# How many atoms are in a single molecule?

The number of atoms in a molecule depends on the type of molecule. Some simple molecules like oxygen (O2) contain only 2 atoms. More complex molecules can contain hundreds or even thousands of atoms bonded together. To determine the number of atoms in a particular molecule, you need to look at its molecular formula.

## Counting Atoms in Molecular Formulas

Molecular formulas represent the number and types of atoms in a molecule. For example, water has the formula H2O. This tells us it contains 2 hydrogen atoms and 1 oxygen atom, so there are 3 total atoms in a molecule of water. Some key points about molecular formulas:

• The numbers in subscripts represent the quantity of that atom. So O2 has 2 oxygen atoms.
• No subscript number means there is just 1 of that atom. So H2O has just 1 oxygen.
• The order of atoms doesn’t matter, so H2O is the same as HO2.

Let’s look at some examples to practice counting atoms:

Formula # of Atoms
H2O 3
CO2 3
C6H12O6 24

As you can see, we simply count up the number of each atom represented in the formula. For more complex formulas, carefully account for any subscripts – this is where people often make mistakes.

## Counting Atoms in Ionic Compounds

Ionic compounds are formed between metals and nonmetals. Their formulas require a special approach to counting atoms.

For ionic compounds, you cannot just count the subscripts. This is because the formula represents the smallest whole number ratio of ions, not individual atoms.

For example, NaCl represents sodium chloride, or table salt. The formula is showing the ratio of Na+ cations to Cl- anions, which is 1:1. But it does NOT mean NaCl has just 1 sodium and 1 chlorine atom.

To count atoms in ionic compounds:

1. Write out the total number of each ion based on subscripts.
2. Multiply by the number of atoms per ion.

Let’s try this on MgCl2:

• 1 Mg2+ cation
• 2 Cl- anions
• Mg2+ has 1 Mg atom
• Cl- has 1 Cl atom
• So total atoms = 1 Mg + 2 Cl = 3 atoms

This method works for any ionic compound. Be sure to account for transition metals that can form ions with multiple charges, like Fe2+ vs Fe3+.

## Counting Atoms in Macromolecules

Some very large molecules with thousands of atoms are represented by simplified formulas. Important examples include synthetic polymers and biological macromolecules like proteins and DNA.

These formulas use parentheses to show repetitive units. For instance, the polymer polyethylene is written as (C2H4)n. The “n” means the C2H4 unit repeats over and over.

To count atoms:

1. Count atoms in the repeating unit
2. Multiply by the number of repeating units

If we know a polyethylene chain has 1000 repeating units, then:

• C2H4 has 2 C atoms and 4 H atoms
• So 1000 units has 1000 x 2 = 2000 C atoms
• And 1000 x 4 = 4000 H atoms

This method can be applied to any polymer or macromolecule with a repeating structural unit. Again, be sure to account for the quantity of repeating units.

## Counting Atoms in Mixtures

Mixtures contain two or more different chemical substances, each with their own molecular or empirical formula. To calculate the total atom count in a mixture, you simply sum up the atoms from each component compound or element.

For example, air is approximately 78% nitrogen (N2) and 21% oxygen (O2). To find the number of atoms in a 100 gram sample of air:

• 78 g N2 has (78 g / 28 g/mol) = 2.8 moles of N2 molecules
• Each N2 has 2 N atoms, so 2.8 moles x 2 = 5.6 moles N atoms
• 21 g O2 has (21 g / 32 g/mol) = 0.7 moles of O2 molecules
• Each O2 has 2 O atoms, so 0.7 moles x 2 = 1.4 moles O atoms
• Total atoms = 5.6 moles N + 1.4 moles O = 7 moles atoms

This step-by-step method works for determining the total atom count in any mixture, once you know the composition by mass.

## Counting Atoms in Unknown Substances

Sometimes you may need to determine the number of atoms in a sample of an unknown solid. If the substance is pure and the identity is unknown, there are a few ways to calculate its molecular or empirical formula.

### Determining Empirical Formula

The empirical formula shows the lowest whole number ratio of atoms in a compound. It can be found using percent composition data from analytical techniques like mass spectrometry.

For example, mass spectrometry shows a compound contains 40% carbon, 6.7% hydrogen, and 53.3% oxygen. To calculate the empirical formula:

1. Assume 100 g sample so percents = grams of each element
2. Convert grams to moles using molar masses
3. Divide moles of each by smallest # of moles
4. Whole number ratio gives empirical formula
• 40 g C = 40/12 = 3.3 moles C
• 6.7 g H = 6.7/1 = 6.7 moles H
• 53.3 g O = 53.3/16 = 3.3 moles O
• Smallest # of moles is 3.3
• C:H:O ratio = 3.3:6.7:3.3 = 1:2:1
• Empirical formula = CH2O

Once you have the empirical formula, calculating atoms is straightforward stoichiometry. For ionic compounds, remember to account for the ratio of ions, not just empirical formula subscripts.

### Determining Molecular Formula

If the molar mass of the unknown substance is known, you can also calculate its molecular formula. This gives the actual number of atoms in each molecule, not just a ratio.

First derive the empirical formula as shown above. Then:

1. Calculate molar mass of empirical formula
2. Divide molar mass of substance by empirical formula molar mass
3. Multiple empirical formula by this ratio
4. Result gives molecular formula

Let’s say the empirical formula of a compound is found to be CH2O. If the molar mass is determined to be 180 g/mol:

• CH2O has a molar mass of (12 + 2 + 16) = 30 g/mol
• 180 g/mol / 30 g/mol = 6
• Multiply empirical formula by 6: (CH2O)6
• Molecular formula is C6H12O6

Now you can easily count 24 total atoms in the C6H12O6 molecular formula. This method ties together empirical formula calculations with molecular weight data to derive the molecular formula needed to count atoms.

## Conclusion

Determining the number of atoms in a molecule requires identifying the substance molecular or empirical formula. Simple molecular formulas can be counted directly. Ionic compounds require accounting for the ratio of ions. Macromolecules and polymers use the repeating unit and quantity. For unknown substances, analytical data allows derivation of empirical and molecular formulas to enable atom counting. With the right approach, counting atoms is a straightforward process applicable to any scenario where you need to find the exact number of atoms present.