Problem 22 - Chemistry The Science in Context

Question

How many atoms of iron are there in 2.5 moles of each of the following? a. wolframite, FeWO \(_{4}\) b. pyrite, \(\mathrm{FeS}_{2}\) c. magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) d. hematite, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\)

Step-by-Step Solution

Answer

Question: Calculate the number of iron atoms present in 2.5 moles of each of the following iron-containing compounds: Wolframite (FeWO4), Pyrite (FeS2), Magnetite (Fe3O4), and Hematite (Fe2O3). Answer: The number of iron atoms in 2.5 moles of each compound is as follows: a. Wolframite (FeWO4): 1.505 x 10^24 iron atoms b. Pyrite (FeS2): 1.505 x 10^24 iron atoms c. Magnetite (Fe3O4): 4.516 x 10^24 iron atoms d. Hematite (Fe2O3): 3.011 x 10^24 iron atoms

Step 1: Recall the concept of moles and Avogadro's number

A mole is a unit used to express the amount of a chemical substance. Avogadro's number, which is approximately 6.022 x 10^23, represents the number of particles (such as atoms, molecules, or ions) in one mole of a substance.

Step 2: Determine the number of iron atoms in one mole of each compound

We need to find out how many iron atoms are present in one mole of each compound. The stoichiometric coefficients in the formulas for each compound tell us this information. a. Wolframite, FeWO_4: There is 1 iron atom in 1 molecule of FeWO_4. b. Pyrite, FeS_2: There is 1 iron atom in 1 molecule of FeS_2. c. Magnetite, Fe_3O_4: There are 3 iron atoms in 1 molecule of Fe_3O_4. d. Hematite, Fe_2O_3: There are 2 iron atoms in 1 molecule of Fe_2O_3.

Step 3: Calculate the number of iron atoms in 2.5 moles of each compound

Now that we know the number of iron atoms in one mole of each compound, we can multiply that by the given number of moles and Avogadro's number to find the total number of iron atoms in 2.5 moles of each compound. a. Wolframite, FeWO_4: 1 iron atom/molecule x 2.5 moles x 6.022 x 10^23 molecules/mole = 1.505 x 10^24 iron atoms b. Pyrite, FeS_2: 1 iron atom/molecule x 2.5 moles x 6.022 x 10^23 molecules/mole = 1.505 x 10^24 iron atoms c. Magnetite, Fe_3O_4: 3 iron atoms/molecule x 2.5 moles x 6.022 x 10^23 molecules/mole = 4.516 x 10^24 iron atoms d. Hematite, Fe_2O_3: 2 iron atoms/molecule x 2.5 moles x 6.022 x 10^23 molecules/mole = 3.011 x 10^24 iron atoms

Key Concepts

Avogadro's number

Understanding Avogadro's number is essential for anyone delving into the study of chemistry. It's the bridge that connects the micro world of atoms and molecules to the macro world we can measure and observe. Avogadro's number, named after the scientist Amedeo Avogadro, is approximately 6.022 x 10^23. This huge figure is the standard quantity in one mole and signifies the number of atomic or molecular units within that mole.

Imagine you have a bag with 6.022 x 10^23 grains of sand; that's a mole of sand grains. The same number applies to atoms, ions, and molecules, providing a uniform way to discuss huge quantities in chemistry. When you grasp that each mole of any substance will have Avogadro's number of particles, you can transition smoothly into calculations involving atomic and molecular scales.

Stoichiometry

Stoichiometry can be thought of as the recipe for chemistry. It involves the calculation of reactants and products in chemical reactions. Stoichiometry uses the law of conservation of mass, which states that in any chemical reaction, matter is neither created nor destroyed. Thus, the quantity of each element must remain the same throughout the reaction.

To accomplish this, you will often deal with balanced chemical equations, which show how much of each substance is involved. For example, if you're baking and the recipe calls for two eggs for every cup of flour, you're using stoichiometry. Translated to chemistry, if a reaction requires two hydrogen molecules for every oxygen molecule to form water, that's stoichiometry in action. It lays the groundwork for predicting the amounts of products and reactants and is an indispensable tool for any chemist.

Mole concept

The mole concept is akin to a dozen eggs or a pair of shoes; it's a counting unit used in chemistry to express large quantities of very small entities such as atoms, molecules, or other particles. One mole represents Avogadro's number of particles, which is 6.022 x 10^23. The mole allows chemists to convert between the mass of a substance and the number of atoms or molecules it contains. This is incredibly valuable because weighing out a mole of a substance gives you a tangible quantity of that substance.

For instance, 12 grams of carbon-12 is precisely one mole, which means it contains 6.022 x 10^23 carbon atoms. Using the mole concept, chemists can relate mass (something we can measure) to counting atoms and molecules (which we cannot directly count), thus bridging a gap in scales between the visible world and the atomic level.

Atomic count in compounds

When analyzing compounds, knowing how many atoms of each element are present is crucial. This counts as the atomic count or sometimes referred to as the composition of a compound. For example, the chemical formula H2O indicates that each molecule of water is comprised of two hydrogen atoms and one oxygen atom.

The stoichiometric coefficients in a chemical formula provide insight into the atomic count within that molecule. Throughout chemical reactions, understanding the atomic count allows for precise stoichiometric calculations, ensuring that chemical equations can be balanced and that the relationships between reactants and products are accurately determined. For students tackling chemistry problems, identifying the atomic count in compounds is key to converting moles into actual numbers of atoms using Avogadro's number and the mole concept, facilitating a deeper understanding of chemical equations and reactions.