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Chemistry 2e · Composition of Substances and Solutions

Molarity

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Numerical values (molar masses, concentrations) are commonly taught reference values; verify against current sources before relying on them in assessments.
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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Check yourself
  8. Study tools
  9. Sources & references

In 30 seconds

Molarity (symbol M) is the most widely used concentration unit in chemistry. It answers a practical question: how much is packed into a given volume of ? Molarity is the number of moles of solute dissolved in one liter of solution — not one liter of , a distinction that matters, as we will see:

M = moles of soluteliters of solution   or   M = nV

where n is the amount of solute in moles and V is the volume of the solution in liters. Molarity ties the mole concept (this chapter's first topic) to solution behavior and appears throughout the book wherever reactions happen in water — titrations, equilibria, kinetics, and electrochemistry all lean on it. Because liquids expand when heated, molarity is temperature-sensitive; mass-based units such as molality (next topic) are not.

Why this matters

Nearly all laboratory chemistry happens in solution, and molarity is the language of solution chemistry. When a chemist writes "0.100 M NaCl," they mean 0.100 mol of sodium chloride per liter of total solution. Knowing how to prepare such a solution — and how to dilute a concentrated stock to a target concentration — is a core lab skill used in hospital pharmacies (IV solutions are prepared by of sterile concentrates), environmental testing, and every quantitative experiment. Molarity also converts directly between the particle scale (moles) and the practical scale (measurable volumes). Concentration errors are not just exam mistakes: in real settings they produce failed reactions, wasted reagents, or unsafe dosing. Knowing what molarity measures — and what it does not — prevents the most common solution-chemistry traps.

The college version

Core Concepts

Solute, solvent, solution

A solution is a homogeneous mixture of two or more substances. The solute is the substance present in smaller amount (the one being dissolved); the solvent is present in larger amount (the one doing the dissolving). In an aqueous solution, water is the solvent. Molarity always refers to the total solution volume: after the solute dissolves, solvent is added until the mixture reaches a specific final volume — hence the standard recipe "dissolve the solute in a little solvent, then dilute to the mark," not "mix solute with exactly one liter of solvent."

Molarity as a conversion factor

The real power of molarity is that it is a conversion factor between volume and moles:

moles of solute = M × V   V = nM

For example, 0.500 L of 0.250 M glucose contains 0.250 × 0.500 = 0.125 mol of glucose. This conversion is the backbone of reaction stoichiometry (Chapter 4): molarity and volume give the moles of each reactant, which the balanced equation turns into moles of products.

Preparing a solution of known molarity

The correct procedure: (1) weigh out the required moles of solute using its ; (2) transfer it to a and dissolve in less than the final volume of solvent; (3) add solvent until the meniscus sits on the calibration mark, then mix. The key idea: the final volume, not the solvent volume, defines the concentration. Volumetric flasks are calibrated at a stated temperature, which is why molarity changes if the solution warms or cools. (General safety principle: follow your institution's PPE and waste-disposal rules when handling concentrated reagents.)

Dilution: conserving moles

Dilution adds solvent to a more concentrated solution, lowering its molarity while keeping the moles of solute unchanged. Because moles are conserved,

M1 V1 = M2 V2

where M1, V1 describe the stock (concentrated) solution and M2, V2 the diluted one. This single relationship powers every serial dilution in biology, pharmacy, and analytical chemistry, because n = M1V1 before dilution equals n = M2V2 after.

Molarity versus molality

Molality (symbol m) is moles of solute per kilogram of solvent (next topic). Because masses do not change with temperature, molality is temperature-independent; molarity is not. The two numbers are nearly equal for dilute aqueous solutions (1 kg of water ≈ 1 L), which tempts students to treat them as interchangeable — but for concentrated solutions and for colligative-property calculations (Chapter 11), the difference is real.

How It Works / Step-by-Step Process

  1. Decide the target molarity M and final volume V (in liters).
  2. Compute moles needed: n = M × V.
  3. Convert moles to mass: mass (g) = n × molar mass (g/mol).
  4. Weigh the solute, dissolve in less than the final volume of solvent, dilute to the mark, and mix.
  5. For a dilution: identify stock (M1, V1) and target (M2, V2), then solve M1V1 = M2V2 for the unknown.

