Difficulty: Intermediate to Advanced | Prerequisites: Solutions and solubility basics, moles and molar mass, equilibrium concepts
This set of notes covers how we measure the amount of solute in a solution (concentration units) and what happens at equilibrium in solution (Ksp, ion product, complex ions, and the common ion effect). You should be comfortable with basic solution terminology before starting here. The concentration formulas come up repeatedly in later topics, so learning when to use each one is worth the time.
Concentration is measured in several ways (molarity, molality, normality, mole fraction, percent composition), each suited to different calculations. In solution equilibria, the solubility product constant (Ksp) tells you how much of a sparingly soluble salt can dissolve; comparing the ion product to Ksp tells you whether a solution will precipitate or dissolve more. Complex ion formation increases solubility, while the common ion effect decreases it.
Molarity (M)
Moles of solute per litre of solution (not solvent).
Think of it as the most common way to express concentration. Used in rate laws, equilibrium expressions, pH calculations, and the Nernst equation.
Molality (m)
Moles of solute per kilogram of solvent.
Think of it as the concentration unit that does not change with temperature, because it is based on mass rather than volume. Used for boiling point elevation and freezing point depression.
Normality (N)
Number of equivalents of interest per litre of solution, where an equivalent is one mole of the reactive species (protons, hydroxide ions, or electrons, depending on the reaction).
In simple terms, it is the molarity of the specific reactive species you care about in a given reaction.
Mole fraction (X)
The ratio of moles of one component to the total moles of all components in the mixture.
Think of it as the fraction of the total particles that belong to one substance. All mole fractions in a system sum to 1.
Percent composition by mass
The mass of one component divided by the total mass of the solution, multiplied by 100.
In simple terms, how much of the total weight comes from one particular substance.
Solubility product constant (Ksp)
The equilibrium constant for the dissolution of a sparingly soluble ionic compound in water. It equals the product of the equilibrium concentrations of the ions, each raised to the power of its coefficient.
Think of it as a number that tells you how much of a barely-soluble salt can dissolve. Smaller Ksp means lower solubility.
Ion product (IP)
The same formula as Ksp, but using the actual concentrations of ions at any given moment, not just at equilibrium.
Think of it as the reaction quotient (Q) for dissolution. Comparing IP to Ksp tells you whether the solution will dissolve more or precipitate.
Molar solubility
The molarity of the solute in a saturated solution.
In simple terms, how many moles of the compound dissolve per litre when the solution is at its limit.
Complex ion (coordination compound)
A molecule in which a central metal cation is bonded to one or more electron-pair donors (ligands) through coordinate covalent bonds.
Think of it as a metal ion surrounded by molecules or ions that donate electrons to it.
Ligand
An electron-pair donor that bonds to a central metal cation in a complex ion.
In simple terms, the molecules or ions that attach themselves to the metal.
Chelation
When a single large organic ligand bonds to the central metal cation at multiple sites.
Think of it as a ligand wrapping around the metal and grabbing on in several places at once.
Formation constant (Kf)
The equilibrium constant for the formation of a complex ion in solution. It is usually very large because complex ions are stable.
In simple terms, how strongly the complex holds together.
Common ion effect
The reduction in solubility of a salt when it is dissolved in a solution that already contains one of its constituent ions.
Think of it as Le Chatelier's Principle applied to dissolution: adding more of one product ion pushes the equilibrium back toward the undissolved salt.
Percent composition by mass
Calculated as (grams of component A / total grams) x 100%
Mole fraction
X_B = moles of B / (moles of A + moles of B + moles of C + ...)
