Empirical formula and formula mass from reacting masses (easy start, no moles!)

 Empirical formula and formula mass from reacting masses (easy start, no moles!)

The EMPIRICAL FORMULA of a compound can be worked out by knowing the exact masses of the elements that combine to form a given mass of a compound.
The empirical formula of a compound is the simplest whole number ratio of atoms present in a compound.


 Here the word 'empirical' means from experimental data.

Do not confuse with molecular formula which depicts the actual total numbers of each atom in a molecule.
The molecular formula and empirical formula can be different or the same.
They are the same if the molecular formula cannot be simplified on a whole number basis.

Examples where molecular formula = empirical formula

e.g. for sodium sulfate Na₂SO₄  and  propane C₃H₈
You cannot simplify the atomic ratios 2 : 1 : 4 or 3 : 8 to smaller whole number (integer) ratios

Examples of where molecular formula and empirical formula are different e.g.

butane molecular formula C₄H₁₀, empirical formula C₂H₅

numerically, the empirical formula of butane is 'half' of its molecular formula

4 : 10 ==> 2 : 5

glucose molecular formula C₆H₁₂O₆, empirical formula CH₂O

numerically, the empirical formula of glucose is '¹/₆th' of the full molecular formula

6 : 12 : 6 ==> 1 : 2 : 1

The following examples illustrate the ideas using numbers more easily appreciated than in real experiments.

In real laboratory experiments only a fraction of a gram or a few grams of elements would be used, and a more 'tricky' mole calculation method is required than shown here

However the examples below show in principal how formulae are worked out from experiments.

Any calculation method must take into account the different relative atomic masses of the elements in order to get to the actual ratio of the atoms in the formula.

For example, just because 10g of X combines with 20g of Y, it does not mean that the formula of the compound is XY₂ !

If you divide the mass of each element by its atomic mass, you actually get the atomic ratio.

• Empirical formula calculation Example 5.1 The compound formed between lead and sulfur
• It is found that 207g of lead combined with 32g of sulphur to form 239g of lead sulphide.
• From the data work out the formula of lead sulphide. (Relative atomic masses: Pb = 207 and S = 32)
• In this case it easy to see that by the atomic mass ratio, 239 splits on a 1 to 1 basis of 1 atom of lead to 1 atom of sulphur (1 x 207 to 1 x 32 by mass)
• so the formula is simply PbS
• You can set out the calculation in a simple table format, in this case the numbers are very easy to deal with!
 

RATIOS ...	lead (Ar = 207)	sulphur S (Ar = 32)	Comments and tips
Reacting mass	207g	32g	not the real atom ratio
atom ratio from mass / atomic mass values	207/207 = 1	32/32 = 1	work out the simplest whole number ratio
simplest whole number atom ratio by trial & error	1	1
therefore the integer simplest ratio of 1 : 1 gives the empirical formula for lead sulphide as PbS

• -
• Empirical formula calculation Example 5.2 The empirical formula of a lead oxide
• It is found that 207g of lead combined with oxygen to form 239g of a lead oxide.
• From the data work out the formula of the lead oxide. (Relative atomic masses: Pb = 207 and O = 16)
• In this case, you first have to work out the amount of oxygen combined with the lead.
• By simple logic from the law of conservation of mass, this is 239 - 207 = 32g
• In atomic ratio terms, the 207 is equivalent to 1 atom of lead and the 32 is equivalent to 2 atoms of oxygen (1 x 207 to 2 x 16),
• so the formula is simply PbO₂
• Note: The mass of oxygen combined with the lead is deduced by subtracting the original mass of lead from final total mass of lead oxide.

 

RATIOS ...	lead (Ar = 207)	oxygen O (Ar = 16)	Comments and tips
Reacting mass	207g	239-207 = 32g	not the real atom ratio
atom ratio from mass / atomic mass values	207/207 = 1	32/16 = 2	work out the simplest whole number ratio
simplest whole number atom ratio by trial & error	1	2
therefore the simplest whole number ratio of 1 : 2 gives the empirical formula for this lead oxide as PbO2 Its actually called lead(IV) oxide

Credit to Docbrown