Question

Various iron ores have different amounts of iron per kilogram of ore. Calculate the mass percent composition of iron for each iron ore: Fe2O3 (hematite), Fe3O4 (magnetite), FeCO3 (siderite). Which ore has the highest iron content?

Short answer

The mass percent of iron in Fe2O3 is 70.0%, in Fe3O4 is 72.4%, and in FeCO3 is 48.2%. Magnetite (Fe3O4) has the highest iron content.

Step-by-step solution

Calculate Mass Percent for Fe2O3

Determine the molar mass of Fe2O3 by summing the atomic masses of all atoms involved: 2 atoms of Fe (55.85 u each) and 3 atoms of O (16.00 u each). The molar mass of Fe2O3 is therefore 2(55.85) + 3(16.00) u. Calculate the mass percent of iron in Fe2O3 by dividing the total mass of iron by the molar mass of Fe2O3, then multiply by 100%.

Calculate Mass Percent for Fe3O4

Determine the molar mass of Fe3O4 by summing the atomic masses of all atoms involved: 3 atoms of Fe (55.85 u each) and 4 atoms of O (16.00 u each). Calculate the mass percent of iron in Fe3O4 by dividing the total mass of iron by the molar mass of Fe3O4, then multiply by 100%.

Calculate Mass Percent for FeCO3

Determine the molar mass of FeCO3 by summing the atomic masses of all atoms involved: 1 atom of Fe (55.85 u), 1 atom of C (12.01 u) and 3 atoms of O (16.00 u each). Calculate the mass percent of iron in FeCO3 by dividing the mass of iron by the molar mass of FeCO3, then multiply by 100%.

Compare Iron Content

Compare the calculated mass percent composition of iron for each of the three ores to determine which one has the highest iron content.

Key concepts

Understanding Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In the context of calculating mass percent composition for iron ores, stoichiometry helps us to understand the quantitative relationships and to calculate how much iron there is in a given amount of ore. It involves the use of the mole concept, which is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles.

For instance, if we know the formula of an ore and the chemical formula represents the ratio of atoms within, we can use this information to calculate the molar mass of the ore, and consequently determine what portion of it is iron. This ratio is crucial when comparing different iron ores, as it allows us to calculate the efficiency of the ore in terms of how much iron it can produce per kilogram. Thus, stoichiometry isn't just about balancing equations; it's a tool for translating between the micro (atoms, molecules) and macro (grams, kilograms) worlds.

The Significance of Molar Mass

Molar mass is the weight of one mole (6.022 x 10²³ particles) of a substance and is usually expressed in grams per mole (g/mol). It is equivalent to the sum of the atomic masses of all atoms in a molecule of the substance. This concept is pivotal when it comes to determining mass percent composition because it provides the basis for our calculations.

For example, in step 1 of the solution, the molar mass of Fe₂O₃ is found by adding together the atomic masses of the iron and oxygen atoms. Once we have the molar mass, we can then figure out what percentage of that mass is due to iron alone. Calculating molar mass is like finding the 'recipe' for a molecule, understanding the 'ingredients' (atoms), and their 'quantities' (molar ratio).

Iron Ores and Their Variations

Iron ores are rocks and minerals from which metallic iron can be economically extracted. The primary iron ores are hematite (Fe₂O₃), magnetite (Fe₃O₄), and siderite (FeCO₃). Each ore contains iron in different proportions and this affects their suitability for various industrial processes.

When analyzing the mass percent composition, we see how much iron each ore contributes to its total mass. Here's the interesting part: despite having iron in their composition, not all iron ores have the same efficiency in terms of yielding iron. That's why we calculate the mass percent composition - to identify which ore offers the most iron per unit mass. This information has practical implications for mining, economics, and industry efficiency. Siderite, for example, might have the benefit of being more abundant but, due to a lower iron content compared to hematite or magnetite, it might not always be the most economically viable option.