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D3.3 · Explain the relationship between empirical and molecular formulas

Learn to explain the relationship between empirical and molecular formulas through clear examples and targeted practice.

Ontario Grade 11 Chemistry

Quantities in Chemical Reactions

How the simplest atom ratio relates to the actual number of atoms in a molecule

Two substances can have the same simplest ratio of atoms but different numbers of atoms in each molecule. For example, particles with formulas that are different multiples of one another can share the same simplest ratio. An empirical formula shows that simplest ratio. A molecular formula shows the actual number of each type of atom in one molecule. The link between the formulas is a whole-number multiplier.

What you will learn

1. From atom counts to a simplest ratio

A chemical formula uses element symbols and subscripts to show the atoms in a substance. A subscript is the small number written after an element symbol. It tells how many atoms of that element are represented. If there is no subscript, the count is one.
Before comparing formulas, recall a ratio. A ratio compares amounts. For example, the ratio of six red counters to twelve blue counters is six to twelve. Dividing both numbers by six gives the simplest whole-number ratio, one to two. The ratio stays the same even though the numbers become smaller.
An empirical formula is the chemical formula that gives the simplest whole-number ratio of the different atoms in a substance. It does not always show the actual number of atoms in a molecule. For instance, a formula with two carbon atoms and four hydrogen atoms has the same simplest ratio as one carbon atom to two hydrogen atoms.
This is a particle-level idea: count the atoms of each element in a particle, then compare those counts. The empirical formula records the reduced ratio. It is a useful way to describe the proportion of elements without claiming that the particle contains only that many atoms.
612=12\frac{6}{12}=\frac{1}{2}

2. What a molecular formula adds

A molecular formula gives the actual number of each type of atom in one molecule. It keeps the full atom counts rather than reducing them. The word molecule refers here to a particle made from atoms joined together.
The empirical and molecular formulas are related. The molecular formula is the empirical formula multiplied by the same whole number for every subscript. That number is called the multiplier. It must be a positive whole number because the actual atom counts are whole numbers.
For example, if every subscript in a molecular formula is three times the matching empirical-formula subscript, the molecule contains three times as many atoms of each element as the simplest ratio indicates. Dividing all molecular-formula subscripts by that multiplier returns the empirical formula.
A formula can already be in its simplest ratio. In that case, the empirical and molecular formulas are the same. A formula in simplest form has a multiplier of one. The relationship does not mean that every substance must have a molecular formula; this lesson focuses on substances described by molecules.
molecular formula=(empirical formula)n\text{molecular formula}= (\text{empirical formula})_n

3. Finding the multiplier from molar mass

Molar mass is the mass of one mole of a substance, measured in grams per mole. A mole is a counting unit used in chemistry. For this relationship, compare the substance's molar mass with the mass per mole represented by its empirical formula.
The empirical-formula mass is found by adding the relative atomic masses for the atoms shown in the empirical formula. Use the atomic masses from the course periodic table. The result is expressed in grams per mole when used in this calculation.
Divide the given molar mass by the empirical-formula mass. The quotient gives the multiplier. It should be a whole number, or very close to one because of rounding in the supplied data. Apply that same multiplier to every subscript in the empirical formula.
Finally, check the result by reducing all subscripts in the molecular formula by their greatest common factor. The reduced formula should match the empirical formula. This check confirms that the proposed formula has the required simplest ratio.
n=molar massempirical-formula massn=\frac{\text{molar mass}}{\text{empirical-formula mass}}

4. Units, rounding, and reasonableness

Keep units in the mass comparison. Both the molar mass and empirical-formula mass are measured in grams per mole, so their units cancel in the division. The multiplier has no units because it is a count.
Do not round a value such as 5.9 to a molecular-formula multiplier of 5.9. Subscripts count atoms, so they must be whole numbers. If the calculated value is close to a whole number, use the nearest whole number and check whether the given measurements reasonably explain the small difference.
Use the significant digits of the data when reporting measured masses. The multiplier is still reported as a whole number because it represents how many times the empirical ratio repeats. After multiplying, write subscripts as whole numbers and omit a subscript of one.
A result is reasonable only if it preserves the element ratio and gives whole-number atom counts. A different multiplier applied to different elements would change the ratio, so it would not describe the same empirical formula.

