Ch 5 · Stability constants, Kstab · AS & A Level Chemistry 9701
Topic 5 of 5 in Chemistry of transition elements — AS & A Level Chemistry 9701 — 46 lessons.
Introduction
Ligand exchange reactions were described qualitatively earlier in this module. The stability constant gives that qualitative picture a numerical footing: it is simply an equilibrium constant, K_c, applied to the formation of a complex ion, and its size tells you directly how far a ligand exchange equilibrium lies towards the new complex.
Key ideas — Defining the stability constant
The stability constant, K_stab, of a complex is the equilibrium constant for its formation from the constituent hydrated metal ion (or a simpler complex) and the free ligand, in aqueous solution. For example, for the formation of the tetraamminecopper(II) complex,
🧑🏫 Teacher's explanation
Imagine you are at a party where people are dancing in pairs. Most people are in pairs (the complex), but a few are standing alone (the free ions). The 'stability constant' is like a popularity score for the dance. If the score is huge, it means almost everyone is dancing together in pairs and very few are standing alone. If the score is tiny, the dance is a failure and everyone is just standing around by themselves.
📖 Definitions
🔍 Worked example — Easy
Write the expression for the stability constant, K_stab, for the following reaction: [Ag(H_2O)_2]^+ (aq) + C_2O_4^2- (aq) leftharpoons [Ag(C_2O_4)]^- (aq) + 2H_2O (l)
🔍 Worked example — Exam-style
A complex ion ML_n forms from M^x+ and L. The reaction is M^x+ + nL leftharpoons ML_n. If the concentration of M^x+ is 1.0 × 10^-3 mol dm^-3, the concentration of L is 2.0 × 10^-2 mol dm^-3, and the concentration of ML_n is 8.0 × 10^-4 mol dm^-3, calculate K_stab for n=3.
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🎯 Exam question
[Co(H_2O)_6]^3+(aq) + 6NH_3(aq) leftharpoons [Co(NH_3)_6]^3+(aq) + 6H_2O(l)
Key ideas — Writing and using the expression
The expression is written from the equation in the usual way, omitting water since it is the solvent and present in such large excess that its concentration is effectively constant:
🧑🏫 Teacher's explanation
Imagine you are hosting a party. You have a group of 'host' ions (like Cu^2+) and 'guest' ligands (like NH_3). The stability constant, K_stab, is like a measure of how much the guests prefer staying with the host rather than wandering around alone. If K_stab is huge, it means once the guests arrive, they are staying put; the complex is very stable.
📖 Definitions
🔍 Worked example — Easy
Write the expression for the stability constant (K_stab) for the formation of the complex [Ag(NH_3)_2]^+ from the silver(I) aqua-ion [Ag(H_2O)_2]^+ and ammonia molecules.
🔍 Worked example — Exam-style
A solution contains 0.10 mol dm^-3 of [Co(H_2O)_6]^2+ and 0.20 mol dm^-3 of Cl^-. If the K_stab for [CoCl_4]^2- is 1.5 × 10^2, calculate the concentration of [CoCl_4]^2- at equilibrium. Assume the reaction is [Co(H_2O)_6]^2+ + 4Cl^- leftharpoons [CoCl_4]^2- + 6H_2O.
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🎯 Exam question
Key ideas — Stability constant calculations
Because K_stab expressions are equilibrium constant expressions, they are rearranged and solved exactly like K_c: given a numerical K_stab and three of the four equilibrium concentrations in a mononuclear ligand-substitution equilibrium, the fourth can be calculated directly by rearranging the expression, as shown in the worked example. The very large size of most K_stab values often means the concentration of the original hydrated ion remaining at equilibrium is extremely small, even though it is never exactly zero.
🧑🏫 Teacher's explanation
Think of a stability constant (K_stab) as a measure of how much a complex 'prefers' to stay together rather than breaking apart into its individual ions. Imagine a dance floor where couples are paired up. If the 'stability constant' of a dance is very high, it means once people pair up, they stay together for a long time. If it is low, they quickly split up to find new partners.
📖 Definitions
🔍 Worked example — Easy
Calculate the concentration of the complex [Ag(NH_3)_2]^+ in a solution where [Ag^+] = 2.0 × 10^-4 mol dm^-3, [NH_3] = 0.50 mol dm^-3, and K_stab = 2.0 × 10^7.
🔍 Worked example — Standard
A solution of [Cu(NH_3)_4]^2+ has a concentration of 0.050 mol dm^-3. If the concentration of free Cu^2+ is 1.0 × 10^-12 mol dm^-3 and [NH_3] = 0.10 mol dm^-3, calculate K_stab for the reaction Cu^2+ + 4NH_3 leftharpoons [Cu(NH_3)_4]^2+.
