Solution Equilibria
Solution equilibria compare how much of a compound is dissolved to how much could dissolve at equilibrium.
Many MCAT solubility questions come down to one relationship: comparing how much of a compound is dissolved to how much could dissolve at equilibrium. This article covers how to write a net ionic equation, the solubility product constant (Ksp) that describes equilibrium for sparingly soluble salts, how Ksp relates to the broader family of equilibrium constants, the formation constant (Kf) for complex ions, the ion product (IP) used to predict whether a precipitate forms, and the common ion effect.
Key Takeaways
A net ionic equation is built in three steps — molecular equation, total ionic equation, then removing spectator ions — and shows which species actually drive a reaction.
The solubility product constant (Ksp) describes equilibrium for a sparingly soluble salt AₘBₙ: Ksp = [Aⁿ⁺]ᵐ[Bᵐ⁻]ⁿ (solids excluded).
Ksp belongs to a family of equilibrium constants sharing the same law-of-mass-action form: Keq (general reactions), Ka/Kb (acid/base dissociation), and Kf (complex ion formation) — a larger Kf means a more stable, more favored complex.
The ion product (IP) uses the same expression as Ksp but with actual, current ion concentrations; comparing IP to Ksp classifies a solution as unsaturated (IP < Ksp), saturated (IP = Ksp), or supersaturated (IP > Ksp, precipitate forms).
The common ion effect reduces a compound's solubility when one of its own ions is already present in solution — a direct result of Le Chatelier's principle shifting the equilibrium toward the undissolved solid.
Net Ionic Equations
A net ionic equation represents a reaction in aqueous solution by showing only the species that actually participate in it. Writing one is a three-step process. Take the reaction between silver nitrate and sodium chloride as an example:
Molecular equation — all reactants and products are written in their neutral, undissociated form: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
Total ionic equation — every strong electrolyte is written as its dissociated ions, since that's the form it actually exists in solution. Silver nitrate, sodium chloride, and sodium nitrate are all strong electrolytes, so each is split into ions. Silver chloride is not a strong electrolyte (it's the insoluble product), so it stays undissociated: Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)
Net ionic equation — remove the spectator ions, ions that appear unchanged on both sides of the equation (here, Na⁺ and NO₃⁻): Ag⁺(aq) + Cl⁻(aq) → AgCl(s)
Net ionic equations are useful for three reasons: they show which species are actually reacting, they reveal the driving force behind the reaction, and they let you recognize the same underlying pattern across many different aqueous electrolyte reactions.
The Solubility Product Constant (Ksp)
The AgCl example above introduces the MCAT's most heavily tested solubility topic: sparingly soluble salts, ionic compounds with very low solubility in water. Applying the law of mass action to the equilibrium between a sparingly soluble solid and its dissolved ions gives the solubility product constant, Ksp.
For a saturated solution of an ionic compound AₘBₙ, dissociation proceeds as:
AₘBₙ(s) ⇌ mAⁿ⁺(aq) + nBᵐ⁻(aq)
and the solubility product constant is:
Ksp = [Aⁿ⁺]ᵐ[Bᵐ⁻]ⁿ
As with any equilibrium constant, it's the concentration of products (here, the dissolved ions) raised to their stoichiometric coefficients — solids are never included. For silver chloride specifically, this simplifies to Ksp = [Ag⁺][Cl⁻].
Worked example — AgCl has a Ksp of 1.8 × 10⁻¹⁰ at 25°C. What is its molar solubility in pure water?
Let s = molar solubility (mol/L of AgCl that dissolves). Since AgCl dissociates 1:1 into Ag⁺ and Cl⁻, [Ag⁺] = [Cl⁻] = s:
Ksp = [Ag⁺][Cl⁻] = s × s = s²
s² = 1.8 × 10⁻¹⁰
s = √(1.8 × 10⁻¹⁰) ≈ 1.3 × 10⁻⁵ M
Ksp and the Family of Equilibrium Constants
Ksp is one member of a broader family of equilibrium constants that all follow the same law-of-mass-action form but apply to different reaction types:
Keq — the general equilibrium constant for any chemical reaction.
