Counting Atoms Inside Molecules

Introduction

One molecule of water, H₂O, contains three atoms: two hydrogen and one oxygen. So what does one mole of water contain? The answer is simple but important: two moles of hydrogen atoms and one mole of oxygen atoms. Being able to "look inside" a formula in this way is the key to many later calculations, from percentage composition to reacting masses.

Core explanation

Subscripts scale up. A chemical formula tells you the atoms in one molecule. Because a mole is just a fixed number of molecules, the same ratio holds for moles:

- 1 molecule of H₂O contains 2 H atoms and 1 O atom. - 1 mol of H₂O contains 2 mol of H atoms and 1 mol of O atoms. - 0.5 mol of H₂O contains 1 mol of H atoms and 0.5 mol of O atoms.

To find the moles of any atom, multiply the moles of the compound by that atom's subscript:

moles of atom X = moles of compound × number of X atoms in the formula

A symbol with no subscript has an understood subscript of 1.

Total moles of atoms. Add the subscripts to find the total atoms in one molecule. Water has 2 + 1 = 3 atoms per molecule, so 1 mol of water contains 3 mol of atoms altogether.

Examples.

Substance Atoms per molecule Moles of atoms in 1 mol --- --- --- O₂ 2 O 2 mol O CO₂ 1 C, 2 O 1 mol C, 2 mol O (3 in total) NH₃ 1 N, 3 H 1 mol N, 3 mol H (4 in total) CH₄ 1 C, 4 H 1 mol C, 4 mol H (5 in total) C₂H₅OH 2 C, 6 H, 1 O 9 mol of atoms in total C₆H₁₂O₆ 6 C, 12 H, 6 O 24 mol of atoms in total

Note that ethanol, C₂H₅OH, contains hydrogen in two places in the formula: 5 + 1 = 6 hydrogen atoms. Always scan the whole formula.

Molecules versus atoms of an element. "1 mol of oxygen" is ambiguous. One mole of O₂ molecules contains 2 mol of oxygen atoms. Writing the formula removes the doubt.

From moles of atoms to numbers of atoms. Once you know the moles of atoms, multiply by the Avogadro constant as before: N = n × Nₐ.

Step-by-step reasoning

1. Write the formula and the amount of compound in moles. 2. List each element and its subscript, remembering hidden 1s and repeated symbols. 3. Multiply the moles of compound by each subscript. 4. Add the results if the total moles of atoms is needed. 5. Multiply by 6.02 × 10²³ if a number of atoms is required.

Visual explanation

Picture a ball-and-stick model of methane: one black carbon ball joined to four white hydrogen balls. Now imagine a mole of these models in a heap. If you pulled every model apart and sorted the balls, you would have one heap of carbon (1 mol) and a heap of hydrogen four times as large (4 mol).

Real-world analogy

A bicycle has 1 frame and 2 wheels. A shop that stocks 50 bicycles holds 50 frames and 100 wheels. The "formula" of a bicycle tells you the ratio of parts, and that ratio stays the same however many bicycles you have.

Real-world example

In the body, glucose, C₆H₁₂O₆, is broken down to release energy. Each mole of glucose supplies 6 mol of carbon atoms, and each carbon atom ends up in a carbon dioxide molecule that we breathe out. So every mole of glucose used produces 6 mol of CO₂.

Why?

Why does the ratio in one molecule hold for a mole? A mole is simply 6.02 × 10²³ molecules. If each molecule contains two hydrogen atoms, then 6.02 × 10²³ molecules contain 2 × 6.02 × 10²³ hydrogen atoms, which is 2 mol.

Common misconception

"One mole of water contains one mole of atoms." It contains three moles of atoms: two of hydrogen and one of oxygen. One mole of molecules is not the same as one mole of atoms unless each molecule has only one atom, as in a noble gas.

Worked example

Question: For 0.500 mol of glucose, C₆H₁₂O₆, find (a) the moles of each type of atom and (b) the total number of atoms.

Reasoning: (a) C: 0.500 × 6 = 3.00 mol; H: 0.500 × 12 = 6.00 mol; O: 0.500 × 6 = 3.00 mol. (b) Total moles of atoms = 3.00 + 6.00 + 3.00 = 12.0 mol. Number of atoms = 12.0 × 6.02 × 10²³ = 7.22 × 10²⁴.

Answer: (a) 3.00 mol C, 6.00 mol H, 3.00 mol O; (b) 7.22 × 10²⁴ atoms.

Quick check

1. How many moles of hydrogen atoms are in 2.00 mol of methane, CH₄? Answer: 2.00 × 4 = 8.00 mol of hydrogen atoms.

Exam focus

Questions often ask for "the number of atoms" rather than "the number of molecules". Read carefully: if atoms are wanted, multiply by the number of atoms per molecule as well as by Nₐ. Show both steps so method marks are available.

Advanced insight

For molecules with brackets, such as propanone written as (CH₃)₂CO, multiply everything inside the bracket by the number outside: 2 × (1 C + 3 H) + 1 C + 1 O gives C₃H₆O, so 1 mol contains 3 mol C, 6 mol H and 1 mol O. Structural formulae group atoms to show bonding, but the atom count is unchanged.

Summary

A formula's subscripts give the moles of each atom in one mole of compound. Multiply the moles of compound by each subscript to find moles of each atom, add them for the total, and multiply by Nₐ to get numbers of atoms. One mole of molecules usually contains several moles of atoms.

Practice questions

1. How many moles of oxygen atoms are in 3.0 mol of carbon dioxide, CO₂? Answer: 3.0 × 2 = 6.0 mol of oxygen atoms. 2. Find the total moles of atoms in 0.25 mol of ethanol, C₂H₅OH. Answer: Each molecule has 2 + 6 + 1 = 9 atoms, so 0.25 × 9 = 2.25 mol, about 2.3 mol of atoms. 3. How many atoms are there in 2.0 mol of ammonia, NH₃? Answer: 2.0 × 4 = 8.0 mol of atoms; 8.0 × 6.02 × 10²³ = 4.8 × 10²⁴ atoms. 4. A sample of ozone, O₃, contains 0.60 mol of oxygen atoms. How many moles of ozone molecules are present? Answer: 0.60 ÷ 3 = 0.20 mol of O₃ molecules.