# DETERMINING AN EMPIRICAL FORMULA_1_ by hcj

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```									                              PERCENT COMPOSITION
Percent composition is the percent by mass of each element in a compound. To
determine the percent composition, first find the molar mass of the compound. Then find
the total mass of each element in the compound. Divide the mass of the element by the
mass of the compound and then multiply by 100 and that is the percent composition of that
element in the compound.

EX:    Na2CO3

Molar Mass = 105.99g                  C: 12.01g/ 105.99g x 100 =
Mass of Na = 45.98g
Mass of C = 12.01g
Mass of O = 48.00g

DETERMINING AN EMPIRICAL FORMULA

The empirical formula of a compound is the smallest whole number ratio of elements
in the compound. It is based on percent composition. In a sample of a compound, the ratio
of the moles of each element present in the sample will form a small whole number ratio.
These ratios can help determine the subscripts of the empirical formula of the compound.

EX. A sample of an unknown Carbon-Hydrogen compound contains 18 grams of
Carbon and 6 grams of Hydrogen. What is the empirical formula of the compound?

First, take your values and covert them into moles.

18 g C x    1 mole C = 1.5 moles C
12.01 g

6 g H x _1 mole H       = 6 moles H
1.01 g

Then, determine the simplest whole number ratio between the two elements. To do
this, divide both molar values by the smallest molar value. *If you get a ratio that does not
give you a whole number but rather a half (.5), then double all values to get the simplest
whole number ratio.

1.5 moles C     = 1          6 moles H = 4
1.5 moles                   1.5 moles

The ratio is the subscript of that element in the formula, CH 4.
More often, you will be given the percent composition of the compound. When this
happens, assume you have a 100g sample of the compound. And then logically, you
would have the percent’s value in grams. Then continue on as normal.

1)     Assume 100g.
2)     Convert grams into moles.
3)     Determine the simplest ratio by dividing all values by the smallest number.
4)     Ratio is the subscript (within 0.05). *If you get a 0.5 value – double all ratios!

EX. An unknown compound contains 74.2% Sodium and 25.8% Oxygen. What is
the empirical formula of the compound?

74.2% of a 100g sample is Sodium, therefore 74.2 g of the sample is Na.
25.8% of a 100g sample is Oxygen, therefore 25.8 g of the sample is O.

74.2g Na x    1 mole Na     = 3.23 moles Na = 2
22.99g             1.61

25.8g O x    1 mole O     = 1.61 moles O = 1
16.00g             1.61

Formula = Na2O

HYDRATES
A hydrate is a compound that has water molecules surrounding each compound molecule.
It has the same number of water molecules around each compound molecule. Since this is
a set situation, the compound must be named for its water molecules also. The formula is
written normally for the compound, then there is a dot, then a number, and then the formula
for water. The compound is named the same but then the prefix and the word “hydrate” is
added to the end of it. The prefix is for the number of water molecules there are. For
example, a common hydrate is BaCl 2  6H 2O, this is named Barium Chloride Hexahydrate.

Hydrates are compounds too. So you can calculate the percent composition for them by
element or as a percent of water. For the above example, Barium Chloride Hexahydrate,
BaCl2  6H2O, you can determine the percent Barium, Chlorine, Hydrogen, and Oxygen.
You could also determine the percent of Barium, Chlorine, and Water, or you could find the
percent of Barium Chloride and the percent water.

EX. Barium Chloride can exist as 2 possible hydrates. One of them is a
hexahydrate, the other has a 25.74% water. What is the formula of the hydrate?

25.74 g H2O x 1 mole H2O = 1.428 moles H2O = 3.99 ~ 4                        Therefore the
18.02g         0.3572                                         hydrate is a
tetrahydrate,
74.26 g BaCl2 x 1 mole BaCl2 = 0.3572 moles BaCl2          = 1               BaCl2  4H2O
207.90g          0.3572
DETERMINING A MOLECULAR FORMULA
A molecular formula is the actual formula of a compound. The empirical is the
simplest. Therefore the molecular compound is a whole number ratio to the empirical.
Once the empirical formula is determined, you must then compare the molar mass of the
empirical to the given molar mass of the molecular compound. Divide them to get the ratio
and multiply all subscripts by the ratio. You may have to rearrange the formula to
acknowledge polyatomic ions.

EX. An unknown compound has 79.85% carbon and 20.15% Hydrogen and a molar
mass of 30.08g. What is the Empirical formula? Molecular formula?

PART 1
79.85 g C x 1 mole C = 6.649 moles C =        1
12.01 g       6.649

20.15 g H x 1 mole H = 19.95 moles H =        3.000         The empirical formula is CH 3
1.01 g      6.649

PART 2
The Molecular Formula Mass given is 30.08g. The molar mass of the empirical formula is
15.04g.

So, 30.08g = 2      So, 2xs all the subscripts giving you a molecular formula of C2H6
15.04g

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