Ka and Kb — the equilibrium constants for acid dissociation and base dissociation, respectively.
Ksp — the equilibrium constant for the dissolution of a sparingly soluble salt.
Kf — the formation constant, the equilibrium constant for the formation of a complex ion from a metal ion and its ligands.
Which constant applies depends on the specific reaction, but the underlying form — products over reactants, each raised to its stoichiometric coefficient — stays consistent across all of them.
Kf measures how stable a complex ion is: a larger Kf means the complex is more stable and its formation is more strongly favored. It's important not to confuse Ksp and Kf when a complex ion forms from a dissolving salt: Ksp describes the original compound's dissolution into ions, while Kf describes those ions coming back together into a complex ion.
Worked example — Silver ion forms the diamminesilver(I) complex with ammonia: Ag⁺(aq) + 2NH₃(aq) ⇌ [Ag(NH₃)₂]⁺(aq), with Kf = 1.7 × 10⁷ at 25°C. If 0.10 M of the complex is at equilibrium in a solution with 1.0 M excess NH₃ remaining, how much free Ag⁺ is left uncomplexed?
Rearranging Kf = [Ag(NH₃)₂⁺] / ([Ag⁺][NH₃]²) to solve for [Ag⁺]:
[Ag⁺] = [Ag(NH₃)₂⁺] / (Kf × [NH₃]²) = 0.10 / (1.7 × 10⁷ × 1.0²) ≈ 5.9 × 10⁻⁹ M
The large Kf drives the equilibrium almost entirely toward the complex, leaving only a tiny trace of free Ag⁺ — this is exactly why complex ion formation can pull a sparingly soluble salt like AgCl into solution.
The Ion Product (IP) and Saturation
As a solute dissolves, the system approaches saturation — the point where no more solute can dissolve and any excess precipitates. To determine where a solution stands relative to that point, calculate the ion product (IP): the same expression as Ksp, but using the ion concentrations actually present at that moment, whether or not the system is at equilibrium. For AgCl, IP = [Ag⁺][Cl⁻] — the IP is to Ksp what the reaction quotient Q is to Keq.
Comparing IP to a salt's known Ksp at a given temperature tells you the solution's state:
IP < Ksp — the solution is unsaturated; more solute can still dissolve.
IP = Ksp — the solution is saturated and at equilibrium.
IP > Ksp — the solution is supersaturated; precipitation will occur.
Worked example — 50 mL of 2.0 × 10⁻⁴ M AgNO₃ is mixed with 50 mL of 2.0 × 10⁻⁴ M NaCl. Does a precipitate form? (AgCl Ksp = 1.8 × 10⁻¹⁰)
Mixing the two 50 mL volumes doubles the total volume to 100 mL, halving each ion's concentration:
[Ag⁺] = [Cl⁻] = (2.0 × 10⁻⁴ M) / 2 = 1.0 × 10⁻⁴ M
IP = [Ag⁺][Cl⁻] = (1.0 × 10⁻⁴)(1.0 × 10⁻⁴) = 1.0 × 10⁻⁸
Since IP (1.0 × 10⁻⁸) > Ksp (1.8 × 10⁻¹⁰), the mixture is supersaturated with respect to AgCl, and a precipitate forms.
The Common Ion Effect
The common ion effect describes how the solubility of a compound decreases when one of its own constituent ions is already present in the solution. It's a direct consequence of Le Chatelier's principle: a system at equilibrium shifts to counteract any imposed change.
Consider magnesium phosphate dissolving in water:
Mg₃(PO₄)₂(s) ⇌ 3Mg²⁺(aq) + 2PO₄³⁻(aq), with Ksp = [Mg²⁺]³[PO₄³⁻]²
If a solution already containing Mg²⁺ (say, from dissolved MgCl₂) is added, the increased [Mg²⁺] pushes the equilibrium left by Le Chatelier's principle, favoring the solid Mg₃(PO₄)₂. The result: more Mg₃(PO₄)₂ precipitates, and the salt's overall solubility in that solution decreases.
