GoalWrite Ka, compare the strengths of weak acids by their Ka values, and explain why the hydrogen ion in water is the hydronium ion H₃O⁺.
New words
ionisation constant Ka · the equilibrium constant of the ionisation of a weak acid, [H⁺][A⁻] ÷ [HA]hydronium ion · H₃O⁺, a proton joined to a water moleculeionic equilibrium · the equilibrium between the molecules of a weak electrolyte and the ions they form
Explanation
For a weak acid HA the ionisation is reversible: HA ⇌ H⁺ + A⁻. The law of mass action gives its constant: Ka = [H⁺][A⁻] ÷ [HA], the ionisation constant. Water, the solvent, is left out. Ka belongs to the acid and changes only with temperature. The larger Ka is, the more the acid ionises, so the stronger it is among weak acids; a very small Ka, such as 10⁻¹⁰, means a very weak acid. Compare the exponent first: 10⁻³ is much larger than 10⁻⁶. A free proton does not exist in water. It is attracted to a lone pair of electrons on the oxygen atom of a water molecule and joins it through a co-ordinate bond, which gives the hydronium ion H₃O⁺. So the equations are written better as HCl + H₂O → H₃O⁺ + Cl⁻ and HA + H₂O ⇌ H₃O⁺ + A⁻. The book often writes H⁺ for short, and so do we: [H⁺] and [H₃O⁺] mean the same thing. The balance between the molecules of a weak electrolyte and its ions is the ionic equilibrium.
ƒIonisation constant of a weak acid
HA + H₂O ⇌ H₃O⁺ + A⁻ ; Ka = [H₃O⁺][A⁻] ÷ [HA]
a larger Ka means a stronger weak acid
Worked examples
ƒKa of an invented acid HA
Ka = (2.0 × 10⁻³)² ÷ 0.10 = 4.0 × 10⁻⁵
Ka from concentrations (invented numbers). At equilibrium [H₃O⁺] = [A⁻] = 2.0 × 10⁻³ mol/L and [HA] = 0.10 mol/L. Ka = (2.0 × 10⁻³)² ÷ 0.10 = 4.0 × 10⁻⁶ ÷ 0.10 = 4.0 × 10⁻⁵. The two ions are equal in number because each HA that ionises gives one of each.
Acid
Ka (invented)
Strength
HX
3.0 × 10⁻³
strongest
HY
4.0 × 10⁻⁶
middle
HZ
2.5 × 10⁻⁹
weakest
Ranking by Ka. Three invented acids have Ka(HX) = 3.0 × 10⁻³, Ka(HY) = 4.0 × 10⁻⁶ and Ka(HZ) = 2.5 × 10⁻⁹. Compare the exponents first: −3 is greater than −6, which is greater than −9. So the order from strongest to weakest is HX > HY > HZ, and HZ ionises least. If two exponents are equal, compare the front numbers: 5.0 × 10⁻⁷ is larger than 3.0 × 10⁻⁷.
Hydronium in an equation. HCl + H₂O → H₃O⁺ + Cl⁻. Count: H 1 + 2 = 3 on the left and 3 in H₃O⁺ on the right; O 1 and 1; Cl 1 and 1. Charge: 0 on the left, +1 − 1 = 0 on the right. The water molecule gives the lone pair and the proton of HCl joins it. Written with H⁺ alone the equation is shorter, but H₃O⁺ is closer to what is in the water.
Class activity
Ranking cards, paper only, with a grown-up. Write these invented Ka values on six cards: HP 5.0 × 10⁻⁷, HQ 2.0 × 10⁻⁴, HR 8.0 × 10⁻⁹, HS 1.0 × 10⁻⁴, HT 3.0 × 10⁻⁷, HU 6.0 × 10⁻¹¹. Sort them from the strongest acid to the weakest, and say what you looked at first. Then ask a friend to mix them and sort again from memory of the rule. You should find that HQ is first and HU last.
Practice
1
Write the Ka expression for HNO₂ ⇌ H⁺ + NO₂⁻.
Ka = [H⁺][NO₂⁻] ÷ [HNO₂].
2
For an invented acid HA at equilibrium, [H₃O⁺] = [A⁻] = 1.0 × 10⁻³ mol/L and [HA] = 0.050 mol/L. Find Ka.
