Question

What three types of information are used to find an empirical formula from percentage composition data?

Short answer

Mass of each element, moles of each element, and the simplest whole-number ratio of moles.

Step-by-step solution

Determine the mass of each element

Convert the percentage composition data into the masses of each element (in grams) assuming you have 100 grams of the compound. This simplifies the percentages directly into grams since the percentage directly translates to mass in grams.

Convert mass to moles

Divide the mass of each element by its atomic mass to get the number of moles of each element. The atomic mass can be found on the periodic table.

Determine the simplest whole-number ratio

Find the simplest whole number ratio of moles of each element by dividing each mole value by the smallest number of moles calculated in step 2. This ratio is the empirical formula.

Key concepts

Percentage Composition

To find an empirical formula, one of the first steps involves understanding the percentage composition of a compound.
Percentage composition tells us the percentage by mass of each element in a compound.
Imagine a compound that is made up of 40% carbon, 6.7% hydrogen, and 53.3% oxygen. This means that in 100 grams of this compound, 40 grams is carbon, 6.7 grams is hydrogen, and 53.3 grams is oxygen.
This step helps to bridge the information given in percentages to actual masses, making it easier to perform further calculations.
Therefore, the key takeaway is:

• Convert percentages directly into masses in grams. If you have 100 grams of the compound, the percentages equal the mass in grams.

Mass to Moles Conversion

Once you have the masses of each element in grams, the next step is to convert these masses to moles.
The formula for this conversion is:
\( \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \).
The molar mass of each element is found on the periodic table and represents the mass of one mole of that element.
For example, if you have 53.3 grams of oxygen and the molar mass of oxygen is 16 g/mol, then:
\( \text{Number of moles of oxygen} = \frac{53.3 \text{ g}}{16 \text{ g/mol}} = 3.33 \text{ moles} \).
This calculation is done for each element, converting their respective masses into moles.
Converting mass to moles is essential since moles describe the actual number of atoms, which is crucial for finding the simplest ratio.

Simplest Whole-Number Ratio

The next step involves finding the simplest whole-number ratio of the moles of each element.
Divide each mole value obtained in the previous step by the smallest number of moles calculated among the elements.
For example, if you have \(3.33 \) moles of oxygen, \(3.33 \) moles of carbon, and \(6.67 \) moles of hydrogen, the smallest number is \(3.33 \).
Now, divide each of these mole values by \(3.33 \):
\( \frac{3.33}{3.33} = 1 \) (Carbon),
\( \frac{6.67}{3.33} \approx 2 \) (Hydrogen),
\( \frac{3.33}{3.33} = 1 \) (Oxygen)
This ratio gives \(CH_2O \).
If the resulting numbers are not whole numbers, you may have to multiply all ratios by the same factor to make them whole numbers.
This final ratio is your empirical formula, representing the simplest whole-number ratio of atoms in the compound.