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Molarity and Solution Stoichiometry

How do you calculate molarity?

IntermediateSolutionsLast reviewed 3 October 2026
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What is it?

A solution is a mixture in which one substance, the solute, is dissolved in another, the solvent (often water).

Molarity tells you how concentrated a solution is: the number of moles of solute per litre of solution.

molarity=moles of solutelitres of solution\text{molarity} = \frac{\text{moles of solute}}{\text{litres of solution}}

Its unit is mol/L, written M (read “molar”). A 0.500 M solution contains 0.500 mol of solute in every litre.

Key idea

Molarity turns a volume of solution into moles: moles = molarity × volume (in litres). That makes reactions in solution work just like the stoichiometry you already know.

Why does it matter?

Most chemistry in the lab, in medicine and in living things happens in solution. Chemists can’t weigh a substance once it’s dissolved, but they can measure volumes very accurately. Molarity connects the volume measured with a pipette or burette to the number of moles that react, for example in a titration, where an acid is measured against a base to find an unknown concentration.

How does it work?

1. Calculating molarity

Find the moles of solute, convert the volume of solution to litres (mL ÷ 1000), then divide.

2. Making a solution

Rearranging gives moles = molarity × volume. Convert those moles into a mass with the molar mass, weigh it out, dissolve it in some water, then add water up to the final volume (usually in a volumetric flask).

3. Diluting a solution

Adding water spreads the same number of moles through a bigger volume. The moles of solute don’t change, so:

M1V1=M2V2M_1 V_1 = M_2 V_2

where M1,V1M_1, V_1 are the concentration and volume before dilution and M2,V2M_2, V_2 after. The volumes can be in any unit, as long as both use the same one.

4. Solution stoichiometry

Use the same road map as before, with volumes in place of masses: volume → moles → (mole ratio) → moles → volume.

Think of it like this

Think of fruit squash. Adding more water doesn’t change the amount of sugar in the jug; it only spreads it out, so each glass tastes weaker. That’s dilution: same moles of solute, bigger volume, lower molarity.

More precisely

Molarity depends slightly on temperature, because the volume of a solution expands or contracts as it warms or cools. For work where that matters, chemists sometimes use molality (moles of solute per kilogram of solvent), which doesn’t change with temperature.

Visualise it

Solution stoichiometry road map. Volume of solution A in litres, times the molarity of A, gives moles of A. Times the mole ratio, B over A, from the balanced equation, gives moles of B. Divide by the molarity of B to get the volume of solution B in litres. Key link: moles equals molarity times volume in litres.
Solution stoichiometry: volume → moles → moles → volume.

Worked example

Worked example: Calculating molarity

Question: 5.85 g of sodium chloride is dissolved in water to make 250.0 mL of solution. What is the molarity? (Na = 22.99, Cl = 35.45)

  1. Moles: M(NaCl)=58.44M(\ce{NaCl}) = 58.44 g/mol, so n=5.8558.44=0.1001n = \dfrac{5.85}{58.44} = 0.1001 mol
  2. Volume in litres: 250.0 mL ÷ 1000 = 0.2500 L
  3. Molarity = 0.1001 mol0.2500 L=0.400\dfrac{0.1001\ \text{mol}}{0.2500\ \text{L}} = 0.400 M

Worked example: Making a solution

Question: What mass of sodium hydroxide is needed to make 500.0 mL of 0.200 M NaOH solution? (Na = 22.99, O = 16.00, H = 1.008)

  1. Moles needed: 0.200 mol/L×0.5000 L=0.10000.200\ \text{mol/L} \times 0.5000\ \text{L} = 0.1000 mol
  2. Molar mass of NaOH\ce{NaOH}: 22.99 + 16.00 + 1.008 = 40.00 g/mol
  3. Mass: 0.1000×40.00=4.000.1000 \times 40.00 = 4.00 g

Answer: dissolve 4.00 g of NaOH and make the solution up to 500.0 mL.

Worked example: Dilution

Question: 25.0 mL of 6.00 M HCl is diluted with water to 150.0 mL. What is the new concentration?

M2=M1V1V2=6.00×25.0150.0=1.00M_2 = \dfrac{M_1 V_1}{V_2} = \dfrac{6.00 \times 25.0}{150.0} = 1.00 M

Worked example: Titration

Question: What volume of 0.100 M NaOH exactly neutralizes 25.00 mL of 0.150 M HCl? HCl+NaOH→NaCl+HX2O\ce{HCl + NaOH -> NaCl + H2O}

  1. Moles of HCl: 0.150×0.02500=0.0037500.150 \times 0.02500 = 0.003750 mol
  2. Mole ratio 1 : 1, so moles of NaOH = 0.003750 mol
  3. Volume of NaOH: 0.0037500.100=0.0375\dfrac{0.003750}{0.100} = 0.0375 L = 37.5 mL

Common mistake

Common mistake: Forgetting to convert mL to litres

Molarity uses litres. Using 250.0 instead of 0.2500 in the first example gives 0.000400 M, a thousand times too small.

Common mistake: Volume of solvent instead of volume of solution

“Make 250.0 mL of solution” means the final volume is 250.0 mL. Dissolving the solid in 250.0 mL of water gives a slightly different volume, and therefore a slightly different molarity.

Common mistake: Ignoring the mole ratio in titrations

Sulfuric acid, HX2SOX4\ce{H2SO4}, has two protons: HX2SOX4+2 NaOH→NaX2SOX4+2 HX2O\ce{H2SO4 + 2NaOH -> Na2SO4 + 2H2O}. It needs twice as many moles of NaOH as HCl does. Always use the balanced equation.

