CDS Chemistry · Mole Concept and Stoichiometry

The Mole, Equivalent Weight and Concentration

Moles from mass and molar mass, counting atoms with Avogadro's number, equivalent weight from the n-factor, and molarity against molality.

All Mole Concept and Stoichiometry notes

Why this matters

Six CDS questions. Two are short calculations (hydrogen atoms in glucose, moles of helium); the rest are definitions: molar mass, equivalent weight, molarity and molality, and counting atoms in a formula.

Concept 1 of 3: Moles, molar mass and Avogadro's number

A mole is a counting unit, like a dozen, only far bigger: 6.022 × 10²³ particles. The mass of one mole in grams is the molar mass, and it equals the formula mass in u. So grams divided by molar mass gives moles, and moles times Avogadro's number gives particles.

Definition

The rules:

1 mole = 6.022 × 10²³ particles (Avogadro's number, Nₐ).
Molar mass = mass of one mole in grams, numerically equal to the atomic or molecular mass.
Moles n = mass ÷ molar mass; particles N = n × Nₐ.
To count atoms of one element, multiply the molecules by that element's subscript (glucose C₆H₁₂O₆ has 12 H per molecule).
Helium is monatomic: its molar mass is 4 g/mol.

Moles and particles

n = \frac{m}{M} \qquad N = n \times N_A, \quad N_A = 6.022 \times 10^{23}

$n$ number of moles
$m$ mass in grams
$M$ molar mass in g/mol
$N$ number of particles

Worked example

How many molecules are there in 9 g of water? (H = 1, O = 16)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2017 · CDS (II) 2017 — General Knowledge · Q18Moderate

Example 1 · Mole Concept and Stoichiometry · Mole Concept, Avogadro's Law and Molar Calculations

How many hydrogen atoms are contained in 1.50 g of glucose

\mathrm{(C_6H_{12}O_6)}

Count atoms, not molecules, when asked for atoms

After finding the moles of a compound, multiply by the number of that atom in the formula. Glucose has 12 hydrogen atoms per molecule, so hydrogen atoms = 12 × the molecules.

Equal in number is not equal in mass

Ethyne, C₂H₂, has as many carbon atoms as hydrogen atoms, but the carbon's mass is 24 and the hydrogen's 2. Multiply each count by its atomic mass before comparing masses.

Helium is monatomic

Helium exists as single atoms, so its molar mass is 4 g/mol, not 8. Moles of helium = mass ÷ 4.

A mole is a number, not a mass

One mole of anything has 6.022 × 10²³ particles, but its mass depends on the substance: 1 mol of H₂ is 2 g, 1 mol of O₂ is 32 g.

Drill 3 more on moles, molar mass and avogadro's number

Concept 2 of 3: Equivalent weight

Equivalent weight is the mass that does one 'unit' of reacting: gives one H⁺, takes one H⁺ or one electron. Divide the molar mass by how many such units one formula unit supplies.

Definition

The rule:

Equivalent weight = molar mass ÷ n-factor.
For an acid, n-factor = basicity (replaceable H⁺): HCl 1, H₂SO₄ 2.
For a base, n-factor = acidity (OH⁻ per formula): NaOH 1, Ca(OH)₂ 2, Ba(OH)₂ 2.

Equivalent weight

E = \frac{M}{n\text{-factor}}

$E$ equivalent weight
$M$ molar mass

Worked example

Find the equivalent weight of sulphuric acid, H₂SO₄ (molar mass 98).

Practice this conceptself-check · 2 quick reps

The same idea in a real exam question:

CDS · 2018 · CDS (II) 2018 — General Knowledge · Q24Moderate

Example 2 · Mole Concept and Stoichiometry · Mole Concept, Avogadro's Law and Molar Calculations

The equivalent weight of

\mathrm{Ba(OH)_2}

is (given, atomic weight of Ba is

137 \cdot 3

)

Divide by the n-factor, not by the number of atoms

A base with two OH⁻ per formula, such as Ca(OH)₂, has acidity 2, so its equivalent weight is half its molar mass, not the molar mass itself.

Basicity counts only replaceable hydrogens

Acetic acid, CH₃COOH, has four hydrogens but only the one in –COOH is given up as H⁺, so its basicity is 1.

Concept 3 of 3: Molarity and molality

Both count moles of solute. Molarity divides by the volume of the whole solution; molality divides by the mass of the solvent alone. Molality does not change with temperature because mass does not, while volume does.

Definition

The two measures:

Molarity (M) = moles of solute ÷ litres of solution.
Molality (m) = moles of solute ÷ kilograms of solvent.
Both are standard ways to state concentration, as is mass percentage.

Molarity and molality

M = \frac{n_{\text{solute}}}{V_{\text{solution}}\,(\text{L})} \qquad m = \frac{n_{\text{solute}}}{m_{\text{solvent}}\,(\text{kg})}

Worked example

4 g of NaOH (molar mass 40) is dissolved to make 500 mL of solution. Find its molarity.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

CDS · 2026 · CDS (II) 2026 — General Knowledge · Q71Easy

Example 3 · Mole Concept and Stoichiometry · Mole Concept, Avogadro's Law and Molar Calculations

Concentration of a solution can be expressed in : 1. Molarity 2. Molality Select the answer using the code given below :

Molarity uses the solution, molality the solvent

Molarity divides by the volume of the solution in litres; molality divides by the mass of the solvent in kilograms. Mixing them up gives the wrong number.

Molality does not change with temperature

Heating a solution expands its volume, so its molarity falls slightly. Molality uses mass, which does not change, so it stays the same.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Moles, molar mass and Avogadro's number
Moles and particles
$n = \frac{m}{M} \qquad N = n \times N_A, \quad N_A = 6.022 \times 10^{23}$
Equivalent weight
Equivalent weight
$E = \frac{M}{n\text{-factor}}$
Molarity and molality
Molarity and molality
$M = \frac{n_{\text{solute}}}{V_{\text{solution}}\,(\text{L})} \qquad m = \frac{n_{\text{solute}}}{m_{\text{solvent}}\,(\text{kg})}$

Watch out for (8)

Count atoms, not molecules, when asked for atoms
→ Moles, molar mass and Avogadro's number
Equal in number is not equal in mass
→ Moles, molar mass and Avogadro's number
Helium is monatomic
→ Moles, molar mass and Avogadro's number
A mole is a number, not a mass
→ Moles, molar mass and Avogadro's number
Divide by the n-factor, not by the number of atoms
→ Equivalent weight
Basicity counts only replaceable hydrogens
→ Equivalent weight
Molarity uses the solution, molality the solvent
→ Molarity and molality
Molality does not change with temperature
→ Molarity and molality

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