smaller volumes → more accurate curve produced

• repeat until alkali in excess

why may a pH meter be washed with distilled water in between measurements?

to wash off any residual solution and prevent different solutions from contaminating each other

what are indicators?

weak acids where HA and A^- are different colours

HA ⇌ H⁺ + A^-

• at low pH, high H⁺ so equilibrium shifts left so more HA present

• at high pH, less H⁺ so equilibrium shifts right so more A^- present

pKa for an indicator

the pH at which [HA] = [A^-]

pH range over which indicator changes colour = pKa ± 1

how to select a suitable indicator for acid-alkali titration

indicator must have a colour change / pH range within the steep / vertical part of the pH titration curve, where the equivalence point occurs

phenolphthalein

• pH range = 8.20 - 10.00

• alkaline = pink

• acid and neutral = colourless

methyl orange

• pH range = 3.20 - 4.40

• acidic = red

• alkaline and neutral = yellow

half-equivalence point

exactly half of the acid has been turned into A^- / has reacted with OH^-

• [HA] = [A^-]

• therefore Ka = [H⁺] as [HA] and [A] cancel in expression

• pKa = -logKa = -log[H⁺] = pH

• pKa = pH

pH of mixture when strong acid reacts with strong base

• find excess n H⁺ or n OH^-

  • x2 diprotic mol for H⁺ mol

• find conc, using n and new total volume

• if H⁺ in excess, use -log

• if OH^- in excess, use K_w

pH of mixture when weak acid reacts with strong base

• HA + OH^- → A^- + H₂O

• find excess n HA and n A^-

• use Ka to find [H⁺]

  • volume may cancel, fine to use moles