All mole fractions in a system sum to 1
Molarity
Moles of solute per litre of solution (not just solvent)
The most commonly used concentration unit
Used for rate laws, law of mass action, osmotic pressure, pH and pOH, and the Nernst equation
For dilute solutions, the volume of solution is approximately equal to the volume of solvent, which can simplify calculations
Molality
Moles of solute per kilogram of solvent
For dilute aqueous solutions at 25 °C, molality is roughly equal to molarity because the density of water is approximately 1 kg/L
As concentration increases, solution density increases, and molality and molarity diverge
Used for boiling point elevation and freezing point depression calculations
Normality
Equals the number of equivalents of the species of interest per litre of solution
An equivalent is one mole of the reactive species relevant to the reaction (protons, hydroxide ions, or electrons)
Reaction-dependent: the same solution can have different normalities depending on which reaction it participates in
Example: in acidic solution, permanganate ion accepts five moles of electrons, so its normality is five times its molarity
Dilution
M₁V₁ = M₂V₂, where M is molarity and V is volume
Adding solvent changes the concentration but not the total moles of solute
The equilibrium of a solution is its saturation point
When solute is first placed in solution, dissolution dominates
As the solution becomes more concentrated, the rate of precipitation increases and the rate of dissolution decreases
At the saturation point, the system is in dynamic equilibrium: rate of dissolution equals rate of precipitation, and the concentration of dissolved solute is constant
Free energy is zero at equilibrium
An ionic solid in a polar solvent dissociates: A_m B_n dissolves into m A^(+n) ions and n B^(-m) ions
For a saturated solution of a sparingly soluble ionic compound, Ksp = [A^(m+)]^x [B^(n+)]^y
The concentrations used are equilibrium concentrations
No denominator in the expression (pure solids and liquids are not included)
Temperature-dependent; for gases dissolved in liquids, also pressure-dependent
Increased temperature raises solubility for most solids but decreases solubility for gases
High pressure favours dissolution of gas solutes
Ksp shortcuts (where M is a metal and X is a halogen, and x is the molar solubility):
For MX: Ksp = x²
For MX₂: Ksp = 4x³
For MX₃: Ksp = 27x⁴
Same formula as Ksp, but uses actual ion concentrations at a given moment rather than equilibrium concentrations
Analogous to the reaction quotient Q
Each salt has its own Ksp at a given temperature
If IP < Ksp: solution is unsaturated, more solute will dissolve
If IP > Ksp: solution is supersaturated, precipitation is spontaneous
If IP = Ksp: solution is at equilibrium, saturated
A complex ion is a cation bonded to one or more ligands (electron-pair donors) through coordinate covalent bonds
Example: haemoglobin contains a complex ion that binds O₂, CO₂, or CO
Coenzymes and cofactors often contain similar complexes
Formation of complex ions increases the solubility of a salt in solution because the complex has multiple polar bonds and a high Ksp
Kf (formation constant) is usually very large because complex ions are stable
Complex ions form because they are more stable in solution than the original compound
Chelation occurs when a large organic ligand bonds to the central cation at multiple sites
The solubility of a salt is reduced when it is dissolved in a solution that already contains one of its constituent ions
This reduces the molar solubility but does not change the Ksp
It is an application of Le Chatelier's Principle: adding more of one product ion shifts the equilibrium back toward the undissolved salt
Percent composition by mass:
\% \text{Composition A} = \frac{\text{grams A}}{\text{total grams}} \times 100\%Mole fraction:
X_B = \frac{\text{moles of B}}{\text{moles of A} + \text{moles of B} + \text{moles of C} + \cdots}Molarity:
M = \frac{\text{moles of solute}}{\text{litres of solution}}Molality:
m = \frac{\text{moles of solute}}{\text{kg of solvent}}Dilution equation:
M_1 V_1 = M_2 V_2Solubility product constant (general form):
K_{sp} = [A^{m+}]^x [B^{n-}]^yKsp shortcuts:
Salt type | Ksp expression | Where x = molar solubility |
|---|---|---|
MX | Ksp = x² | 1:1 salt |
MX₂ | Ksp = 4x³ | 1:2 salt |
MX₃ | Ksp = 27x⁴ | 1:3 salt |
Ion product comparison:
Condition | Meaning | What happens |
|---|---|---|
IP < Ksp | Unsaturated | More solute dissolves |
IP = Ksp | Saturated (equilibrium) | No net change |
IP > Ksp | Supersaturated | Precipitation occurs |
Molarity is the standard unit in clinical labs for reporting blood chemistry results (electrolyte panels, glucose levels). Understanding concentration units is essential for anyone preparing solutions in a lab or pharmacy.
The common ion effect is why adding table salt to icy roads works more effectively when the salt is already partially dissolved: the presence of Na⁺ and Cl⁻ ions suppresses the solubility of other salts and alters the freezing equilibrium.
Students often confuse molarity and molality. Molarity uses litres of solution; molality uses kilograms of solvent. They are approximately equal only for dilute aqueous solutions at 25 °C.
