Question

What is the mass of rust, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\), that contains \(10.0 \mathrm{~g}\) of iron?

Short answer

The mass of Fe2O3 containing 10.0 g of iron is approximately 14.3 g.

Step-by-step solution

Determine the Molar Mass of Fe

First, we need to find the molar mass of iron (Fe). The atomic mass of Fe is approximately 55.85 g/mol.

Calculate the Moles of Iron

Given that we have 10.0 g of iron, we need to calculate how many moles this is by using the formula:\[ ext{moles of Fe} = \frac{ ext{mass of Fe}}{ ext{molar mass of Fe}} \]Substituting the known values, we get:\[ ext{moles of Fe} = \frac{10.0 ext{ g}}{55.85 ext{ g/mol}} \approx 0.179 ext{ mol}\]

Understand the Composition of Fe2O3

Iron (III) oxide, \( ext{Fe}_2 ext{O}_3\), consists of 2 moles of iron per mole of \( ext{Fe}_2 ext{O}_3\). Thus, we need to divide the moles of Fe by 2 to find the moles of \( ext{Fe}_2 ext{O}_3\).

Calculate the Moles of Fe2O3

Using the moles of iron calculated, we find the moles of \( ext{Fe}_2 ext{O}_3\) as:\[ ext{moles of Fe}_2 ext{O}_3 = \frac{ ext{moles of Fe}}{2} = \frac{0.179}{2} = 0.0895 ext{ mol} \]

Determine the Molar Mass of Fe2O3

Calculate the molar mass of \( ext{Fe}_2 ext{O}_3\):- Molar mass of \( ext{Fe}_2\) is \(2 \times 55.85 ext{ g/mol} = 111.7 ext{ g/mol}\)- Molar mass of \( ext{O}_3\) is \(3 \times 16.00 ext{ g/mol} = 48.00 ext{ g/mol}\)Therefore, the molar mass of \( ext{Fe}_2 ext{O}_3\) is \(111.7 + 48.00 = 159.7 ext{ g/mol}\).

Calculate the Mass of Fe2O3

Now, calculate the mass of \( ext{Fe}_2 ext{O}_3\) using the formula:\[ ext{mass of Fe}_2 ext{O}_3 = ext{moles of Fe}_2 ext{O}_3 \times ext{molar mass of Fe}_2 ext{O}_3 \]Substitute the known values:\[ ext{mass of Fe}_2 ext{O}_3 = 0.0895 ext{ mol} \times 159.7 ext{ g/mol} \approx 14.3 ext{ g}\]

Key concepts

Molar Mass

In chemistry, the molar mass is a fundamental concept that helps us relate the mass of a substance to the amount of substance. Molar mass is essentially the mass of one mole of a chemical element or compound. It is usually expressed in grams per mole (g/mol). For elements, the molar mass is numerically equivalent to the atomic mass in atomic mass units (amu). For instance, the atomic mass of iron (Fe) is approximately 55.85 amu, which translates to a molar mass of 55.85 g/mol.
This conversion helps chemists accurately measure stoichiometric amounts of a substance when performing reactions. Knowing the molar mass of elements and compounds allows us to convert between weight and moles easily, which is vital in quantitative chemistry.
For compounds, the molar mass is calculated by summing the molar masses of its constituent elements, multiplied by their respective number of atoms in the molecule. For example, in the compound iron(III) oxide (ext{Fe}_{2}ext{O}_{3}), it contains two iron atoms and three oxygen atoms. Therefore, its molar mass is the sum of the mass of iron and oxygen in the compound, leading to a total molar mass of approximately 159.7 g/mol.

Iron Oxide

Iron oxide, often referred to by its chemical formula ext{Fe}_{2}ext{O}_{3}, is a compound formed by the reaction of iron with oxygen. It is a common form of rust and can be found in nature as the mineral hematite. Iron oxides are widely used in various industries, including as pigments in paints and coatings, and as magnetic materials.
The chemical composition of iron(III) oxide consists of two iron atoms and three oxygen atoms, symbolized as ext{Fe}_{2}ext{O}_{3}. This composition means that each molecule of iron oxide contains twice as many iron atoms as there are units of oxygen, which is critical when calculating mass and ratios in chemical reactions.

• Formation of Iron Oxide: Iron rusts when it reacts with oxygen in the presence of water. This reaction forms layers of iron oxide on the surface of the metal, leading to what is commonly referred to as rust.
• Properties of Iron Oxide: Iron oxide is typically a red-brown to black color, solid at room temperature, and does not dissolve in water, making it suitable for various applications.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the measurement of reactants and products in chemical reactions. It uses the concept of moles and molar masses to balance chemical equations and make quantitative predictions about the amounts of substances consumed and produced in reactions. Stoichiometry is based on the conservation of mass, meaning the mass of reactants equals the mass of products in a chemical process.
In solving stoichiometric problems, such as determining the mass of rust (ext{Fe}_{2}ext{O}_{3}) that can be formed from a given amount of iron, it is important to:
- First, determine the moles of the reactants involved by using their molar masses.
- Understand the mole-to-mole ratios outlined in balanced chemical equations. For instance, 2 moles of ext{Fe} is needed to form 1 mole of ext{Fe}_{2}ext{O}_{3}.
- Use these ratios to find the corresponding moles for products formed, considering the stoichiometric coefficients.
This method allows chemists to predict precisely how much of a product will be produced from a known quantity of reactant, which is indispensable in laboratory settings and industrial processes.