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.)2. Convert grams to moles (using the molar mass of each

element). 3. Find the mole ratio by dividing everything by the smallest # of

moles.4. If those numbers are whole numbers you have just found the

subscripts for the formula.

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

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.

Calculating Molecular Formulas

This is done using the following equation:

You get a number to multiply the subscripts of the empirical formula by to get the molecular formula.

Let’s do some practice problems.

given molar mass of compound

mass of empirical formula

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.

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

116.10 /4.001

29.02 /

g mol

g mol

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