Question

An iron ore contains 38% Fe2O3 by mass. What is the maximum mass of iron that can be recovered from 10.0 kg of this ore?

Short answer

The maximum mass of iron that can be recovered from 10.0 kg of ore is 2.65732 kg.

Step-by-step solution

Determine the mass percentage of iron in Fe2O3

The molar mass of Fe2O3 is 55.845 (Fe) * 2 + 15.999 (O) * 3 = 159.69 g/mol. Iron constitutes 2 * 55.845 / 159.69 = 0.6994, or 69.94% of Fe2O3 by mass.

Calculate the mass of Fe2O3 in the ore based on percentage

Since the ore is 38% Fe2O3 by mass, the mass of Fe2O3 in 10.0 kg of ore is 0.38 * 10.0 kg = 3.8 kg.

Calculate the mass of iron that can be recovered

The mass of iron that can be recovered is the mass of Fe2O3 multiplied by the mass percentage of iron in Fe2O3. Therefore, the maximum mass of iron that can be recovered from the ore is 3.8 kg * 0.6994 = 2.65732 kg.

Key concepts

Percent Composition

Percent composition in chemistry is the percentage by mass of each element in a compound. It's a fundamental concept when it comes to analyzing the makeup of a given compound and is crucial when wanting to know how much of each element is present. To find the percent composition for iron (Fe) in iron(III) oxide (Fe2O3), we start by calculating the molar mass of the compound. With the molar mass known, we can determine what fraction of the compound's mass is due to iron.

As in our exercise, if Fe2O3 represents 38% of the ore by mass, the iron percentage within Fe2O3 can help us understand how much of that ore is actually iron. This knowledge is vital when considering the commercial viability of mining operations, as high percentages often mean a more valuable mine. For students, mastering percent composition calculations is a stepping stone for more advanced chemistry topics like stoichiometry and thermodynamics.

Molar Mass Calculation

The molar mass of a substance is the mass of one mole of that substance. It is typically expressed in grams per mole (g/mol) and can be thought of as the molecular weight of a compound. To calculate molar mass, we sum the masses of all atoms in the molecule based on atomic weights from the periodic table. For instance, for Fe2O3, we have two iron atoms and three oxygen atoms; by adding their atomic masses together, we find the molar mass of the compound.

Understanding how to calculate molar mass is essential in chemistry for converting between grams and moles, a common task in lab and industrial settings. Correct molar mass determination influences stoichiometric calculations, which in turn are imperative to predict reaction yields and to scale up reactions for production. Students often struggle with this concept initially, but practicing with various compounds can build familiarity with the periodic table and confidence in molar mass calculations.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles. This area of chemistry requires a solid understanding of how compounds interact in balanced equations, and how to use these equations to predict the amount of product formed from given reactants or vice versa. In the context of our iron ore example, stoichiometry is applied by using the percent composition and molar mass to calculate the maximum amount of iron that can be recovered from the ore.

Key steps in stoichiometric calculations include balancing chemical equations, converting mass to moles, and applying the mole ratios from the balanced equation. For students and industry professionals alike, stoichiometry is indispensable for making predictions about chemical processes. By practicing stoichiometry, one gains a deeper appreciation for the predictive power of chemistry and its role in practical applications such as manufacturing, medication dosage, and environmental monitoring.