Problem 13 - Chemistry: An Atoms-Focused Approach

Question

Two of the more common oxides of iron have the formulas \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) How much more oxygen combines with a given mass of iron to form \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) than combines with the same mass of iron to form FeO?

Step-by-Step Solution

Answer

Answer: 7.8 % more oxygen is needed to form Fe₂O₃ than to form FeO.

Step 1: Calculate the molar masses of the given compounds

We will calculate the molar masses of FeO and Fe₂O₃, using atomic masses: - For FeO: one atom of iron (Fe) has a molar mass of 55.85 g/mol and one atom of oxygen (O) has a molar mass of 16.00 g/mol. Therefore, the molar mass of FeO is 55.85 g/mol + 16.00 g/mol = 71.85 g/mol. - For Fe₂O₃: two atoms of iron (Fe) have a combined molar mass of 2 × 55.85 g/mol = 111.70 g/mol. Likewise, three atoms of oxygen (O) have a combined molar mass of 3 × 16.00 g/mol = 48.00 g/mol. Therefore, the molar mass of Fe₂O₃ is 111.70 g/mol + 48.00 g/mol = 159.70 g/mol.

Step 2: Calculate the mass percentage of oxygen in each compound

Now we will determine the mass percentage of oxygen in each compound: - For FeO: mass percentage of oxygen = (molar mass of O / molar mass of FeO) × 100 = (16.00 g/mol / 71.85 g/mol) × 100 = 22.3 % - For Fe₂O₃: mass percentage of oxygen = (molar mass of 3O / molar mass of Fe₂O₃) × 100 = (48.00 g/mol / 159.70 g/mol) × 100 = 30.1 %

Step 3: Determine the difference in mass percentage of oxygen

Finally, we calculate the difference in mass percentage of oxygen for the two compounds: Difference = mass percentage of oxygen in Fe₂O₃ - mass percentage of oxygen in FeO = 30.1 % - 22.3 % = 7.8 % In conclusion, 7.8% more oxygen is needed to combine with a given mass of iron to form Fe₂O₃ than with the same mass of iron to form FeO.

Key Concepts

Molar Mass Calculation

When dealing with chemical compounds, understanding their molar mass is crucial for many calculations. The molar mass is essentially the mass of one mole of a substance. It is typically expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you need to sum the molar masses of each individual atom in the compound based on its chemical formula.

For example, let's look at two iron oxides: FeO and Fe₂O₃.

• For FeO: Add the molar mass of one iron (Fe) atom, 55.85 g/mol, to one oxygen (O) atom, 16.00 g/mol. This gives us a total molar mass for FeO of 71.85 g/mol.


• For Fe₂O₃: Multiply the molar mass of one iron by two (for the two Fe atoms), giving 111.70 g/mol, and add it to the molar mass for three oxygen atoms (48.00 g/mol). The total molar mass for Fe₂O₃ is then 159.70 g/mol.

This calculation helps us compare the weights of different compounds, allowing for further analyses such as mass percentage calculations.

Mass Percentage

Mass percentage is a way of expressing the concentration of an element within a compound. It tells you how much of the compound's total mass is made up by a particular element. This is particularly useful in understanding how much of an element is present relative to the other components in the compound.

To find the mass percentage of an element in a compound, you divide the total mass of the element in one mole of the compound by the compound's molar mass, then multiply by 100 to convert it to a percentage.

• In FeO, the mass percentage of oxygen is calculated as (16.00 g/mol / 71.85 g/mol) × 100, equating to 22.3%.


• In Fe₂O₃, it is (48.00 g/mol / 159.70 g/mol) × 100, resulting in 30.1%.

Knowing the mass percentage allows us to compare how different amounts of oxygen incorporate into varying iron oxide structures, showing us that Fe₂O₃ holds a substantially higher proportion of oxygen compared to FeO.

Chemical Formula

A chemical formula is a symbolic representation of a compound, showcasing which elements are present and the ratio of atoms in a molecule of that compound. It provides essential information about the composition and can guide us in determining molar masses and mass percentages.

For instance, the chemical formula FeO indicates a simple binary compound of iron and oxygen in a 1:1 ratio. Fe₂O₃, on the other hand, suggests a compound with two iron atoms for every three oxygen atoms.

• This distinction in ratios reflects how much more oxygen element is incorporated into Fe₂O₃ compared to FeO.

The chemical formula directly leads into calculating important metrics like molar mass and mass percentage because it shows the number of each type of atom present. In this way, it is a key foundational aspect of chemical analysis and understanding the behavior of compounds.