IONIC EQUILIBRIUM
ACID & BASES
Bronsted-Lowry theory of acids & bases
acid: subs that donates hydrogen ion (or proton), H⁺(aq) in it aq sol
base: subs that accepts hydrogen ion (or proton), H⁺(aq) in it aq sol
conjugate pairs
acid gives proton > conjugate base
base accepts proton > conjugate acid
Acid / base strength
strength of acid/base measured in terms of hydrogen/hydroxide ion conc
strength can be expressed in pH or acid/base dissociation constant, K_a/K_b
strong acid/base: high degree of ionisation of molecule > high conc of H⁺/OH^-
weak acid/base: low degree of ionisation (partially ionised) of molecule > high conc of H⁺/OH^- (mostly undissociated molecule)

Acid dissociation constant, K_a
aq sol of monobasic acid, HX(aq) in dynamic equilbm w/ ions H⁺(aq) & X^-(aq)
HX(aq) H⁺(aq) + X^-(aq)
K_a = [H⁺][X^-]/[HX]
-not valid for 100% dissociated molecules & changes w/ temp

Base dissociation constant, K_b
aq sol of base, B(aq) in dynamic equilbm w/ ions BH⁺(aq) & OH^-(aq)
B(aq) + H₂O(l) BH⁺(aq) + OH^-(aq)
K_c = [BH⁺][OH^-]/[B][H₂O]
assume [H₂O] = 1000/18 = 55.5 mol/dm³
K_b = K_c × [H₂O] = [BH⁺][OH^-]/[B]

pK_a or pK_b = -log₁₀k_a or -log₁₀k_b = -ve logarithm to base 10 of acid / base dissociation constant

Ionic product of water at 25°C, K_w:-product of [H⁺][OH] => K_w = [H⁺][OH]
water: very weak electrolyte- ionized slightly to give v.low conc of H⁺(aq) & OH^-(aq)
H₂O(l) H⁺(aq) + OH^-(aq), ΔH = +ve
at 25°C: [H⁺] = [OH] = 10^-7 mol/dm³
K_w always constant at 25°C
high temp: [H⁺] & [OH] increase > K_w increase

Acid dissociation constant of water at 25°C, K_a
H₂O(l) H⁺(aq) + OH^-(aq)
K_a = [H⁺][OH]/[H₂O] => K_a = K_w/[H₂O]

pH scale
pH: -ve logarithm to base 10 of [H⁺(aq)] in aq sol
pH = -log₁₀[H⁺]
-based on K_w value of water at 25°C
if acid / base accidentally added; -K_a remains constant, - pH changes
temp changeChange of pH in acid-base titration
pH-vol of acid/base curve obtained by placing glass electrode in titration mixture > record pH during titration
pH changes gradually to neutral (neutral- equilvalent pt, [H⁺] = [OH^-])

all acid-base titrations have sharp change in pH (at equivalence pt- from acidic quick change to alkaline) except titration bet weak base & weak acid

strong acid + strong base:
equivalence pt: [OH^-] = [H⁺] at pH 7
due to complete ionization

strong acid + weak base [HCl + NH₃(aq)]:
equivalence pt: [OH^-] = [H⁺] at acidic pH due to NH₄⁺ & OH^- combining to form NH₃ & H₂O > decrease in [OH^-]
NH₄Cl(aq) > NH₄⁺(aq) + Cl^-(aq)
H₂O(aq) OH^-(aq) + H⁺(aq)
=> NH₄⁺(aq) + OH^-(aq) NH₃(aq) + H₂O(aq) [HCl formed > completely ionized]

weak acid + strong base [HX + NaOH]:
equivalence pt: [OH^-] = [H⁺] at alkaline pH due to H⁺ & X^- combining to form HX molecule > decrease in [H⁺]
NaX(aq) > X^-(aq) + Na⁺(aq)
H₂O(aq) H⁺(aq) + OH^-(aq)
=> H⁺(aq) + X^-(aq) HX(aq) [NaOH formed> completely ionized]

(half-titrated mixture, salt & acid equal amts <=> [NaX] = [HX])
NaX(aq) > X^-(aq) + Na⁺(aq)
HX(aq) H⁺(aq) + X^-(aq)
[X^-] ≈ [NaX] since most X^- comes from NaX (little comes from HX dissociating)
K_a = [H⁺][X^-]/[HX] ≈ [H⁺][NaX]/[HX] = [H⁺]        since [NaX] = [HX]
K_a = [H⁺]

weak acid + weak base:
equivalence pt at pH 7- pH changes at equivalence pt is very gradually (no sharp change at equivalence pt)

for non-monobasic acid: multiple sharp pH changes

Acid-base indicators
weak organic acid / base: undissociated molecule one colour, ions another colour

indicator	pH range and colour
methyl orange	red	3.1 - 4.4	yellow
methyl red	red	4.2 - 6.3	yellow
bromothymol blue	yellow	6.0 - 7.6	blue
phenol red	yellow	6.8 - 8.4	red
phenolphthalein	colourless	8.3 - 10.0	red
thymolphthalein	colourless	9.3 - 10.5	blue

