Calculating Empirical Formulas

If percent composition is given:
1.
Assume that the total mass of the compound is 100.00 g.
(Percentages of each element equals the mass in grams.)
Convert grams to moles (using the molar mass of each
element).
Find the mole ratio by dividing everything by the smallest # of
moles.
If those numbers are whole numbers you have just found the
subscripts for the formula.
2.
3.
4.

If actual masses are given you can skip to step 3.
Example Problem:

What is the empirical formula for a compound that
contains 10.89% magnesium, 31.77% chlorine and
the rest is oxygen?
K:
UK:
MgCl2O8

Determine the empirical formula of a compound
containing 2.644g of gold and 0.476g of chlorine.
K:
UK:
AuCl

BUT…often in determining empirical
formulas, the calculated mole ratios are still
not whole numbers. In such cases all the
mole ratio values must be multiplied by the
smallest factor that will make them whole
numbers.
More Examples:
1. A blue solid is found to contain 36.84% nitrogen
and 63.16% oxygen. What is the empirical formula
for the solid?
K:
UK:
N2O3
2.
Propane is a hydrocarbon. It is composed of
81.82% carbon and 18.18% hydrogen. What is
the empirical formula?
K:
UK:
C3H8
Calculating Molecular Formulas

In order to determine the molecular formula
for an unknown compound, you must know
the molar mass of the compound in addition
to its empirical formula.

Then you can compare the molar mass of
the compound with the molar mass
represented by the empirical formula.

This is done using the following equation:
given molar mass of compound
mass of empirical formula
You get a number to multiply the subscripts
of the empirical formula by to get the
molecular formula.
 Let’s do some practice problems.

Practice Problems:
1) Maleic acid is a compound that is used in the plastics
and textiles industries. The composition of maleic acid
is 41.39% carbon, 3.47% hydrogen, and 55.14%
oxygen. Its molar mass is 116.10 g/mol. Calculate the
molecular formula for maleic acid.
K:
UK:

Start by determining the empirical formula:

What is the mole ratio of the elements? 1C:1H:1O

So the empirical formula is: CHO
Next, calculate the molar mass represented
by the empirical formula. 29.02 g/mol
 As stated in the problem, the molar mass of
maleic acid is known to be 116.10 g/mol.
 To determine the molecular formula for
maleic acid, calculate the whole number
multiple to apply to its empirical formula.

116.10 g / mol
 4.001
29.02 g / mol



This calculation shows that the molar mass of
maleic acid is four times the molar mass of its
empirical formula CHO.
Therefore, the molecular formula must have four
times as many atoms of each element as the
empirical formula.
Thus, the molecular formula is C4H4O4
To Review:
=n
More Practice Problems:
2) Caffeine is 49.48% C, 5.15% H, 28.87% N and
16.49% O. It has a molar mass of 194 g/mol. What is
its molecular formula?
K:
UK:
3) A compound was found to contain 49.98 g carbon and 10.47 g
hydrogen. The molar mass of the compound is 58.12 g/mol.
Determine the molecular formula.
K:
UK:
C4H10
11.5 – The Formula
for a Hydrate
What is a hydrate?
A hydrate is a compound that has a specific
number of water molecules that are
“trapped” inside its crystal structure.
 Common ones are opal and cobalt chloride.

Images from wikipedia
What’s in a name?
To show the number of water molecules in a
formula unit of a hydrate chemists write the
formula with a dot and the number of water
molecules in it.
 Example: CaCl2 . 2H2O
 The name is calcium chloride dihydrate
 This means that for every one formula unit of
calcium chloride there are 2 water molecules
associated with it.

Counting the Water Molecules



Chemists use prefixes
to count how many
water molecules are
associated with a
hydrated compound.
Each prefix means a
certain number.
The root word hydrate
means water
Prefix
Molecules of H2O
mono-
1
di-
2
tri-
3
tetra-
4
penta-
5
hexa-
6
hepta-
7
octa-
8
nona-
9
deca-
10
Analyzing a Hydrate



To analyze a hydrate you must remove the water
of hydration.
Usually this is done by heating it so that the
remaining substance has no water. It is then
called an anhydrous substance.
You must find the number of moles of water
associated with one mole of the hydrate.
Hydrated cobalt chloride
anhydrous cobalt chloride
Example:
Suppose you have a sample of a hydrate of
copper(II) sulfate.
 The formula is CuSO4 . xH2O. You must
determine “x”. The “x” is the number of
moles of water associated with one mole of
CuSO4.
 We are going to heat a sample and figure it
out together.

Uses of hydrates


They can absorb water
into their structure so
they are used as
drying agents in the lab
or in stores.
Examples: Calcium
sulfate in the lab and
the silica packets that
sometimes come in
shoe boxes or purses