Notation note

  • The letter M is used for two different things: molar mass (g/mol, often italic M) and the unit molar (mol/L). Read the context and the units carefully.
  • IUPAC calls molarity the amount concentration, with symbol cc and unit mol/L, also written mol dm⁻³ (1 dm³ = 1 L), especially in UK courses.
  • Square brackets show a concentration: [NaCl] = 0.400 M.

Remember this

Remember this

  • Molarity (M) = moles of solute ÷ litres of solution.
  • moles = molarity × volume (L).
  • Dilution: M1V1=M2V2M_1V_1 = M_2V_2 (moles stay the same).
  • Solutions in reactions: volume → moles → mole ratio → moles → volume.

Test yourself

Check your understanding before moving on.

Flashcards

10 cards

  1. Question
    What is molarity?
    Answer

    Moles of solute per litre of solution (unit mol/L, written M).

  2. Question
    How do you find moles from molarity and volume?
    Answer

    moles = molarity × volume (in litres)

  3. Question
    What does 0.250 M mean?
    Answer

    0.250 mol of solute in every litre of solution.

  4. Question
    What is the dilution equation?
    Answer

    M1V1=M2V2M_1 V_1 = M_2 V_2, because the moles of solute stay the same.

  5. Question
    How many moles of solute are in 250.0 mL of 0.400 M solution?
    Answer

    0.400×0.2500=0.1000.400 \times 0.2500 = 0.100 mol

  6. Question
    10.0 mL of 12.0 M HCl is diluted to 250.0 mL. What is the new concentration?
    Answer

    12.0×10.0250.0=0.480\dfrac{12.0 \times 10.0}{250.0} = 0.480 M

  7. Question
    Why must you convert mL to L in molarity calculations?
    Answer

    Molarity is per litre. Using mL makes the answer 1000 times wrong.

  8. Question
    What is the difference between the solute and the solvent?
    Answer

    The solute is the substance dissolved; the solvent is what it dissolves in (often water).

  9. Question
    What is a titration?
    Answer

    A method that measures the exact volume of one solution needed to react with another, used to find an unknown concentration.

  10. Question
    What does the symbol [NaCl] mean?
    Answer

    The concentration of NaCl, in mol/L.

Quiz

7 questions

  1. Question 1EasyHow many moles of solute are in 250.0 mL of a 0.400 M solution?
    Show answer

    Answer: 0.100 mol

    moles = molarity × volume = 0.400 mol/L × 0.2500 L = 0.100 mol. The answer 100. mol forgets to convert mL to L.

  2. Question 2Medium7.46 g of potassium chloride, KCl, is dissolved to make 500.0 mL of solution. What is the molarity? (K = 39.10, Cl = 35.45)
    Show answer

    Answer: 0.200 M

    Moles = 7.46 ÷ 74.55 = 0.1001 mol. Molarity = 0.1001 ÷ 0.5000 L = 0.200 M.

  3. Question 3Medium10.0 mL of 12.0 M HCl is diluted to a final volume of 250.0 mL. What is the new concentration?
    Show answer

    Answer: 0.480 M

    M2=M1V1V2=12.0×10.0250.0=0.480M_2 = \dfrac{M_1V_1}{V_2} = \dfrac{12.0 \times 10.0}{250.0} = 0.480 M. Dilution keeps the moles the same but spreads them through a larger volume.

  4. Question 4EasyWhen a solution is diluted with water, which quantity stays the same?
    Show answer

    Answer: The moles of solute

    Adding water changes the volume and lowers the molarity, but no solute is added or removed, so the moles of solute are unchanged. That is why M1V1=M2V2M_1V_1 = M_2V_2.

  5. Question 5MediumWhat volume of 0.125 M NaOH neutralizes 20.00 mL of 0.250 M HCl?
    Show answer

    Answer: 40.0 mL

    Moles of HCl = 0.250 × 0.02000 = 0.005000 mol. The ratio is 1 : 1, so NaOH needed = 0.005000 mol, and volume = 0.005000 ÷ 0.125 = 0.0400 L = 40.0 mL. The answer 10.0 mL puts the concentrations the wrong way round.

  6. Question 6HardWhat volume of 0.200 M NaOH neutralizes 20.00 mL of 0.100 M HX2SOX4\ce{H2SO4}? HX2SOX4+2 NaOH→NaX2SOX4+2 HX2O\ce{H2SO4 + 2NaOH -> Na2SO4 + 2H2O}
    Show answer

    Answer: 20.0 mL

    Moles of HX2SOX4\ce{H2SO4} = 0.100 × 0.02000 = 0.00200 mol. The ratio is 2 : 1, so NaOH needed = 0.00400 mol, and volume = 0.00400 ÷ 0.200 = 0.0200 L = 20.0 mL. The answer 10.0 mL ignores the 2 : 1 ratio.

  7. Question 7HardA student dissolves 0.100 mol of a solid in 250.0 mL of water. Why might the molarity not be exactly 0.400 M?
    Show answer

    Answer: Molarity uses the volume of solution, not of water added

    Dissolving a solid changes the total volume slightly. To make exactly 0.400 M, dissolve the solid and then add water up to a final volume of 250.0 mL.

Notes and downloads

  • Worksheet

    Molarity Worksheet

    9 questions on molarity, making and diluting solutions, and titration calculations. Answer key included.

    IntermediateFree

References

  1. Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Murphy, C. J.; Woodward, P. M.; Stoltzfus, M. W. Chemistry: The Central Science, 15th ed.; Pearson, 2022.

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