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

Acid dissociation constant expressions

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

Base dissociation constant expression for 1-phenylmethanamine

pK_a and pK_b 

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

Table of K_a values

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

pK_a = -logK_a                 K_a= 10^-pK_a

pK_b = -logK_b                 K_b= 10^-pK_b

Table of pK_a values

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

Relative Strengths of Acids and Bases

• The larger the K_a value, the stronger the acid
• The larger the pK_a value, the weaker the acid
• The larger the K_b value, the stronger the base
• The larger the pK_b value, the weaker the base

pK_a and pK_b tell us the relative strengths of acids and bases 

• For conjugate acid-base pairs, K_a and K_b are related to K_w

K_a K_b = K_w

• 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 K_a expression

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 K_b expression

Base dissociation constant for the ethanoate ion

• Now, these two expressions can be combined, which corresponds to
  • K_a K_b = K_w
  • K_a K_b = 10^-14

• Or we could say that
  • pK_a + pK_b = pK_w
  • pK_a + pK_b = 14
  • This makes the numbers much more easy to deal with as using K_a K_b = 10^-14 will give very small numbers

Combining K_a K_b expressions

• Or rearranging these:
  • K_a =  K_w / K_b
  • K_b =  K_w / K_a 

The ionic product of water, K_w

• 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 K_w 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 K_w and temperature