IBChemistry: HLDPRevision Notes18. HL Acids & Bases18.2 Calculations Involving Acids & Bases18.2.1 Acid & Base Dissociation Constants

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Acid & Base Dissociation Constants (DP IB Chemistry: HL)

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Acid & Base Dissociation Constants

Weak acids

  • A weak acid is an acid that partially (or incompletely) dissociates in aqueous solutions
    • For example, most carboxylic acids (e.g. ethanoic acid), HCN (hydrocyanic acid), H2S (hydrogen sulfide) and H2CO3 (carbonic acid)
    • In general, the following equilibrium is established:

HA (aq) + H2O (l) ⇌  A- (aq) + H3O+ (aq)

OR

HA (aq) ⇌  A- (aq) + H+ (aq)

  • At equilibrium, the majority of HA molecules remain unreacted
  • The position of the equilibrium is more over to the left and an equilibrium is established
  • As this is an equilibrium, we can write an equilibrium constant expression for the reaction
  • This constant is called the acid dissociation constant, Ka, and has the units mol dm-3

Ka expression, downloadable IB Chemistry revision notes

Acid dissociation constant expressions

  • Carboxylic acids are weak acids
    • For example, propanoic acid, CH3CH2COOH (aq), dissociates according to the following equation which leads to the Ka expression for propanoic acid:

CH3CH2COOH (aq) + H2O (l) ⇌ CH3CH2COO– (aq) + H3O+ (aq)

OR

CH3CH2COOH (aq) ⇌ CH3CH2COO– (aq) + H+ (aq)

Ka expression for propanoic acid, downloadable IB Chemistry revision notes

Acid dissociation constant expressions for propanoic acid

  • Values of Ka are very small
    • For example, Ka  for propanoic acid = 1.34 x 10-5 mol dm-3 
  • When writing the equilibrium expression for weak acids, we assume that the concentration of H3O+ (aq) due to the ionisation of water is negligible

Weak bases

  • A weak base will also ionise in water and we can represent this with the base dissociation constant, Kb
  • In general the equilibrium established is:

B (aq) + H2O (l) ⇌  BH+ (aq) + OH- (aq)

Kb expression, downloadable IB Chemistry revision notes

Base dissociation constant expression

  • Amines are weak bases
    • For example, 1-phenylmethanamine, C6H5CH2NH2 (aq), dissociates according to the following equation which leads to the Ka expression for 1-phenylmethanamine:

C6H5CH2NH2 (aq) + H2O (l) ⇌ C6H5CH2NH3+ (aq) + OH- (aq)

Kb expression for 1-phenylmethanamine, downloadable IB Chemistry revision notes

Base dissociation constant expression for 1-phenylmethanamine

pKa and pKb 

  • The range of values of Ka and Kb is very wide and for weak acids, the values themselves are very small numbers

Table of Ka values

Table of Ka values, downloadable AS & A Level Chemistry revision notes

  • For this reason, it is easier to work with another term called pKa for acids or pKb for bases
  • In order to convert the values we need to apply the following calculations:

pKa = -logKa                 Ka= 10-pKa

pKb = -logKb                 Kb= 10-pKb

Table of pKa values

Table of pKa values, downloadable AS & A Level Chemistry revision notes

  • The range of pKa values for most weak acids lies between 3 and 7

Relative Strengths of Acids and Bases

  • The larger the Ka value, the stronger the acid
  • The larger the pKa value, the weaker the acid
  • The larger the Kb value, the stronger the base
  • The larger the pKb value, the weaker the base

relative strengths of acids and bases, downloadable IB Chemistry revision notes

pKa and pKb tell us the relative strengths of acids and bases 

Relating Kw to Ka

The Ionic Product of Water and Temperature

  • In all aqueous solutions, an equilibrium exists in water where a few water molecules dissociate into protons and hydroxide ions
  • We can derive an equilibrium constant for the reaction:

2H2O (l) ⇌ H3O+ (aq) + OH- (aq)

  • The concentration of water is constant, so the expression for Kw is:

Kw = [H3O+][OH-]

  • This is a specific equilibrium constant called the ionic product for water
  • The product of the two ion concentrations is 1 x 10-14 mol2 dm-6 at 25 °C

  • For conjugate acid-base pairs, Ka and Kb are related to Kw

Ka Kb = Kw

  • The conjugate base of ethanoic acid is the ethanoate ion, CH3COO– (aq) 

CH3COOH (aq) + H2O (l) ⇌ CH3COO– (aq) + H3O+ (aq)

                                                                                       acid                              conjugate base

  • We can then put this in to the Ka expression

Ka expression for Ethanoic acid, downloadable IB Chemistry revision notes

Acid dissociation constant for ethanoic acid

  • The ethanoate ion will react with water according to the following equation

CH3COO– (aq) + H2O (l) ⇌ CH3COOH (aq) + OH- (aq)

  • We can then put this in to the Kb expression

Kb expression for ethanoate ion, downloadable IB Chemistry revision notes

Base dissociation constant for the ethanoate ion

  • Now, these two expressions can be combined, which corresponds to
    • Ka Kb = Kw
    • Ka Kb = 10-14

  • Or we could say that
    • pKa + pKb = pKw
    • pKa + pKb = 14
    • This makes the numbers much more easy to deal with as using Ka Kb = 10-14 will give very small numbers

Combining Ka and Kb expressions, downloadable IB Chemistry revision notes

Combining Ka Kb expressions

  • Or rearranging these:
    • Ka =  Kw / Kb
    • Kb =  Kw / Ka 

The ionic product of water, Kw

  • The ionisation of water is an endothermic process

2H2O (l) ⇌ H3O+  aq) + OH- (aq) 

  • In accordance with Le Châtelier's principle, an increase in temperature will result in the forward reaction being favoured
    • This causes an increase in the concentration of the hydrogen and hydroxide ions
    • This leads to the magnitude of Kw increasing
    • Therefore, the pH will decrease

  • Increasing the temperature, decreases the pH of water (becomes more acidic)
  • Decreasing the temperature, increases the pH of water (becomes more basic)

Relationship between temperature and Kw, downloadable IB Chemistry revision notes

Relationship between Kw and temperature 

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