Question

Calculate Analysis of a compound composed of iron and oxygen yields 174.86 g of Fe and 75.14 g of O. What is the empirical formula for this compound?

Short answer

The empirical formula for the compound composed of iron and oxygen is Fe₂O₃.

Step-by-step solution

Calculate the moles of iron and oxygen in the compound

To calculate the moles of an element, we need to use the formula: Moles = mass (g) / molar mass (g/mole) Given: Mass of Fe = 174.86 g Mass of O = 75.14 g Molar mass of Fe = 55.85 g/mole Molar mass of O = 16.00 g/mole Moles of Fe = 174.86 g / 55.85 g/mole = 3.131 moles Moles of O = 75.14 g / 16.00 g/mole = 4.696 moles

Find the ratio of moles of iron to the moles of oxygen

To find the simplest whole number ratio of iron to oxygen, divide the moles of both elements by the smallest number of moles. Smallest moles = 3.131 moles (Fe) Ratio of moles of Fe = 3.131 moles / 3.131 = 1 Ratio of moles of O = 4.696 moles / 3.131 = 1.50 Since we need a whole number ratio, multiply both ratios by 2. New Ratio of moles of Fe = 1 * 2 = 2 New Ratio of moles of O = 1.50 * 2 = 3

Write the empirical formula

Based on the whole number ratio obtained for iron and oxygen, the empirical formula for the compound is: Fe₂O₃ Thus, the empirical formula for this compound composed of iron and oxygen is Fe₂O₃.

Key concepts

Moles of Elements

When you are asked to find the empirical formula of a compound like an iron oxide, calculations often start with determining the number of moles of each element in the compound. Moles are a standard unit of measurement in chemistry that relate to the quantity of substance. It's like speaking the universal language of particles, molecules, or compounds in chemistry.

To calculate the moles of an element, use the formula: \[\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mole)}}\]If you know the mass of each element in grams and their respective molar masses (found on the periodic table), you can find out how many moles you have.

• For Fe (iron), with a mass of 174.86 grams, and a molar mass of 55.85 g/mole, it results in approximately 3.131 moles.


• For O (oxygen), with a mass of 75.14 grams, and a molar mass of 16.00 g/mole, it results in approximately 4.696 moles.

Understanding how to calculate moles is essential, as this step forms the foundation of finding the empirical formula.

Molar Mass Calculation

Molar mass acts like a bridge that connects the mass of a substance to its mole equivalent. It is an important figure and tool in chemistry, usually expressed in grams per mole (g/mole).

The molar mass reflects the mass of one mole of an element and is numerically equivalent to the atomic weight you would find on the periodic table. For example:

• Iron (Fe) has a molar mass of 55.85 g/mole.


• Oxygen (O) has a molar mass of 16.00 g/mole.

Knowing the molar mass allows you to convert between the mass of a sample in grams and the amount of substance in moles.
When you are tasked with finding the empirical formula of a compound, this conversion is very crucial, as it directly influences the calculation of the moles of elements involved.

Whole Number Ratio

The empirical formula is all about the simplest whole number ratio of elements in a compound. After calculating the moles for each element, you may find that the moles don't form a neat, whole-number ratio on their own.

To address this, divide all mole values by the smallest number of moles among them:

• The moles for Fe (iron) are 3.131, which becomes 1 when divided by itself.


• The moles for O (oxygen) are 4.696, which becomes roughly 1.50 when divided by 3.131.

The ratio isn't a whole number ratio yet. To fix this, it’s often necessary to multiply all ratios by a factor that turns them into whole numbers. Here, multiplying by 2 gives:

• Fe becomes 2, and O becomes 3.

This ratio of 2:3 is the simplest whole number ratio that corresponds to the empirical formula FeₓOᵧ, specifically Fe₂O₃.

Iron Oxide Compound

Iron oxide is a common term for a family of compounds consisting of iron and oxygen. The empirical formula provides its simplest form representation.

In this case, through our calculations, we discovered the simplest whole number ratio of iron to oxygen was 2:3. This helps us write the empirical formula: - The formula Fe₂O₃ tells us that in this molecule, there are 2 iron atoms for every 3 oxygen atoms.

Real iron oxide, however, may come with different structures and properties, but Fe₂O₃ is commonly known as ferric oxide or rust.
It's essential not just for chemistry enthusiasts or students solving homework problems but also widely useful in various industrial applications.
This empirical formula is significant in basic chemistry as it provides the ratio in which the atoms combine to form stable compounds.