Worked example

Use molar mass to find a molecular formula

A substance has empirical formula CH₂O and molar mass 180.0 g/mol. Find its molecular formula. Use C = 12.01 g/mol, H = 1.008 g/mol, and O = 16.00 g/mol.
  1. Find the empirical-formula mass
    The empirical formula has one carbon atom, two hydrogen atoms, and one oxygen atom. Add the corresponding atomic masses. The result represents one mole of the empirical-formula ratio.
    12.01 g/mol+2(1.008 g/mol)+16.00 g/mol=30.026 g/mol12.01\ \mathrm{g/mol}+2(1.008\ \mathrm{g/mol})+16.00\ \mathrm{g/mol}=30.026\ \mathrm{g/mol}
  2. Calculate the multiplier
    Divide the given molar mass by the empirical-formula mass. The units cancel, and the quotient is very close to a whole number.
    n=180.0 g/mol30.026 g/mol≈5.995≈6n=\frac{180.0\ \mathrm{g/mol}}{30.026\ \mathrm{g/mol}}\approx 5.995\approx 6
  3. Multiply each subscript
    Use six for every element in the empirical formula. Carbon's implied subscript of one also becomes six.
    (CH2O)6=C6H12O6(\mathrm{CH_2O})_6=\mathrm{C_6H_{12}O_6}
  4. Check the ratio
    Divide the molecular-formula subscripts by six. This returns the given empirical formula, so the relationship is consistent.
    C6H12O6÷6=CH2O\mathrm{C_6H_{12}O_6}\div 6=\mathrm{CH_2O}
Answer: The molecular formula is C₆H₁₂O₆.
Check: Its empirical-formula mass is 30.026 g/mol, and six times this value is 180.156 g/mol, which is consistent with the given 180.0 g/mol after rounding.

Common mistakes and how to avoid them

Treating the empirical formula as the actual atom count in every molecule.
Correction: The empirical formula gives the simplest ratio. The molecular formula gives actual counts in one molecule.
Using a different multiplier for each element.
Correction: Apply one shared whole-number multiplier to every subscript.
Leaving a decimal value as a molecular-formula subscript.
Correction: Subscripts count atoms and must be whole numbers. Check the mass calculation and use the nearest whole-number multiplier when the difference is due to rounding.
Assuming empirical and molecular formulas are always different.
Correction: They are the same when the molecular formula is already in its simplest whole-number ratio.

Lesson summary

Check your understanding

Question 1

A molecule has molecular formula N₂O₄. What is its empirical formula?
  1. NO₂
  2. N₂O₂
  3. N₂O₄
  4. NO
Show answer and explanation
NO₂
Divide both subscripts by two. The simplest ratio is one nitrogen atom to two oxygen atoms.

Question 2

An empirical formula is AB₂, and the molecular formula has multiplier four. What is the molecular formula?
  1. A₄B₈
  2. A₄B₂
  3. AB₈
  4. A₂B₄
Show answer and explanation
A₄B₈
Multiply both subscripts by four. The resulting formula is A₄B₈.

Question 3

A substance's molar mass is about three times its empirical-formula mass. What is the multiplier?
  1. One
  2. Two
  3. Three
  4. Six
Show answer and explanation
Three
The multiplier is the molar mass divided by the empirical-formula mass. A ratio of about three gives a whole-number multiplier of three.

Key terms

Empirical formula
A formula showing the simplest whole-number ratio of the different atoms.
Molecular formula
A formula showing the actual number of each type of atom in one molecule.
Subscript
A small number after an element symbol that gives the number of those atoms.
Molar mass
The mass of one mole of a substance, measured in grams per mole.
Multiplier
The whole number used to multiply every empirical-formula subscript to obtain the molecular formula.

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