Common Confusions

Do Not ConfuseWithDifference
Liters of solutionLiters of solventMolarity uses total solution volume — solvent is added to the mark
Molarity (M)Molality (m)M = mol solute / L solution (volume-based); m = mol solute / kg solvent (mass-based)
Moles of soluteGrams of soluteConvert via molar mass; molarity counts moles, not mass
Dilution (M1V1 = M2V2)EvaporationDilution adds solvent (moles constant, volume up); evaporation removes solvent (moles constant, M up)
1 M solution1 mol solute + 1 L waterA 1 M solution has total volume 1 L — add solute first, then water to the mark
ConcentrationAmount of soluteSame amount of solute can give many concentrations depending on final volume
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine making lemonade: molarity tells you how much sugar powder (solute) is in each full pitcher of lemonade (solution). A pitcher with lots of sugar is "high-molarity"; one that is mostly water is low. To make a weaker pitcher you don't throw sugar away — you add more water, spreading the same sugar through more drink. That "same sugar, more water" trick is exactly what the dilution formula M1V1 = M2V2 describes.

Worked example

Example 1: Preparing a solution from solid

Problem: How many grams of NaCl (molar mass 58.44 g/mol) are needed to prepare 250.0 mL of 0.500 M NaCl solution?

Step 1 — Convert volume to liters:

V = 250.0 mL × 1 L1000 mL = 0.2500 L

Step 2 — Apply the molarity formula:

n = M × V = 0.500 molL × 0.2500 L = 0.125 mol NaCl

Step 3 — Convert moles to grams:

mass = 0.125 mol × 58.44 gmol = 7.31 g NaCl

Answer: Dissolve 7.31 g of NaCl in water and dilute to a final volume of 250.0 mL.

Example 2: Diluting a stock solution

Problem: You have 6.00 M HCl. How many milliliters are needed to make 200.0 mL of 0.360 M HCl?

Use the dilution relationship (moles conserved):

M1 V1 = M2 V2

Solve for the stock volume V1:

V1 = M2 V2M1 = 0.360 M × 0.2000 L6.00 M = 0.0120 L = 12.0 mL

Answer: Measure 12.0 mL of 6.00 M HCl, transfer to a 200.0 mL volumetric flask, and dilute with water to the mark. (General principle: add acid to water slowly with mixing, per your lab's rules.)

Example 3: Finding molarity from a weighed mass

Problem: 5.85 g of NaCl is dissolved in water and diluted to 250.0 mL. What is the molarity?

Step 1 — Convert mass to moles:

n = 5.85 g × 1 mol58.44 g = 0.100 mol

Step 2 — Divide by volume in liters (0.2500 L):

M = nV = 0.100 mol0.2500 L = 0.400 M

Answer: The solution is 0.400 M NaCl. Unit check: mol ÷ L = mol/L = M.

Key takeaways

  • Molarity = moles of solute ÷ liters of solution (total volume, not solvent volume); unit is mol/L, written M.
  • Molarity is a conversion factor: moles = M × V.
  • Preparing a solution: weigh solute → dissolve in less than final volume → dilute to the mark in a volumetric flask.
  • Dilution conserves moles: M1 V1 = M2 V2.
  • Molarity is temperature-dependent (volume changes); molality is not.
  • To find molarity from a weighed mass: mass → moles via molar mass, then divide by solution volume in liters.

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

  1. Write the definition of molarity in words and in symbols.

    Show answer

    Molarity is the number of moles of solute per liter of solution: M = n/V.

  2. How many moles of solute are in 0.500 L of 0.250 M glucose solution?

    Show answer

    n = M × V = 0.250 mol/L × 0.500 L = 0.125 mol.

  3. A student mixes 1 mol of NaCl with 1 L of water and calls it "1 M." What is wrong?

    Show answer

    The final volume would exceed 1 L once the salt dissolves and water is added to the mark, so the concentration would be slightly less than 1 M. Molarity needs total solution volume, not solvent volume.

  4. You dilute 25.0 mL of 2.00 M KMnO₄ to 100.0 mL. What is the new molarity?

    Show answer

    M2 = M1 V1 / V2 = (2.00 M)(0.0250 L)/(0.1000 L) = 0.500 M.

  5. Why is molarity temperature-dependent while molality is not?

    Show answer

    Volume changes with temperature, so moles-per-liter changes; molality is based on masses, which do not change with temperature.

  6. What mass of glucose (molar mass 180.16 g/mol) is needed for 500.0 mL of 0.200 M glucose?

    Show answer

    n = 0.200 × 0.5000 = 0.100 mol; mass = 0.100 × 180.16 = 18.0 g.

Keep learning

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Molarity (M)
Moles of solute per liter of solution
Solution
A homogeneous mixture of two or more substances
Solute
The substance dissolved (present in smaller amount)
Solvent
The substance doing the dissolving (larger amount)
Volumetric flask
Glassware calibrated to hold an exact volume at a given temperature
Dilution
Adding solvent to lower concentration without changing moles of solute
Molar mass
Mass in grams of one mole of a substance (g/mol)

Sources & references

  1. openstax.org — Chemistry 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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