Stoichiometry

The Mole Concept

5th Year · 6th Year (Leaving Cert)

✓By the end of this lesson students will be able to define the mole as a unit of amount of substance.
✓By the end of this lesson students will be able to state and apply Avogadro's number in calculations involving the number of particles.
✓By the end of this lesson students will be able to calculate the molar mass of elements and compounds from relative atomic masses.
✓By the end of this lesson students will be able to interconvert between mass, moles, and molar mass using the formula n = m/M.
✓By the end of this lesson students will be able to solve problems involving the mole concept in various chemical contexts.

Key concepts

The Mole

The mole (symbol: mol) is the SI unit for amount of substance. It is defined as the amount of substance that contains as many elementary entities (atoms, molecules, ions, electrons, etc.) as there are atoms in exactly 12 grams of carbon-12. Essentially, it's a counting unit, similar to how a 'dozen' represents 12 items, a 'mole' represents a specific, very large number of particles.

Avogadro's Number

Avogadro's number (N_A) is the number of elementary entities (atoms, molecules, ions, etc.) in one mole of any substance. Its accepted value is 6.02 x 10²³ mol⁻¹. This means that one mole of water contains 6.02 x 10²³ water molecules, and one mole of sodium atoms contains 6.02 x 10²³ sodium atoms.

Number of particles = Number of moles × Avogadro's Number (N_A)

Molar Mass

Molar mass (symbol: M) is the mass of one mole of a substance. It is expressed in grams per mole (g mol⁻¹). Numerically, the molar mass of an element is equal to its relative atomic mass (Aᵣ) in grams, and the molar mass of a compound is equal to its relative molecular mass (Mᵣ) or relative formula mass in grams. For example, if the relative atomic mass of carbon is 12, then its molar mass is 12 g mol⁻¹.

M = Σ(Aᵣ of each atom in the formula)

Relationship between Moles, Mass, and Molar Mass

The number of moles (n) of a substance can be calculated if its mass (m) and molar mass (M) are known. This fundamental relationship is crucial for all stoichiometric calculations.

n = m / M (where n = number of moles, m = mass in grams, M = molar mass in g mol⁻¹)

Key facts to remember

1The mole is the SI unit for amount of substance.
2One mole of any substance contains Avogadro's number of particles (6.02 × 10²³ mol⁻¹).
3Molar mass (M) is the mass of one mole of a substance, expressed in g mol⁻¹.
4The numerical value of molar mass is equal to the relative atomic mass (for elements) or relative molecular/formula mass (for compounds).
5The key formula linking moles, mass, and molar mass is n = m / M.
6Always include units in your calculations and final answers.
7Relative atomic masses are typically found on the Periodic Table or provided in the question.

Worked examples

Example 1

Calculate the molar mass of sulfuric acid, H₂SO₄. (Relative atomic masses: H = 1, S = 32, O = 16)

IIdentify the number of atoms of each element in the formula: 2 hydrogen atoms, 1 sulfur atom, 4 oxygen atoms.

IIMultiply the number of atoms of each element by its relative atomic mass:

III Hydrogen: 2 × 1 = 2

IV Sulfur: 1 × 32 = 32

V Oxygen: 4 × 16 = 64

VISum these values to find the relative molecular mass, which is numerically equal to the molar mass:

VII Molar mass = 2 + 32 + 64 = 98

VIIIState the answer with correct units.

Answer

The molar mass of H₂SO₄ is 98 g mol⁻¹.

Remember to always include the units (g mol⁻¹) for molar mass.

Example 2

How many moles are present in 20.0 g of sodium hydroxide, NaOH? (Relative atomic masses: Na = 23, O = 16, H = 1)

IFirst, calculate the molar mass (M) of NaOH:

II M(NaOH) = Aᵣ(Na) + Aᵣ(O) + Aᵣ(H)

III M(NaOH) = 23 + 16 + 1 = 40 g mol⁻¹

IVIdentify the given mass (m): m = 20.0 g.

VUse the formula n = m / M to calculate the number of moles (n):

VI n = 20.0 g / 40 g mol⁻¹

VII n = 0.5 mol

VIIIState the answer with correct units.

Answer

There are 0.500 moles of NaOH in 20.0 g.

It's good practice to carry an extra significant figure during intermediate calculations and round only the final answer.

Example 3

A sample contains 0.25 moles of carbon dioxide (CO₂). Calculate: (a) The mass of the sample. (b) The number of CO₂ molecules in the sample. (Relative atomic masses: C = 12, O = 16; Avogadro's Number = 6.02 x 10²³ mol⁻¹)

I(a) Calculate the mass of the sample:

II 1. Calculate the molar mass (M) of CO₂:

III M(CO₂) = Aᵣ(C) + 2 × Aᵣ(O)

IV M(CO₂) = 12 + 2 × 16 = 12 + 32 = 44 g mol⁻¹

V 2. Use the formula m = n × M (rearranged from n = m/M):

VI m = 0.25 mol × 44 g mol⁻¹

VII m = 11 g

VIII(b) Calculate the number of CO₂ molecules:

9 1. Use the formula: Number of particles = Number of moles × Avogadro's Number (N_A)

10 2. Number of molecules = 0.25 mol × 6.02 × 10²³ mol⁻¹

11 3. Number of molecules = 1.505 × 10²³

12 4. Round to an appropriate number of significant figures (e.g., 2 or 3, consistent with 0.25 moles): 1.5 × 10²³ molecules.

Answer

(a) The mass of the sample is 11 g. (b) The number of CO₂ molecules in the sample is 1.5 × 10²³ molecules.

Pay attention to the units throughout your calculations. Moles cancel out, leaving grams for mass, and mol⁻¹ cancels out, leaving just a number for particles.

Common mistakes

✗Confusing relative molecular mass (a ratio, no units) with molar mass (mass per mole, units g mol⁻¹).
✗Incorrectly calculating molar mass, especially for compounds with multiple atoms of an element (e.g., H₂SO₄, forgetting to multiply H by 2 and O by 4).
✗Forgetting to include units in calculations or final answers, leading to loss of marks.
✗Using Avogadro's number incorrectly, e.g., multiplying by mass instead of moles.
✗Algebraic errors when rearranging the formula n = m/M (e.g., calculating m = M/n instead of m = n × M).

Exam tips

★Always write down the formula you are using (e.g., n = m/M) before substituting values.
★Show all steps of your working clearly, even for simple calculations, as partial marks may be awarded.
★Pay close attention to units. Ensure they are consistent and cancel out correctly.
★Double-check your molar mass calculations, as an error here will affect all subsequent parts of the question.
★Practise rearranging the mole formula (n = m/M, m = n × M, M = m/n) until it becomes second nature.

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