🔍 Worked example — Exam-style
For the equilibrium [Co(H_2O)_6]^2+ + 6CN^- leftharpoons [Co(CN)_6]^4- + 6H_2O, the K_stab is 1.2 × 10^34. If [Co(H_2O)_6]^2+ = 1.0 × 10^-8 mol dm^-3 and [CN^-] = 0.10 mol dm^-3, calculate the concentration of [Co(CN)_6]^4-.
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🎯 Exam question
Key ideas — Ligand exchange explained by stability constants
Ligand exchange occurs because different ligands form complexes of different stability with the same metal ion. When two ligands compete for the same metal ion, the system shifts towards whichever complex has the larger stability constant, since that is the thermodynamically more stable arrangement. Cyanide, CN^-, forms exceptionally stable complexes with transition metal ions, with K_stab values far larger than those for aqua or ammine complexes of the same metal; consequently, adding cyanide ions to a solution containing mathrm[Cu(H_2O)_6]^2+ or even mathrm[Cu(NH_3)_4(H_2O)_2]^2+ readily displaces the weaker ligands, driving the equilibrium towards the cyanide complex.
🧑🏫 Teacher's explanation
Imagine you are at a party where people are sitting in chairs. Some people are 'weak' guests who sit down easily but leave quickly, while others are 'strong' guests who refuse to leave once they sit down. In chemistry, the metal ion is the chair, and the ligands are the guests. The 'stability constant' (K_stab) is a mathematical way of measuring how much the guests prefer the chair over being free in the room.
📖 Definitions
🔍 Worked example — Easy
Write the expression for the stability constant, K_stab, for the formation of the complex [Ag(NH_3)_2]^+ from the ions Ag^+ and NH_3.
🔍 Worked example — Standard
A solution contains 0.10 mol dm^-3 of Cu^2+ ions and 0.50 mol dm^-3 of NH_3. If the K_stab for [Cu(NH_3)_4]^2+ is 5.5 × 10^12, calculate the concentration of [Cu(NH_3)_4]^2+ assuming the reaction goes to completion.
🔍 Worked example — Exam-style
Consider the following two equilibria in the same solution: 1) [Co(H_2O)_6]^2+ leftharpoons [Co(NH_3)_6]^2+ + 6H_2O (K_1 = 1.0 × 10^30) 2) [Co(NH_3)_6]^2+ leftharpoons [Co(H_2O)_6]^2+ + 6NH_3 (K_2 = 1.0 × 10^-30) Explain why adding NH_3 to a solution of [Co(H_2O)_6]^2+ results in the formation of [Co(NH_3)_6]^2+.
⚠️ Common errors
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🎯 Exam question
(a) Write an expression for K_stab for this reaction. [1] (b) A solution contains 0.010 mol dm^-3 of Ni^2+ and 0.010 mol dm^-3 of NH_3. Predict whether the equilibrium will favor the formation of the complex or the free ions. Justify your answer using the K_stab value. [2] [3 marks]
Worked example
Question. At 298 K, K_stab = 1.3×10^13\ mathrmmol^-4\ dm^12 for mathrm[Cu(H_2O)_6]^2+(aq) + 4NH_3(aq) leftharpoons mathrm[Cu(NH_3)_4(H_2O)_2]^2+(aq) + 4H_2O(l). (a) Write the expression for K_stab. [1] (b) At equilibrium, [mathrm[Cu(NH_3)_4(H_2O)_2]^2+] = 0.020\ mathrmmol\ dm^-3 and [NH_3] = 0.50\ mathrmmol\ dm^-3. Calculate the equilibrium concentration of mathrm[Cu(H_2O)_6]^2+ remaining. [3] (c) Comment on what this value indicates about the position of the ligand exchange equilibrium. [1]
🔍 Worked example — Easy
Write the expression for the stability constant K_stab for the reaction: ce[Ag(NH3)2]+(aq) <=> Ag+(aq) + 2NH3(aq)
🔍 Worked example — Standard
For the reaction ce[Cu(H2O)6]^2+(aq) + 4NH3(aq) <=> [Cu(NH3)4(H2O)2]^2+(aq) + 4H2O(l), the K_stab = 1.3 × 10^13. Calculate the concentration of ce[Cu(H2O)6]^2+ at equilibrium if [[Cu(NH3)4(H2O)2]^2+] = 0.020 mol dm^-3 and [NH_3] = 0.50 mol dm^-3. (Assume [H_2O] is constant and omitted from K expression as per standard convention for aqueous solutions).
🔍 Worked example — Exam-style
A complex ion ML_n has a stability constant K_stab = 5.0 × 10^5. If the concentration of the free metal ion M is 1.0 × 10^-4 mol dm^-3 and the ligand L is 0.10 mol dm^-3, calculate the concentration of the complex ML_n (assume n=3).
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