Worked example 1
What is the molarity of a solution made by dissolving 5.85 g of NaCl in enough water to make 500.0 mL of solution?
Try it first: Convert both the mass and the volume into the units molarity requires.
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Gases, Solutions & SpectroscopySolutionsContent level: Core 18 min
Molarity, Solution Preparation and Dilution
What you'll be able to do: Calculate molarity, prepare a solution of known concentration, and carry out dilution calculations.
Introduction
Concentration answers a single question: how much solute is packed into a given amount of solution. Molarity is the version chemists reach for because it pairs directly with moles.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Calculate molarity from mass and volume data
- Describe how to prepare a solution of a stated molarity
- Use M₁V₁ = M₂V₂ for dilution problems
- Distinguish solute, solvent and solution
Lesson
Defining molarity
Molarity, symbol M, equals moles of solute divided by litres of solution. The denominator is the total volume of the final solution, which is why solutions are made up to a mark rather than by adding a measured volume of solvent.
M = mol solute / L solution
Dissolving 1 mol of solute in 1 L of water does not give exactly a 1 M solution, because the solute itself adds volume.
Preparing a solution
To make 250.0 mL of 0.100 M NaCl, first find the moles needed, which is 0.2500 L x 0.100 mol/L = 0.0250 mol. Multiply by the molar mass to get 1.46 g. Weigh that mass, dissolve it in less than 250 mL of water, transfer to a 250.0 mL volumetric flask, then add water to the calibration mark and invert to mix.
Dilution
Adding solvent spreads the same moles of solute through a larger volume. Because moles do not change, M₁V₁ = M₂V₂. The volumes may be in any unit as long as both sides match, which makes millilitres perfectly acceptable here.
M₁V₁ = M₂V₂
Other concentration units
Parts per million equals milligrams of solute per litre of solution for dilute aqueous samples, and is used for trace contaminants. Molality, moles of solute per kilogram of solvent, appears when temperature changes matter, because mass does not expand the way volume does.
Combine solutions by conserving solute
When two solutions of the same solute are mixed, add their solute moles before dividing by final solution volume. M₁V₁ = M₂V₂ describes dilution of one sample with solvent; it does not account for solute already in a second solution. For a simple classroom calculation, assume volumes are additive when the problem says so.
For mixing: ntotal = M₁V₁ + M₂V₂, then Mfinal = ntotal/Vfinal.
Key ideas
Definition
Molarity
Moles of solute per litre of solution.
Definition
Solute and solvent
The solute is dissolved; the solvent does the dissolving; together they form the solution.
Rule
Dilution rule
Diluting changes concentration and volume but never the moles of solute.
Key concept
Volumetric flask
Glassware calibrated to one precise total volume, used to make solutions up to the mark.
Equation
Molarity
M = n / V
- n = moles of solute
- V = litres of solution
Equation
Dilution
M₁V₁ = M₂V₂
- M₁, V₁ = concentrated stock
- M₂, V₂ = diluted solution
Worked examples
Worked example 2
How would you prepare 100.0 mL of 0.150 M HCl from a 6.00 M stock solution?
Try it first: Identify which of the four dilution quantities is unknown.
0 of 4 steps revealed.
Worked example 3
Mix 100.0 mL of 0.200 M NaCl with 100.0 mL of 0.100 M NaCl. Assume additive volumes. Find the final molarity.
Try it first: Calculate each portion's moles first.
0 of 3 steps revealed.
Common mistakes
Dividing by the volume of solvent added.
Why it's wrong: Molarity uses the total volume of the finished solution.
Check instead: Make the solution up to the mark and use that final volume.
Adding water to concentrated acid.
Why it's wrong: The heat released can spatter acid violently.
Check instead: Always add acid to water, slowly and with stirring.
Thinking dilution changes the moles of solute.
Why it's wrong: Only solvent is added, so the solute count is untouched.
Check instead: Use M₁V₁ = M₂V₂, which is a statement that moles are conserved.
After the lesson · Question bank
Independent practice
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What you should now know
Molarity is moles of solute per litre of solution, not per litre of solvent. A solution is prepared by weighing the solute, dissolving it, and then making up to the mark in a volumetric flask. Dilution adds solvent without changing the moles of solute, which gives M₁V₁ = M₂V₂.
- M = moles of solute per litre of solution
- Prepare solutions by making up to the mark in a volumetric flask
- M₁V₁ = M₂V₂ because dilution conserves moles
- Always add acid to water, never the reverse
- ppm and molality are alternative concentration units
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.