Question

An aqueous solution contains \(3.75 \mathrm{~g}\) of iron(III) sulfate, \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3},\) per liter. What is the molarity of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} ?\) When the compound dissolves in water, the \(\mathrm{Fe}^{3+}\) ions and \(\mathrm{SO}_{4}{ }^{2-}\) ions in the crystal go into the solution. What is the molar concentration of each ion in the solution?

Short answer

Molarity of \(\text{Fe}_2(\text{SO}_4)_3\) is 0.00938 M; \(\text{Fe}^{3+}\) is 0.01876 M; \(\text{SO}_4^{2-}\) is 0.02814 M.

Step-by-step solution

Find the Molar Mass of Iron(III) Sulfate

The molecular formula for iron(III) sulfate is \( \text{Fe}_2(\text{SO}_4)_3 \). Calculate the molar mass by summing the atomic masses of all atoms: - Fe: 55.845 g/mol- S: 32.07 g/mol- O: 16.00 g/molCalculate the total mass:\[2(55.845) + 3[32.07 + 4(16.00)] = 2(55.845) + 3(32.07 + 64.00) = 399.88 \text{ g/mol}\]

Calculate Moles of Iron(III) Sulfate

To find the moles of \( \text{Fe}_2(\text{SO}_4)_3 \), divide the mass of the compound by its molar mass:\[\text{Moles} = \frac{3.75\, \text{g}}{399.88\, \text{g/mol}} \approx 0.00938 \text{ mol}\]

Determine Molarity of Iron(III) Sulfate Solution

Molarity is defined as moles of solute per liter of solution. Since the solution is 1 liter, the molarity of the solution is:\[\text{Molarity} = \frac{0.00938\, \text{mol}}{1\, \text{L}} = 0.00938\, \text{M}\](Molar).

Find Molar Concentration of Ions

Iron(III) sulfate dissociates in water into 2 \( \text{Fe}^{3+} \) ions and 3 \( \text{SO}_4^{2-} \) ions for each formula unit. Thus, the concentration of each ion is:- \( \text{Fe}^{3+} \): \[2 \times 0.00938 \text{ M} = 0.01876 \text{ M}\]- \( \text{SO}_4^{2-} \): \[3 \times 0.00938 \text{ M} = 0.02814 \text{ M}\]

Key concepts

Ion Concentration

Ion concentration refers to the quantity of a particular ion in a solution, typically expressed in moles per liter (Molarity).
In an aqueous solution where a compound dissolves, it breaks into individual ions. Knowing the ion concentration is crucial because it influences the chemical properties and reactions in the solution.
For the compound iron(III) sulfate, represented as \( ext{Fe}_2( ext{SO}_4)_3\), it will dissociate in water to produce ions as follows:

• 2 iron(III) ions \( ext{Fe}^{3+}\)
• 3 sulfate ions \( ext{SO}_4^{2-}\)

The molarity of the iron(III) sulfate given initially helps to determine the concentration of each ion. By calculating these using stoichiometry, you enhance the understanding of how compounds behave in solution.

Molar Mass

The molar mass of a compound is the sum of the atomic masses of its constituent atoms, usually in grams per mole (g/mol).
This is an essential step in finding the molarity as it allows conversion from mass to moles.
For iron(III) sulfate, the molecular formula \( ext{Fe}_2( ext{SO}_4)_3\) requires adding the atomic masses:
Calculate it as follows:

• 2 Iron (Fe): \(2 \times 55.845\, \text{g/mol}\)
• 3 Sulfur (S): \(3 \times 32.07\, \text{g/mol}\)
• 12 Oxygen (O): \(3\times 4 \times 16.00\, \text{g/mol}\)

This results in a total molar mass of approximately 399.88 g/mol.
Understanding molar mass helps in converting measured mass in a lab to moles, enabling the calculation of a solution's molarity, critical for determining ion concentrations.

Dissolution

Dissolution is the process where solutes disperse in a solvent to form a solution. It involves breaking intermolecular bonds in the solute and forming new interactions with the solvent.
For iron(III) sulfate dissolving in water, each molecule separates into its constituent ions:

• 2 \( ext{Fe}^{3+}\)
• 3 \( ext{SO}_4^{2-}\)

This dissociation impacts the ion concentration in the solution and, consequently, the chemical properties of the solution.
This concept is significant in chemistry, influencing everything from reaction rates to material solubility in diverse applications.
Dissolution is pivotal in enabling reactions within a solution by making ions available for interaction, which is crucial for reactions in both natural and industrial processes.

Aqueous Solution

An aqueous solution is one where water is the solvent. Water's polar nature generally makes it very effective at dissolving ionic compounds.
In an aqueous solution, compounds like iron(III) sulfate dissociate into ions, a fundamental concept in the study of chemistry.
Key characteristics of aqueous solutions include:

• The ability to conduct electricity due to the presence of free-moving ions.
• They serve as a medium for various chemical reactions.
• They exhibit unique properties such as specific boiling and freezing points.

Understanding how substances behave in an aqueous solution is essential for applications ranging from laboratory experiments to industrial processes.
The behavior of ions in these solutions determines everything from acidity to reactivity, making aqueous solutions a central topic in many scientific and practical fields.