Empirical Formula and Molecular Formula Chemistry Tutorial

Key Concepts

• Empirical Formula of a compound shows the lowest whole number ratio of elements present in a compound.
• Molecular Formula of a compound shows how many atoms of each element are present in a molecule of the compound.⁽¹⁾
• The empirical formula mass of a compound refers to the sum of the atomic masses of the elements present in the empirical formula.
• The molecular mass (formula mass, formula weight or molecular weight) of a compound is a multiple of the empirical formula mass.

  M_r = n × empirical formula mass
      where M_r = molecular mass
      and n = a whole number (1 ,2 3, etc)

  Alternatively, you can relate the molar mass of the molecular formula and the empirical formula in the same way:
      molar mass of molecular formula = n × molar mass of empirical formula

• Empirical Formula can be calculated from the percentage composition (percent composition) of a compound.
• Empirical formula of a compound can be determined experimentally.

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Comparing Empirical Formula and Molecular Formula

If carbon and hydrogen are present in a compound in a ratio of 1:2, the empirical formula for the compound is CH₂.

The molecular formula for the same compound will equal to n × (CH₂), in other words, the molecular formula for this compound will be C_nH_2n

Using the periodic table of the elements we can determine the empirical formula mass of this compound(CH₂): 12.01 + (2 × 1.008) = 14.026

If we know the molecular mass of the compound is 28.00 (M_r = 28.00) then we can find the value of "n" in the molecular formula C_nH_2n:

Subsitute this value, n = 2, back into the general molecular formula C_nH_2n to get the molecular formula of this compound.
So the molecular formula for the compound is:

C_{(1 × 2)}H_{(2 × 2)} which is C₂H₄

There are many compounds that can have the empirical formula CH₂ and therefore a molecular formula of the form C_nH_2n.

Examples include:

• C₂H₄ (ethene or ethylene) molecular mass=28.0 and n = 2, that is, C_{(1 × 2)}H_{(2 × 2)}
• C₃H₆ (propene or propylene) molecular mass=42.0 and n = 3, that is, C_{(1 × 3)}H_{(2 × 3)}
• C₃H₆ (cyclopropane) molecular mass=42.0 and n = 3, that is, C_{(1 × 3)}H_{(2 × 3)}
• C₄H₈ (butene or butylene⁽²⁾) molecular mass=56.0 and n = 4, that is, C_{(1 × 4)}H_{(2 × 4)}
• C₄H₈ (cyclobutane) molecular mass=56.0 and n = 4, that is, C_{(1 × 4)}H_{(2 × 4)}

Theory Behind Calculating Empirical Formula from Percentage Composition

We can use the percentage composition (percent composition) of a compound to determine an empirical formula for the compound.

Remember that the percentage composition gives us the percent by mass of each element present in the compound, for example

If a compound is made up of 10% by mass of element X and 90% by mass of element Z
Then 100 g of the compound will contain:

• 10 g of element X

  mass of X =

  10 %

  ×

  100 g

  =

  10 100

  × 100

  = 10 g

• 90 g of element Z

  mass of Z =

  90 %

  ×

  100 g

  =

  90 100

  × 100

  = 90 g

10 g of element X and 90 g of element Z is present in 100 g of the compound.

On the other hand, the empirical formula of the compound gives us the lowest whole number ratio of atoms of each element in the compound, for example

Empirical formula XZ tells us that for every 1 atom of X there is 1 atom of Z in the compound.

Empirical formula XZ₂ tells us that for every 1 atom of X there are 2 atoms of Z, etc

Clearly, we will need to convert the "mass" of each element in the compound into a "number of atoms".

6.02 × 10²³ atoms of element X = 1 mole of atoms of element X

Mass of 1 mole of atoms of element X = molecular mass expressed in grams (molar mass)

So we can use the "mass" and "molar mass" (or relative molecular mass) to calculate the moles of atoms of each element present,

moles of element X =	mass of element X in grams         molar mass of element X in grams per mole
moles of element Z =	mass of element Z in grams         molar mass of element Z in grams per mole

Next we need to write the relationship between moles of X and moles of Z in the compound:

moles of element X

:

moles of element Z

and then to find the lowest whole number ratio of these moles

• If moles of Z < moles of X, divide both by moles of Z

  moles of element X moles of element Z

  :

  moles of element Z moles of element Z

  that is

  moles of element X moles of element Z

  : 1

• If moles of X < moles of Z, divide both by moles of X

  moles of element X moles of element X

  :

  moles of element Z moles of element X

  that is

  1 :

  moles of element Z moles of element X

Be aware that the calculation above to get the mole ratio of one element to another may not result in whole numbers.
A further calculation may be needed to get the lowest whole number ratio of moles of one element to another.
This is where a recognition of the decimal equivalent of common fractions, as shown in the table below, can be very helpful:

