Solutions and Mixtures
Revisit analytical concentration, ion concentrations, final volume and amount-preserving dilution.
AP Chemistry Topic 3.7 · CED printed p. 66 / PDF p. 73. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Mole amounts and formula units
- Unit cancellation and ionic dissociation
Molarity counts amount per final solution volume
A homogeneous solution has macroscopic composition and properties that are uniform throughout the sampled material. Solutions can be gaseous, liquid or solid; air and many alloys are useful examples. In a heterogeneous mixture, composition or properties vary with location, such as a suspension with an undissolved solid phase. Uniform appearance at one point is evidence to examine, not a license to ignore other phases.
Molarity is moles of specified solute per liter of final solution: . Here M labels concentration, whereas earlier M labeled molar mass; the context and units distinguish them. Concentration units are mol L−1, often written M. The denominator is solution volume, not the starting solvent volume. Dissolving a solute and making the final solution to a measured mark gives a known final volume. Volumes of separately mixed components need not simply add.
From a mass, first convert to solute moles. From a concentration, multiply by volume in liters to recover solute moles. Always name the solute entity: a salt’s analytical concentration refers to amount of formula units introduced, while complete dissociation creates ion concentrations multiplied by formula subscripts. Molecular solutes such as glucose can remain intact.
Dilution changes concentration without changing amount
In simple dilution with no reaction or solute loss, n before = n after, so M1V1 = M2V2. Use matching volume units in that ratio or liters when calculating actual moles. V2 is the final solution volume, not volume of water added. A representative conceptual preparation uses a measured aliquot and a final measured volumetric volume; no unsafe practical procedure is needed to analyze the method.
A volumetric flask filled above its intended mark has greater final volume at the same solute amount, so actual concentration is too low. A pipetted aliquot smaller than the intended volume transfers less solute, also making the resulting concentration too low at the intended final volume. Temperature can change solution volume, so concentrations based on volume are temperature-dependent.
Let's work through it
Work it through
A solution contains 0.0150 mol Na2SO4 in a final volume of 250. mL. Assume complete dissociation and no other reactions.
- Convert final volume to 0.250 L. Analytical salt concentration = 0.0150/0.250 = 0.0600 mol L−1.
- Each formula unit produces two Na+ and one SO42−: [Na+] = 0.120 M and [SO42−] = 0.0600 M. The sulfate group remains a polyatomic ion, not four separate oxide ions.
- The total dissolved solute-ion count is 3 × 0.0150 × 6.022 × 1023 = 2.71 × 1022 ions.
- Diluting to a final 500. mL halves all concentrations, but preserves each solute amount and total ion count under the stated no-reaction assumptions.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
What volume belongs in the molarity denominator?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
What volume belongs in the molarity denominator?
Worked answer and reason
The final solution volume in liters.
Solvent volume before mixing need not equal solution volume.
Retrieval 2
Does doubling final volume by dilution double dissolved-solute particle count?
Worked answer and reason
No. With no solute loss or reaction, particle amount is unchanged and concentration halves.
Dilution changes amount per volume.
Retrieval 3
For completely dissociated 0.200 M CaCl2, what is [Cl−]?
Worked answer and reason
0.400 M.
The formula contributes two chloride ions per salt formula unit.
Catch the tempting mistake
- A 100 mL aliquot always contains 0.100 mol solute.
- Its amount also depends on concentration: n = MV.
- In a dilution, V2 means water added.
- It is final solution volume.
- All solutes make ions on dissolving.
- Many molecular solutes remain intact; use the specified dissolution model.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 3 problem 16 · ap application · multiple
- Unit 3 problem 17 · ap synthesis · data
- Unit 3 problem 18 · ap application · macroscopic
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For the teacher
- Require the final-volume label and liters in moles calculations.
- Check that students can move from analytical salt concentration to each ion concentration without splitting a polyatomic ion.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 3.7.A
- Calculate the number of solute particles, volume, or molarity of solutions.
- 3.7.A.1
- Solutions, also sometimes called homogeneous mixtures, can be solids, liquids, or gases. In a solution, the macroscopic properties do not vary throughout the sample. In a heterogeneous mixture, the macroscopic properties depend on location in the mixture.
- 3.7.A.2
- Solution composition can be expressed in a variety of ways; molarity is the most common method used in the laboratory. EQN: M = nsolute /Lsolution
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 (supplied source) — Exact topic-numbered learning objectives, essential knowledge, science practices and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §11.2, Electrolytes — Dissociation versus intact molecular dissolution; charge mobility and electrolyte particle evidence.
Glossary and deeper reading · 8 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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Formula unit
A formula unit specifies the simplest whole-number ratio of ions in an ionic compound. It is a counting unit for an extended solid rather than an isolated molecule. For example, one calcium chloride formula unit represents one calcium ion and two chloride ions.
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Alloy
An alloy is a metallic material containing more than one element. Added atoms can replace host atoms or occupy spaces between them, changing properties such as hardness. For example, carbon atoms in steel affect how easily iron atoms can move relative to one another.
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Mixture
A mixture contains two or more substances whose proportions can vary. Its components retain their chemical identities until a chemical reaction changes them. For example, water and ethanol can form mixtures with many different compositions.
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Molarity
Molarity is the amount of a solute in moles divided by the final solution volume in liters. It describes concentration rather than the total amount of solute. For example, 0.10 mole dissolved to make 0.50 liter of solution gives a molarity of 0.20 mole per liter.
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Solute
A solute is a component dispersed in a solvent to form a solution. It need not be a solid, and a solution need not be liquid. For example, carbon dioxide is a gaseous solute in carbonated water.
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Ion
An ion is an atom or group of atoms with a net electric charge. Ordinary ion formation changes electron count without changing the element's proton count. For example, a sodium atom losing one electron becomes a sodium ion with charge +1.
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Aliquot
An aliquot is a measured portion taken from a sample. In analysis, a representative aliquot lets a measured result be related to the original sample's total amount. For example, a 10-milliliter portion of a uniform solution can be an aliquot of a larger prepared sample.