Problem 31 - Chemistry Matter and Change

Question

Iron(III) sulfate \(\left[\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\right]\)s sometimes used in the water purification process. Determine the number of moles of sulfate ions present in 3.00 mol of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)

Step-by-Step Solution

Answer

There are 9.00 moles of sulfate ions (\(\mathrm{SO}_{4}^{2-}\)) present in 3.00 moles of Iron(III) sulfate (\(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)).

Step 1: Identify the stoichiometry of Iron(III) sulfate

In the formula \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), there is a subscript 3 next to the sulfate ion, \(\mathrm{SO}_{4}\). This means that there are three moles of sulfate ions for every one mole of Iron(III) sulfate.

Step 2: Determine the number of moles of sulfate ions

To find the number of moles of sulfate ions (\(\mathrm{SO}_{4}^{2-}\)) present in 3.00 moles of Iron(III) sulfate (\(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)), multiply the given moles of Iron(III) sulfate by the stoichiometric ratio of moles of sulfate ions to moles of Iron(III) sulfate: Number of moles of \(\mathrm{SO}_{4}^{2-}\) = (3.00 moles of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)) × (3 moles of \(\mathrm{SO}_{4}^{2-}\) / 1 mole of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\))

Step 3: Calculate the number of moles

Now we can calculate the number of moles of sulfate ions: Number of moles of \(\mathrm{SO}_{4}^{2-}\) = 3.00 moles × 3 Number of moles of \(\mathrm{SO}_{4}^{2-}\) = 9.00 moles So, there are 9.00 moles of sulfate ions present in 3.00 moles of Iron(III) sulfate.

Key Concepts

Moles Calculation

Understanding the concept of moles is critical in the study of chemistry. The mole is a basic unit in chemistry that measures the amount of a substance. Specifically, one mole represents approximately 6.022 x 10^23 particles of a substance, whether they are atoms, molecules, ions, or electrons. This number is known as Avogadro's number.

When calculating moles, one of the most important skills to master is the conversion between moles and grams. This is achieved by using the molar mass of a compound, which is the sum of the atomic masses of all atoms in a molecule, measured in grams per mole (g/mol). For instance, to find out how many moles are in a given gram amount of a compound, you would divide the mass of the sample by the molar mass of the compound. Conversely, to find out how many grams are in a given mole amount of a compound, you would multiply the number of moles by the molar mass.

In performing these calculations, maintaining unit consistency and proper dimensional analysis are imperative to avoid errors and achieve accurate results.

Chemical Formula Interpretation

Correctly interpreting a chemical formula is essential in stoichiometry and chemical calculations. A chemical formula, such as \(\mathrm{Fe}_2(\mathrm{SO}_4)_3\), tells you the number and types of atoms in a single molecule of a compound. In this formula, the subscript after an element symbol indicates the number of atoms of that element in the molecule.

For example, in the formula for Iron(III) sulfate, \(\mathrm{Fe}_2(\mathrm{SO}_4)_3\), the subscript '2' next to Iron (Fe) means there are two iron atoms in the compound. In the sulfate ion \(\mathrm{SO}_4^{2-}\), the lack of a subscript next to oxygen (O) means there is only one oxygen atom, and since it's part of the sulfate ion, the '4' tells us there are actually four oxygen atoms. The overall subscript '3' outside the parentheses indicates that there are three sulfate ions present in each formula unit of Iron(III) sulfate.

Understanding these nuances is vital to predicting the behavior of compounds during chemical reactions and is a fundamental first step in any stoichiometric problem.

Molar Stoichiometric Ratios

Molar stoichiometric ratios are at the heart of stoichiometry, enabling chemists to understand the quantitative relationships between reactants and products in a chemical reaction. These ratios tell you how many moles of one substance will react with or produce a certain number of moles of another substance.

For instance, in the exercise involving Iron(III) sulfate (\(\mathrm{Fe}_2(\mathrm{SO}_4)_3\)), the chemical formula informs us of the ratio of iron to sulfate within the compound. The subscript '3' next to the sulfate indicates a 1:3 molar ratio; that is, one mole of Iron(III) sulfate contains three moles of sulfate ions. This ratio allows us to extend our calculations to determine the amount of any individual ion or atom in a given amount of compound.

By understanding and applying these stoichiometric ratios, students can accurately predict the outcomes of chemical reactions and calculate the amounts of products formed or reactants used. This is crucial not only in academic problems but also in real-world applications such as pharmaceutical drug creation and industrial chemical processes.