Worked example — Compare AgCl's molar solubility in pure water (calculated above as 1.3 × 10⁻⁵ M) to its molar solubility in a 0.10 M NaCl solution.
In 0.10 M NaCl, the Cl⁻ already present (0.10 M) vastly outweighs the small amount of Cl⁻ that AgCl itself contributes, so [Cl⁻] ≈ 0.10 M. Solving Ksp = [Ag⁺][Cl⁻] for the new molar solubility [Ag⁺]:
[Ag⁺] = Ksp / [Cl⁻] = (1.8 × 10⁻¹⁰) / 0.10 = 1.8 × 10⁻⁹ M
That's roughly 7,000 times less soluble than in pure water — a direct demonstration of the common ion effect. This principle shows up throughout chemistry: predicting whether a precipitate forms when solutions are mixed, stabilizing pH in buffer solutions (a weak acid or base paired with its salt), and controlling ion concentrations during titrations and other analytical procedures.
Common MCAT Mistakes
Including the solid in a Ksp expression. Ksp only includes the dissolved ions, each raised to its stoichiometric coefficient — the undissolved solid is never part of the expression.
Confusing the ion product (IP) with Ksp. Ksp is a fixed equilibrium constant at a given temperature; IP uses whatever ion concentrations are actually present at a given moment, equilibrium or not — IP is to Ksp what Q is to Keq.
Mixing up Ksp and Kf. Ksp describes a salt dissolving into its ions; Kf describes those (or other) ions combining into a complex ion — the two describe opposite directions of ion behavior and are not interchangeable.
Forgetting stoichiometric coefficients as exponents. For a salt like Mg₃(PO₄)₂, Ksp = [Mg²⁺]³[PO₄³⁻]², not [Mg²⁺][PO₄³⁻] — dropping the exponents from the coefficients gives a wrong expression entirely.
MCAT-Style Concept Check
Question: A sparingly soluble salt AB₂ has Ksp = 4.0 × 10⁻⁹. What is its molar solubility in pure water?
A) 1.0 × 10⁻³ M
B) 4.0 × 10⁻⁹ M
C) 2.0 × 10⁻³ M
D) 1.6 × 10⁻⁸ M
Answer: A
Explanation: AB₂ dissociates as AB₂(s) ⇌ A²⁺(aq) + 2B⁻(aq), so if s is the molar solubility, [A²⁺] = s and [B⁻] = 2s. Ksp = [A²⁺][B⁻]² = (s)(2s)² = 4s³. Setting 4s³ = 4.0 × 10⁻⁹ gives s³ = 1.0 × 10⁻⁹, so s = 1.0 × 10⁻³ M.
FAQ
How do you write a net ionic equation?
Start with the molecular equation (all species neutral and undissociated), convert it to the total ionic equation by splitting every strong electrolyte into its ions, then cancel out the spectator ions — the ions that appear unchanged on both sides — to get the net ionic equation.
What is Ksp, and how is it different from Kf?
Ksp is the equilibrium constant for a sparingly soluble salt dissolving into its ions: Ksp = [Aⁿ⁺]ᵐ[Bᵐ⁻]ⁿ, with solids excluded. Kf is the formation constant for the reverse-direction process of ions combining into a complex ion — the two constants describe opposite processes and aren't interchangeable, even when the same ions are involved.
What does the ion product (IP) tell you about a solution?
Comparing IP (calculated from actual current ion concentrations) to a salt's known Ksp tells you whether the solution is unsaturated (IP < Ksp, more can dissolve), saturated (IP = Ksp, at equilibrium), or supersaturated (IP > Ksp, a precipitate will form).
What is the common ion effect, and why does it reduce solubility?
The common ion effect is the decrease in a compound's solubility when one of its own constituent ions is already present in the solution from another source. By Le Chatelier's principle, the added ion shifts the dissolution equilibrium back toward the undissolved solid, reducing how much of the salt can dissolve.
Part of: