Atoms and molecules are far too small to count one by one, so chemistry treats 6.022 × 10²³ of them as a single bundle called one mole (mol).
With the mole, an invisible particle count, a mass on a balance and a gas volume all connect through one number, and the coefficients of a reaction equation read directly as mole ratios.
Attach g to an atomic or molecular mass and you have the mass of 1 mol; at 0 °C and 1 atm, 1 mol of any gas takes up 22.4 L.
The diagrams split this into three: moles as bundles of dots, the different masses of 1 mol of each element as bars, and the conversions among the three quantities as a triangle.
Why a Bundle Called the Mole?
A reaction equation records how many particles meet, but the only thing you can hold in a lab is the gram reading on a balance. Without a link between the two, you could know 2H₂ + O₂ → 2H₂O and still not know how many grams of hydrogen to add. Since atoms cannot be counted one at a time, the mole fixes the size of the bundle first as Avogadro's number N_A and then records how many grams one bundle of each element weighs. Equal moles of different elements contain the same number of particles and differ only in mass, by the molar mass M. So the mole is a counting unit, not another name for mass: 18 g of water is 1 mol because N_A water molecules have a mass of 18 g.
💡 Like a Dozen Pencils or a Ream of Paper
①Just as 12 pencils make 1 dozen
②and 500 sheets of paper make 1 ream
③6.022 × 10²³ atoms or molecules make 1 mol
④The bundle is this large because atoms are so small: it takes this many to reach grams on a balance
⑤1 mol of water is 18 g, about 18 mL, a little more than one tablespoon
Avogadro's Number and the Mole
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A bundle of 40 dots = 1 mol: particle count growing with the amount
In the first diagram, one dashed box of 40 dots stands for 1 mol. Raising the amount from 0.5 mol to 3.0 mol with the slider fills the boxes one by one, and the line at the top gives the actual number of particles, the amount multiplied by N_A. In the second diagram the tray on the left always holds the same number of atoms whatever element is chosen, while the bars on the right set side by side how differently that same count weighs: 1 g for H, 12 g for C, 16 g for O and 56 g for Fe. The third diagram puts the mole at the top corner with mass and particle count at the bottom two corners, writing × M and × N_A on the arrows leaving the mole and ÷ M and ÷ N_A on the arrows coming back.
1 mol
Moles and Particle Count
n = NNA
n: amount (mol), N: number of particles, NA = 6.022 × 10²³ /mol
🔍 How Big Is N_A?
①Counting 100 million per second without a break, it would take about 190 million years to count 1 mol
②Even if all 8 billion people on Earth each counted one per second together, it would take about 2.4 million years
③Treating this enormous count as a single unit, 1 mol, keeps calculations simple
④The coefficient ratio in a reaction equation is a particle ratio and also a mole ratio
Molar Mass: The Link to Atomic Mass
A common slip is to think that the atomic mass with a g attached is the mass of the sample in hand. That number is only the mass of 1 mol, so to find how many moles 36 g of water is, you still divide by 18 g/mol. Gas volume works the same way: 22.4 L pairs with 1 mol only at 0 °C and 1 atm, and at a room temperature of 25 °C the same 1 mol takes up about 24.5 L, so the figure cannot be carried over when the conditions change. Before calculating, check whether the given amount is a particle count, a mass or a gas volume, then divide by N_A, M or 22.4 L respectively to reach moles, and the path stays clear.
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Mass of 1 mol of each element with the same count (N_A) on the tray
C
Mole and Mass
n = mM
m: mass (g), M: molar mass (g/mol)
Moles and Gas Volume
V = n × 22.4 L (0 °C, 1 atm)
At 0 °C and 1 atm, 1 mol of any gas occupies 22.4 L
💡 Rules of Molar Mass
①N_A carbon atoms have a mass of 12 g, the atomic mass 12 with g attached
②Oxygen's atomic mass is 16, so 1 mol of oxygen atoms is 16 g
③For a molecule, add up the atomic masses to get the molecular mass and attach g: water (H₂O) is 1 × 2 + 16 = 18, so 1 mol is 18 g
④1 mol of iron (56 g) is 56 times heavier than 1 mol of hydrogen (1 g) not because it has more atoms but because each atom is 56 times heavier
Three Paths Through the Mole
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The mole triangle: converting among mass, particle count and gas volume
Particles → Moles
n = NNA
NA = 6.022×10²³
Mass → Moles
n = mM
M: molar mass (g/mol)
Gas volume → moles (0 °C, 1 atm)
n = V22.4
V: gas volume at 0 °C and 1 atm (L)
Work It Out
Example 1
How many moles are in 36 g of water (H₂O)? (Atomic masses: H = 1, O = 16)
1
First find the molar mass of water.
M(H₂O) = 2 × 1 + 16 = 18 g/mol
2
Divide the mass by the molar mass.
n = 36 g ÷ 18 g/mol = 2 mol
▸ 2 mol
36 g is twice the mass of 1 mol of water (18 g), so it is 2 mol. The molar mass has the same number as the molecular mass, with the unit g/mol.
Example 2
At 0 °C and 1 atm, find the volume and the number of molecules in 2 mol of oxygen (O₂).
1
At 0 °C and 1 atm, 1 mol of gas occupies 22.4 L, so multiply the amount by 22.4 L.
V = 2 × 22.4 L = 44.8 L
2
For the number of molecules, multiply the amount by NA.
N = 2 × 6.02 × 10²³ = 1.204 × 10²⁴
▸ volume 44.8 L, 1.204 × 10²⁴ molecules
Once the amount in moles is known, you can cross directly to any other corner of the triangle. Volume and molecule count were both found from the same 2 mol.
Summary
2023 KICE mock Chemistry I type, adapted
At 0 °C and 1 atm, what is the volume of 8.8 g of carbon dioxide (CO₂)? (Atomic masses: C = 12, O = 16)
①2.24 L
②4.48 L
③11.2 L
④22.4 L
⑤44.8 L
▸ ② 4.48 L
1
M(CO₂) = 12 + 2 × 16 = 44 g/mol, so n = 8.8 ÷ 44 = 0.2 mol.
2
Cross twice: from mass to moles, then from moles to volume by multiplying by 22.4 L.
V = 0.2 × 22.4 L = 4.48 L
🎯 Exam Points
①Three ways to reach moles: particle count ÷ N_A, mass ÷ M, gas volume ÷ 22.4 L
②N_A = 6.022 × 10²³ /mol
③Atomic (molecular) mass and molar mass share the same number; only the unit g/mol differs
④At 0 °C and 1 atm, 1 mol of gas is 22.4 L; under other conditions do not use this value
⑤Mole calculations appear almost every year, so first check which of the three quantities you are given