Solutions: Molarity, Dilution, and Solubility
Solutions chemistry fits together around a few questions: what is dissolved, how concentration is measured with molarity, when dilution applies, and when you need full reaction stoichiometry. It builds from gas laws before equilibrium.
What you'll learn
13.1 Start Here: What a Solution Is and What the Parts Are Called
A solution is a homogeneous mixture. The solute is the substance being dissolved, and the solvent is the substance doing the dissolving.
Get those three words straight now, because later calculations depend on them. Mixing up solute, solvent, and solution is one of the most common early mistakes in this unit.
In a solution, the solute is spread evenly throughout the solvent.
"Like dissolves like" is the key rule: polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes.
| Term | Definition | Example |
|---|---|---|
| Solute | Substance being dissolved (usually smaller amount) | NaCl in saltwater |
| Solvent | Substance doing the dissolving (usually larger amount) | H2O in saltwater |
| Aqueous solution | Water is the solvent | Most biological fluids |
| Electrolyte | Solute that dissociates into ions, conducts electricity | NaCl → Na+ + Cl- |
| Nonelectrolyte | Solute that stays as molecules, does not conduct | Glucose, C6H12O6 |
Particle count rule
- Strong electrolytes (ionic compounds, strong acids/bases) dissociate 100%.
- Weak electrolytes (weak acids/bases) dissociate partially.
- Nonelectrolytes do not dissociate at all.
- This distinction drives colligative property calculations.
13.2 Solubility: Unsaturated, Saturated, or Supersaturated?
Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature.
Do not miss the temperature part. A solution can be saturated at one temperature and unsaturated at another.
To classify a solution, compare the amount dissolved with the solubility limit at that temperature.
Temperature matters: For most solid solutes in water, solubility increases as temperature increases. For gases dissolved in liquids, solubility usually decreases as temperature increases.
13.3 Particle Diagrams: What Dissolved Solutions Look Like Microscopically
Particle diagrams show solute and solvent particles at the microscopic level. This is where vocabulary, conductivity, and particle-count ideas all come together — if the diagram is wrong, the chemistry interpretation will be wrong too. Key features to represent accurately:
- Ionic solutes (NaCl): show separate Na+ and Cl- ions dispersed through water molecules.
- Molecular solutes (glucose): show intact molecules, no ions.
- Insoluble precipitates (AgCl): show solid clusters at the bottom, separate from dissolved ions.
- Net ionic: spectator ions disappear; only the precipitate and reacting ions remain.
These particle diagrams help you predict three things: whether the solution conducts electricity, how many dissolved particles are present, and whether a precipitate forms.
Na+ and Cl- ions fully dissociated, dispersed throughout
Intact C6H12O6 molecules, no ions form
AgCl(s) settles as granular solid, while NO3- stays in solution above
13.4 Molarity: Moles per Liter of Solution
The most common concentration unit in chemistry. Molarity expresses moles of solute per liter of solution (not solvent).
This is the concentration idea you will use most in reaction problems. The usual mistake is simple but costly: forgetting to convert mL to L.
Rearrangements you'll use constantly:
Common error
- Volume must be in liters.
- Always convert mL → L by dividing by 1000 before plugging in.
- Also, molarity is moles per liter of solution, not per liter of solvent.
13.5 Dilution: Same Solute, Bigger Volume, Lower Concentration
Dilution is the process of adding solvent to reduce the concentration of a solution. The number of moles of solute stays constant — only the volume increases.
Start here if dilution problems keep fooling you. The key idea is that dilution is not a reaction. No new solute appears and none disappears.
Initial State
Small Volume, Higher Molarity
The same solute is packed into less solution, so the particles are more crowded.
`V₁` smaller, `C₁` larger.
Same Solute, More Solvent
Dilution is not a reaction. The solute amount stays constant, so n1 = n2.
Final State
Large Volume, Lower Molarity
The same six solute moles are spread through more solution, so the concentration drops.
`V₂` larger, `C₂` smaller.
Dilution spreads the same solute moles through a larger solution volume, so concentration decreases while the amount of solute stays constant.
- V2 is NOT the volume of water you added — it's the total final volume of the diluted solution.
- If a problem says "add 450 mL of water to 50 mL of solution," the final volume V2 = 500 mL.
- Always ask: "Is this the total volume, or the volume added?" before plugging in.