Once you have calculated the lowest whole number ratio of moles of one element to the other, you are ready to write the empirical formula, for example

• If the mole ratio of X to Z is 1:1, empirical formula is XZ
• If mole ratio of X to Z is 1:2, empirical formula is XZ₂
• If mole ratio of X to Z is 2:3, empirical formula is X₂Z₃

Steps for Calculating Empirical Formula from Percentage Composition

1. Assume 100 g of sample
2. Convert all percentages to a mass in grams
3. Find the relative atomic mass of each element present using the Periodic Table
4. Calculate the moles of each element present: n = mass ÷ relative atomic mass
5. Divide the moles of each element by the smallest of these to get a mole ratio
6. If the numbers in the mole ratio are all whole numbers (integers) convert this to an empirical formula
7. If the numbers in the mole ratio are NOT whole numbers, you will need to further manipulate these until the mole ratio is a ratio of whole numbers (integers)

Worked Example: Empirical Formula from Percentage Composition

Question: A compound is found to contain 47.25% copper and 52.75% chlorine. Find the empirical formula for this compound.

Solution:

1. Assume mass of sample of compound is 100 g
2. Convert all percentages to a mass in grams

   	Elements
   	Cu	Cl
   % by mass	47.25	52.75
   (b) mass in 100 g of compound	47.25 100 × 100 = 47.25 g	52.75 100 × 100 = 52.75 g

3. Find the relative atomic mass (molar mass) of each element present using the Periodic Table

   	Elements
   	Cu	Cl
   % by mass	47.25	52.75
   (b) mass in 100 g of compound	47.25 100 × 100 = 47.25 g	52.75 100 × 100 = 52.75 g
   (c) molar mass / g mol-1	63.55	35.45

4. Calculate the moles of each element present: n = mass ÷ relative atomic mass

   	Elements
   	Cu	Cl
   % by mass	47.25	52.75
   (b) mass in 100 g of compound	47.25 100 × 100 = 47.25 g	52.75 100 × 100 = 52.75 g
   (c) molar mass / g mol-1	63.55	35.45
   (d) moles / mol	47.25 63.55 = 0.7435	52.75 35.45 = 1.488

5. Divide the moles of each element by the smallest of these to get a mole ratio

   	Elements
   	Cu	Cl
   % by mass	47.25	52.75
   (b) mass in 100 g of compound	47.25 100 × 100 = 47.25 g	52.75 100 × 100 = 52.75 g
   (c) molar mass / g mol-1	63.55	35.45
   (d) moles / mol	47.25 63.55 = 0.7435	52.75 35.45 = 1.488
   (e) divide moles by 0.7435	0.7435 0.7435 = 1	1.488 0.7435 = 2

6. If the numbers in the mole ratio are all whole numbers (integers) convert this to an empirical formula:

   mole ratio Cu : Cl is	1:2 (1 and 2 are both whole numbers)
   empirical formula is	CuCl2

7. If the numbers in the mole ratio are NOT whole numbers, you will need to further manipulate these until the mole ratio is a ratio of whole numbers (integers)
   This step is not required since we have already achieved the lowest ratio of whole numbers

Empirical formula for this compound is CuCl₂

Worked Example: Molecular Formula from Percentage Composition and Molar Mass

Question: A compound with a molar mass of 34.0 g mol^-1 is known to contain 5.88% hydrogen and 94.12% oxygen. Find the molecular formula for this compound.

The solution to this problem is in two parts:

• Part 1: determine the empirical formula for the compound based on the percentage composition
• Part 2: determine the molecular formula for the compouund based on the empirical formula and molar mass

Part 1: Determine the empirical formula using the percentage composition of the compound

Part 2: Determine the molecular formula using the empirical formula and molar mass of the compound

1. empirical formula is HO (calculated in part 1 above)
2. molecular formula = whole number × empirical formula
   molecular formula = n × empirical formula
   molecular formula is H_nO_n
3. Calculate the molar mass of the empirical formula HO:
   = 1.008 + 16.00 = 17.008 g mol^-1
4. Calculate "n"
   molar mass of compound = n × molar mass of empirical formula
   34.0 = n × 17.008
   n = 34.0 ÷ 17.008 = 2
5. Write the molecular formula for the compound
   molecular formula is H_nO_n
   n = 2
   substitute this value for n into the molecular formula H_nO_n:
   molecular formula of the compound is therefore H₂O₂