of a compound.

In a previous video, we found the “empirical formula” and this is a related idea, but

they are not the same thing.

The Empirical Formula gives the lowest whole number ratio of the atoms of the elements

in a compound.

This may or may not be the same as the molecular formula for a given compound.

The molecular formula is sometimes called the “true formula” because it tells you

how many of each kind of atom are actually present in the molecule.

It’s important to note that in a molecule, the arrangements of the atoms in 3 dimensions

makes a big difference.

Neither the molecular formula nor the empirical formula spell out what the molecule looks

like in three dimensions.

For that, we need a structural formula, and

we’ll save that complicated idea for another video

So what IS the relationship between these two kinds of chemical formulas?

The molecular formula is either the same as the empirical formula or it is a simple whole-number

multiple of the empirical formula.

It’s going to have the same ratio of atoms as the empirical formula, but the actual number

of atoms may be different.

For example, formaldehyde and acetic acid have the same empirical formula, CH2O, but

different molecular formulas.

Formaldehyde is an interesting case, because its molecular formula is exactly the same

as its empirical formula.

This tells you the actual number of each kind of atom in each molecule of formaldehyde :

1 atom of carbon, 2 atoms of hydrogen, and 1 atom of oxygen.

By contrast, the molecular formula of acetic acid is a multiple of its empirical formula.

If you multiply the empirical formula by 2, you get the molecular formula of acetic acid:

C2H4O2.

Notice the ratio of atoms is the same.

But in each molecule of acetic acid, there are actually

2 atoms of Carbon, 4 atoms of Hydrogen, and 2 atoms of Oxygen.

To find the molecular formula of a compound, you need to have its empirical formula and

its molar mass.

The goal is to find out how many empirical formula units are in one molecule of the compound.

Our strategy is to Calculate the empirical formula mass

Divide the molar mass by the empirical formula mass.

This tells you how many of the empirical formula units are needed to form

one molecule of the compound.

This should be a whole number answer, or very close.

If your answer isn’t an integer or very close to one, you’ve made a mistake somewhere.

Multiply the empirical formula by this value.

Let’s see some examples:

Example 1: A compound has the empirical formula CH2O.

It has a molar mass of 180 g/mol.

What is the molecular formula?

This empirical formula looks familiar - it’s the same empirical formula as formaldehyde

and acetic acid, as we talked about earlier.

Let’s go through the steps and see if it’s one of those.

STEP 1: Calculate the empirical formula mass.

We get that from the periodic table.

12.011 + 2(1.008) + 15.999 = 30.026 g/mol

STEP 2: Divide the molar mass by the empirical formula mass.

180 g/mol / 30.026 g/mol = 5.99 We’re looking for a simple whole number to multiply the

empirical formula by, so we’ll round to 6.

STEP 3: Multiply the empirical formula by this value: 6 times (CH2O) = C6H12O6.

This is glucose.

So now we know 3 compounds that have the same empirical formula,

but different molecularformulas.

Example 2: For our next example, let’s work a problem all the way through from the percent

composition data and the molar mass to get the molecular formula.

This means first we will find the empirical formula, and then go on to find the molecular

formula.

Our experimental data tells us the compound is 94.1% O and 5.9% H. The molar mass is 34g/mol.

First, we’ll find the empirical formula, which only requires the % composition data.

Assume 100g.

Then we have 94.1g Oxygen and 5.9g Hydrogen.

Convert to moles to get the mole ratio.

For oxygen, we have 94.1g (1 mol/15.999g) = 5.88 mol oxygen

For hydrogen, we have 5.9g (1 mol/1.008g)= 5.85 mol Hydrogen

H 5.85 O 5.88 Divide through by the lowest number, 5.85.

We get H1O1 (remember the 1s are understood, so we

get HO as the empirical formula.

Next we find the empirical formula mass.

1.008 g/mol + 15.999 g/mol = 17.007 g/mol

Now we use the molar mass given in the problem.

Molar mass/ empirical formula mass = 34.0 g/mol / 17.007 g/mol = 2

In other words, there are 2 empirical formula units per 1 of these molecules.

So we multiply the empirical formula by 2: 2(HO) = H2O2 hydrogen peroxide.

What if you see a problem asking you to go in the other direction?

Given a molecular formula, what is the empirical formula?

Example 3: Butane has the molecular formula C4H10.

What is the empirical formula?

Notice there is no other information given in the problem.

We don’t need any percent composition data or molar mass information to solve this problem.

The empirical formula is going to be the molecular formula divided by the Greatest Common Divisor

of the subscripts.

The subscripts here are 4 and 10.

If you factor these, 4 is 2x2, and 10 is 2x 5.

The greatest common divisor is 2, so we will divide through by 2 to simplify the molecular

formula down to the empirical formula.

C4/2 H10/2 = C2H5.

Remember, an empirical formula may or may not be the same as the molecular formula.

The molecular formula is always a simple multiple of the empirical formula.

For example, for the empirical formula CH2O, there are many possible multiples that correspond

to different compounds.

CH2O is both the empirical formula and molecular formula for formaldehyde, but if we multiply

that empirical formula by 2, we get C2H4O2,

which is the molecular formula for acetic acid.

If we multiply CH2O by 6, we get C6H12O6, which is glucose.

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