13.6 Percent Concentration: m/m, m/v, and v/v
Three common percent-based concentration expressions used in labs and industry:
Notice that the denominator changes depending on the type. The percent sign is easy to remember — what it is actually comparing is where the setup breaks.
| Type | Formula | Units | Use |
|---|---|---|---|
| % mass/mass (% m/m) | (g solute / g solution) × 100 | % (dimensionless) | Solid solutes, concentrated acids |
| % mass/volume (% m/v) | (g solute / mL solution) × 100 | g per 100 mL | IV bags, pharmaceuticals |
| % volume/volume (% v/v) | (mL solute / mL solution) × 100 | % (dimensionless) | Alcohol content, mixtures of liquids |
Percent reminder
- Always use g of solution (not solvent) in m/m.
- Solution = solute + solvent.
- If 15 g NaCl is dissolved in 135 g water, the solution mass is 150 g.
13.7 Molality: Moles per Kilogram of Solvent
Molality is moles of solute per kilogram of solvent (not solution). It is not related to temperature because it is based on mass, not volume — making it very important for colligative property calculations. Two very important colligative properties are freezing point depression and boiling point elevation.
Watch out because molality looks and sounds a lot like molarity, but the denominator is different. Instead of liters of solution, molality uses kilograms of solvent. That is also why molality stays dependable when temperature changes the solution volume.
Key difference
Molality uses kg of solvent only in the denominator. Solute is still counted in moles, but the denominator is based on solvent mass rather than solution volume.
| Property | Molarity (M) | Molality (m) |
|---|---|---|
| Denominator | L of solution | kg of solvent |
| Temperature dependent? | Yes (volume changes) | No (mass is constant) |
| Use for | Stoichiometry, reactions | Colligative properties |
13.8 Colligative Properties: Count Particles, Not Chemical Names
Colligative properties depend on how many dissolved particles are present in a given amount of solvent, not on the chemical identity of those particles.
This is where the electrolyte idea from the start of the unit starts to matter. More dissolved particles means a larger effect, which is why the van 't Hoff factor matters.
The three rows below show how particle count multiplies the colligative effect at the same molality.
| Same molality | i | Relative effect size |
|---|---|---|
| 1.0 m glucose | 1 | baseline |
| 1.0 m NaCl | 2 | about 2× larger |
| 1.0 m CaCl2 | 3 | about 3× larger |
This is the key comparison: at the same molality, the solution that makes more dissolved particles shows the larger colligative effect.
Why does this happen? Solute particles disrupt the escape of solvent molecules, so more energy is needed — raising the boiling point.
This is why salt and beet solutions melt snow and ice in cold weather — the freezing point drops below 0 °C. Why does this happen? Solute particles interfere with lattice formation; the solution freezes at a lower temperature. New fp = 0 − ΔTf.
Pressure needed to prevent osmosis across a semipermeable membrane. Clinically important for IV solutions.
Adding solute reduces the fraction of solvent molecules at the surface, lowering vapor pressure. Drives both boiling point elevation and freezing point depression.
- The van 't Hoff factor i = number of dissolved particles per formula unit after dissociation.
- NaCl: i = 2 (Na+ + Cl-).
- CaCl2: i = 3 (Ca2+ + 2 Cl-).
- Glucose: i = 1 (no dissociation).
13.9 Solution Stoichiometry: Turn Concentration into Moles First
Solution stoichiometry uses the same mole ratios as any other stoichiometry problem.
Do not rush past the first move. The setup almost always starts with mol = M × L — if you skip that, the rest of the problem falls apart. Then use the balanced equation or net ionic equation to relate those moles to the substance you need.
For precipitation reactions, identify the insoluble product first.
Identify the precipitate using solubility rules. Net ionic: Ag+(aq) + Cl-(aq) → AgCl(s)
- Mole ratios come from the balanced equation — never from molecular masses.
- For solutions: moles = M × L before and after every stoichiometric step.
- For limiting reagent in solution: find mol of each reactant, compare with mol ratio.
Next step after Unit 13
Solutions set up the particle and concentration ideas you need for reversible systems. The next move is chemical equilibrium, where forward and reverse changes compete at the same time. To keep Unit 13 active, use the Unit 13 Practice page and the full practice hub, then pair it with Why Practice Tests Beat Rereading for stronger concentration and setup retrieval.