pH, Ka, pKa & Kw Calculations (CIE A Level Chemistry)

pH

• The pH indicates the acidity or basicity of an acid or alkali
• The pH scale goes from 0.0 to 14.0
  • Acids have a pH below 7.0
  • Pure water is neutral with a pH of 7.0
  • Bases and alkalis have a pH above 7.0
• pH can be calculated using:

pH = -log₁₀ [H⁺]

• • where [H⁺] = concentration of H⁺ ions (mol dm^-3)
• The pH can also be used to calculate the concentration of H⁺ ions in solution by rearranging the equation to:

[H⁺] = 10^-pH 

K_a & pK_a

• The K_a is the acidic dissociation constant
  • It is the equilibrium constant for the dissociation of a weak acid at 298 K
• For the partial ionisation of a weak acid HA, the equilibrium expression to find K_a is:

HA (aq) ⇌ H⁺ (aq) + A^- (aq)

K_a = 

• When writing the equilibrium expression for weak acids, the following assumptions are made:
  • The concentration of hydrogen ions due to the ionisation of water is negligible
  • The dissociation of the weak acid is so small that the concentration of HA is approximately the same as the concentration of A^-
• The value of K_a indicates the extent of dissociation
  • A high value of K_a means that:
    • The equilibrium position lies to the right
    • The acid is almost completely ionised
    • The acid is strongly acidic
  • A low value of K_a means that:
    • The equilibrium position lies to the left
    • The acid is only slightly ionised (there are mainly HA and only a few H⁺ and A^- ions)
    • The acid is weakly acidic
• Since K_a values of many weak acids are very low, pK_a values are used instead to compare the strengths of weak acids with each other

pK_a = -log₁₀ K_a

• The less positive the pK_a value the more acidic the acid is

K_w

• The K_w is the ionic product of water
  • It is the equilibrium constant for the dissociation of water at 298 K
  • Its value is 1.00 x 10^-14 mol² dm^-6
• For the ionisation of water, the equilibrium expression to find K_w is:

H₂O (l) ⇌ H⁺ (aq) + OH^- (aq)

K_w = 

• As the extent of ionisation is very low, only small amounts of H⁺ and  OH^- ions are formed
• The concentration of H₂O can therefore be regarded as constant and removed from the K_w expression
• The equilibrium expression therefore becomes:

K_w = [H⁺] [OH^-]

• As the [H⁺] = [OH⁺] in pure water, the equilibrium expression can be further simplified to:

K_w = [H⁺]²