Students often think that the common ion effect changes Ksp. It does not. Ksp is a constant at a given temperature. The common ion effect reduces molar solubility by shifting the equilibrium, but the equilibrium constant itself stays the same.
Students often forget that normality is reaction-dependent. The same solution of H₂SO₄ has a normality of 2M for acid-base reactions (two protons) but a different normality in redox reactions.
Students often assume IP > Ksp means the solution will simply dissolve more. The opposite is true: IP > Ksp means the solution is supersaturated, and precipitation will occur.
⚠️ Know the difference between molarity and molality, and when each is used. Molarity for equilibrium, pH, and osmotic pressure. Molality for boiling point elevation and freezing point depression.
⚠️ Be able to write the Ksp expression for any given ionic compound and use the Ksp shortcuts to calculate molar solubility.
⚠️ Know how to compare IP to Ksp and predict whether precipitation will occur.
⚠️ Understand how the common ion effect reduces solubility without changing Ksp. Expect a calculation where you find molar solubility in a solution that already contains a common ion.
⚠️ Be able to use the dilution equation M₁V₁ = M₂V₂ to find the concentration or volume after dilution.
True or false: Molarity and molality are the same for all aqueous solutions.
Answer: False. They are approximately equal only for dilute aqueous solutions at 25 °C.
Fill in the blank: If IP > Ksp, the solution is ______ and ______ will occur.
Answer: Supersaturated; precipitation.
True or false: The common ion effect changes the Ksp of a salt.
Answer: False. Ksp is constant at a given temperature. The common ion effect reduces molar solubility.
Fill in the blank: The Ksp shortcut for a salt of the form MX₂ is ______.
Answer: 4x³.
True or false: Normality depends on the reaction in which the solution is being used.
Answer: True.
Q: Calculate the Ksp of AgCl if its molar solubility is 1.3 x 10⁻⁵ M.
A: AgCl is a 1:1 salt (MX type), so Ksp = x² = (1.3 x 10⁻⁵)² = 1.69 x 10⁻¹⁰.
Q: A solution contains 0.10 M NaCl. What is the molar solubility of AgCl in this solution? (Ksp of AgCl = 1.7 x 10⁻¹⁰)
A: The Cl⁻ from NaCl is the common ion. Ksp = [Ag⁺][Cl⁻] = (x)(0.10 + x). Since x is tiny compared to 0.10, approximate: 1.7 x 10⁻¹⁰ = x(0.10), so x = 1.7 x 10⁻⁹ M. The common ion reduced the solubility from ~1.3 x 10⁻⁵ M to 1.7 x 10⁻⁹ M.
Q: You mix 50 mL of 0.002 M AgNO₃ with 50 mL of 0.002 M NaCl. Will AgCl precipitate? (Ksp = 1.7 x 10⁻¹⁰)
A: After mixing, volume doubles to 100 mL, so each ion concentration is halved: [Ag⁺] = 0.001 M, [Cl⁻] = 0.001 M. IP = (0.001)(0.001) = 1 x 10⁻⁶. Since IP (1 x 10⁻⁶) > Ksp (1.7 x 10⁻¹⁰), yes, AgCl precipitates.
Q: What is the normality of a 0.5 M H₂SO₄ solution used in an acid-base reaction?
A: H₂SO₄ provides two protons per molecule, so N = 2 x 0.5 M = 1.0 N.
Q: You have 200 mL of a 3.0 M HCl solution. How much water must you add to make it 0.5 M?
A: M₁V₁ = M₂V₂. (3.0)(200) = (0.5)(V₂). V₂ = 1200 mL. You need to add 1000 mL of water.
Concentration units connect directly to colligative properties: boiling point elevation and freezing point depression use molality, while osmotic pressure uses molarity.
Ksp and the ion product connect to chemical equilibrium more broadly. The logic of comparing Q to K to predict direction of reaction is the same framework used in all equilibrium problems.
Complex ion formation connects to coordination chemistry and biochemistry. Haemoglobin, vitamin B12, and chlorophyll all contain metal-ligand complexes.
Molarity, molality, normality, mole fraction, percent composition, concentration units, dilution equation, M1V1 = M2V2, Ksp, solubility product constant, ion product, molar solubility, complex ion, coordination compound, ligand, chelation, formation constant, Kf, common ion effect, Le Chatelier's Principle, spectator ions, precipitation, saturated, unsaturated, supersaturated, CHEM 101, general chemistry