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# Determining Molecular Formulas

## Calculating the kind and number of atoms of each element in a molecule

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Determining Molecular Formulas

Credit: Ben Mills (Wikimedia: Benjah-bmm27)
Source: http://commons.wikimedia.org/wiki/File:D-glucose-chain-2D-Fischer.png

Credit: User:glycoform/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:Sucrose_3Dprojection.png

#### How can you determine the differences between these two molecules?

Above we see two carbohydrates: glucose and sucrose.  Sucrose is almost exactly twice the size of glucose, although their empirical formulas are very similar.  Some people could distinguish them on the basis of taste, but it’s not a good idea to go around tasting chemicals. The best way is to determine the molecular weights – this approach allows you to easily tell which compound is which.

### Molecular Formulas

Molecular formulas give the kind and number of atoms of each element present in a molecular compound.  In many cases, the molecular formula is the same as the empirical formula.  The molecular formula of methane is CH4 and because it contains only one carbon atom, that is also its empirical formula.  Sometimes, however, the molecular formula is a simple whole-number multiple of the empirical formula.  Acetic acid  is an organic acid that is the main component of vinegar.  Its molecular formula is C2H4O2.  Glucose is  a simple sugar that cells use as a primary source of energy.  Its molecular formula is C6H12O6.  The structures of both molecules are shown in the figure below.  They are very different compounds, yet both have the same empirical formula of CH2O.

Credit: (left) Ben Mills (Wikimedia: Benjah-bmm27); (right) Ben Mills (Wikimedia: Benjah-bmm27), User:Yikrazuul/Wikimedia Commons
Source: Acetic acid: http://commons.wikimedia.org/wiki/File:Acetic-acid-2D-flat.png; Glucose: http://commons.wikimedia.org/wiki/File:D-glucose-chain-2D-Fischer.png

Acetic acid (left) has a molecular formula of C2H4O2, while glucose (right) has a molecular formula of C6H12O6. Both have the empirical formula CH2O.[Figure3]

Empirical formulas can be determined from the percent composition of a compound.  In order to determine its molecular formula, it is necessary to know the molar mass of the compound.  Chemists use an instrument called a mass spectrometer to determine the molar mass of compounds.  In order to go from the empirical formula to the molecular formula, follow these steps:

1. Calculate the empirical formula mass (EFM), which is simply the molar mass represented by the empirical formula.
2. Divide the molar mass of the compound by the empirical formula mass. The result should be a whole number or very close to a whole number.
3. Multiply all the subscripts in the empirical formula by the whole number found in step 2. The result is the molecular formula.

#### Sample Problem One: Determining the Molecular Formula of a Compound

The empirical formula of a compound of boron and hydrogen is BH3.  Its molar mass is 27.7 g/mol.  Determine the molecular formula of the compound.

Step 1: List the known quantities and plan the problem.

Known

• empirical formula = BH3
• molar mass = 27.7 g/mol

Unknown

• molecular formula = ?

Steps to follow are outlined in the text.

Step 2: Calculate.

1. The empirical formula mass (EFM) = 13.84 g/mol

2. \begin{align*}\frac{\text{molar mass}}{\text{EFM}}=\frac{27.7}{13.84}=2\end{align*}

3. \begin{align*}\text{BH}_3 \times 2 =\text{B}_2\text{H}_6\end{align*}

The molecular formula of the compound is B2H6.

The molar mass of the molecular formula matches the molar mass of the compound.

### Summary

• A procedure is described that allows the calculation of the exact molecular formula for a compound.

### Review

1. What is the difference between an empirical formula and a molecular formula?
2. In addition to the elemental analysis, what do you need to know to calculate the molecular formula?
3. What does the empirical formula mass tell you?

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