Question

List three ways compositional data may be given in a problem that involves finding an empirical formula.

Short answer

Mass percentages, masses of each element, and number of moles are three ways to present compositional data for finding an empirical formula.

Step-by-step solution

- Mass Percentages

One common way is to give the mass percentages of each element in a compound. For example, a problem might state that a compound is composed of 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass.

- Mass of Each Element

Another method is by providing the actual masses of each element in a given sample. For instance, the problem might specify that in a 100-gram sample, there are 40 grams of carbon, 6.7 grams of hydrogen, and 53.3 grams of oxygen.

- Number of Moles of Each Element

A third way is to give the number of moles of each element in the compound. For example, a problem could state that a compound contains 3.33 moles of carbon, 6.67 moles of hydrogen, and 3.33 moles of oxygen.

Key concepts

Mass Percentages

Mass percentages tell us the proportion of each element in a compound by mass. This is often given in problems that ask you to find the empirical formula. For example, a problem might say a substance has 40.0% Carbon, 6.7% Hydrogen, and 53.3% Oxygen.

To work with mass percentages, you imagine having a 100-gram sample of the substance. This means:
- 40.0 grams of Carbon (since 40.0% of 100 grams is 40.0 grams)
- 6.7 grams of Hydrogen
- 53.3 grams of Oxygen

Next, you need to convert these masses into moles because the empirical formula is based on the ratio of atoms, not their mass. You do this using the molar mass of each element. For carbon, hydrogen, and oxygen, the molar masses are 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively.

Elemental Masses

Another way to receive compositional data is by the actual mass of each element in a sample. This method is straightforward. For example, if a problem specifies that a 100-gram sample contains 40 grams of Carbon, 6.7 grams of Hydrogen, and 53.3 grams of Oxygen, you are directly provided with the masses you need.

Just like with mass percentages, the next step is to convert these masses into moles using the molar mass of each element. Remember:
- Carbon: 12.01 g/mol
- Hydrogen: 1.01 g/mol
- Oxygen: 16.00 g/mol

These conversions allow you to determine how many moles of each atom are present in your sample. Knowing the number of moles of each element will bring you a step closer to finding the empirical formula.

Mole Calculation

The third way to present compositional data is by providing the number of moles of each element directly. This simplifies the process because you skip the mass-to-mole conversion step. For example, a problem might state a compound contains 3.33 moles of Carbon, 6.67 moles of Hydrogen, and 3.33 moles of Oxygen.

To find the empirical formula, you need to find the simplest whole number ratio among the moles of the elements. To do this:
- Divide each mole amount by the smallest number of moles in the set.

In our example, the smallest number of moles is 3.33. Dividing: - Carbon: 3.33 / 3.33 = 1
- Hydrogen: 6.67 / 3.33 = 2
- Oxygen: 3.33 / 3.33 = 1

The simplest whole number ratio is 1:2:1. Thus, the empirical formula for the compound is CH₂O. All these methods, whether through mass percentages, actual masses, or moles, aim to help you deduce the empirical formula by understanding the proportions of elements in a compound.