weak acid indicator
HX(aq) H⁺(aq) + X^-(aq)
+ [H⁺]: eqbm shift to left > [HX] increase > HX colour
+ [OH^-]: eqbm shift to right ([H⁺] decreases) > [X^-] increase > X^- colour

weak base indicator
B(aq) + H₂O(l) BH⁺(aq) + OH^-(aq)
+ [H⁺]: eqbm shift to right > [BH⁺] increase > BH⁺ colour
+ [OH^-]: eqbm shift to left > [B] increase > B colour

equivalence-pt: equal amts of acid and base react
end-pt: when indicator changes colour

indicator chosen is one which will change colour over range of sharp pH change in titration
strong acid & strong base: all indicators- wide range
strong base & weak acid: indicator that changes in alkaline condition
strong acid & weak base: indicator that changes in acidic condition
weak acid & weak base: no indicators suitable

Buffer solution (acid / base buffer)
-sol that can maintain pH to constant value if little bit of acid / alkaline added (due to shift in eqbm)

acid buffer- mixture of weak acid & Na salt of acid / mixture of 2 acid salts of same acid
partially ionized: HX(aq) H⁺(aq) + X^-(aq)
100% ionized: NaX(aq) > X^-(aq) + Na⁺(aq)
+ [H⁺]: H⁺ combines w/ X^- > HX
+ [OH^-]: OH^- combines w/ H⁺ > more HX dissociates to H⁺
K_a = [H⁺][X^-]/[HX]
assumptions:
  -[X^-] ≈ [NaX] since most X^- from salt, little from ionized acid
  -final [HX] ≈ initial [HX] since little ionization
K_a = [H⁺][X^-]/[HX] ≈ [H⁺][NaX]/[HX]
[H⁺] = K_a [HX]/[NaX]

alkaline buffer: mixture of weak base & salt of base when reacted w/ strong acid [NH₃/NH₄Cl]
partially ionized: NH₃(aq) + H₂O(aq) OH^-(aq) + NH₄⁺(aq)
100% ionized: NH₄Cl(aq) > NH₄⁺(aq) + Cl^-(aq)
+ [H⁺]: H⁺ combines w/ OH^- > more NH₃(aq) dissociated
+ [OH^-]: OH^- combines w/ NH₄⁺ > more NH₃(aq) molecules formed

K_b = [NH₄⁺][OH^-]/[NH₃]
assumptions:
  -[NH₄⁺] ≈ [NH₄Cl] since most NH₄⁺ from salt, little from ionized base
  -final [HX] ≈ initial [HX] since little ionization
K_b = [NH₄⁺][OH^-]/[NH₃] ≈ [NH₄Cl][OH^-]/[NH₃]
[OH^-] = K_b [NH₃]/[NH₄Cl]
[H⁺] = K_w/[OH^-]

Uses of buffer solution; to keep pH constant in:
-in intravenous injection; keep solution same pH as blood > or else dangerous
-in fermentation; or else organism may die
-biological experiments

Buffer solution in human blood
blood: pH ≈ 7.4
carbonic acid,H₂CO₃ & hydrogen carbonate ion, HCO₃^-
CO₂ breathed in combines w/ H₂O in blood: CO₂ + H₂O H₂CO₃
H₂CO₃ H⁺ + HCO₃^-

amino acids in form of zwitterions can also act as buffers

Solubility product, K_sp (of a sparingly soluble ionic salt): product of molar conc of aq ions raised to power of respective stoichiometric coefficient in eqn
A_mB_n(s) +aq mAⁿ⁺(aq) + nB^m-(aq)
K_sp = [Aⁿ⁺(aq)]^m[B^m-(aq)]ⁿ

valid for:
-sparingly soluble salt w/ total molar conc < 0.01 mol/dm³ (higher: K_sp not const)
-const temp (solubility dpds on tem)
-saturated solutions

pptn occurs if [Aⁿ⁺(aq)]^m[B^m-(aq)]ⁿ K_sp (pptn continues until [Aⁿ⁺(aq)]^m[B^m-(aq)]ⁿ = K_sp, ie until sol just saturated w/ ions)

Common ion effect
-shift in position of eqbm when an ion (which is already present in reactn) is added to system
(ammonium ion added to mixture / aq ammonia: ion reacts to form ammonia molecule)
can be used to investigate metal hydroxides w/ v.low K_sp value
metal ion added to mixture of NH₄Cl + aq NH₃: only metal hydroxides w/ v.low K_sp values ppted

pH of hydrolysed salt soltn
salt solutn from salt formed bet:
-strong acid & strong base; neutral sol
-weak acid & strong base; alkaline sol (H⁺ removed to form acid molecules)
-strong acid & weak base; acidic sol (OH^- removed to form base molecules)
-weak acid & weak base; neutral/ alkaline/ acidic depending on strength of acid & base formed in hydrolysis
for hydrolysed salt soltn: K_a × K_b = K_w
aq sol: K_w = [H⁺][OH^-] = 10^-14
aq sol of hydrolysed salt: K_w = K_a × K_b


Back to 'A' level notes index

Back to notes index