Question

Iron(II) sulfate is a soluble ionic compound added as a source of iron in vitamin tablets. Determine the mass of iron (mg) in one tablet that has been dissolved in \(10.0 \mathrm{~mL}\) of water and titrated with \(14.92 \mathrm{~mL}\) of \(0.0100 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) solution. The net ionic equation is: $$ \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+6 \mathrm{Fe}^{2+}(a q)+14 \mathrm{H}^{+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+6 \mathrm{Fe}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The tablet contains 50 mg of iron (Fe).

Step-by-step solution

Understand the Chemical Reaction

The balanced chemical equation is given as \( \text{Cr}_2\text{O}_7^{2-}(aq) + 6 \text{Fe}^{2+}(aq) + 14 \text{H}^+(aq) \rightarrow 2 \text{Cr}^{3+}(aq) + 6 \text{Fe}^{3+}(aq) + 7 \text{H}_2\text{O}(l) \). This implies that 1 mole of \( \text{Cr}_2\text{O}_7^{2-} \) reacts with 6 moles of \( \text{Fe}^{2+} \).

Calculate Moles of \( \text{Cr}_2\text{O}_7^{2-} \)

We use the molarity formula to calculate moles: \( \text{Moles} = \text{Molarity} \times \text{Volume in Liters} \). For \( \text{K}_2\text{Cr}_2\text{O}_7 \), \( 0.0100 \, \text{M} \times \frac{14.92 \, \text{mL}}{1000 \, \text{mL/L}} \approx 0.0001492 \, \text{moles} \).

Determine Moles of \( \text{Fe}^{2+} \)

From the stoichiometry of the equation, 1 mole of \( \text{Cr}_2\text{O}_7^{2-} \) reacts with 6 moles of \( \text{Fe}^{2+} \). Therefore, the moles of \( \text{Fe}^{2+} = 6 \times 0.0001492 = 0.0008952 \text{ moles} \).

Calculate Mass of \( \text{Fe} \)

The molar mass of iron (Fe) is approximately 55.85 g/mol. The mass of iron is \( 0.0008952 \, \text{moles} \times 55.85 \, \text{g/mol} = 0.050 \text{g} \). Convert grams to milligrams by multiplying by 1000, which gives \( 50 \, \text{mg} \).

Key concepts

Iron(II) sulfate

Iron(II) sulfate, also known as ferrous sulfate, is a chemical compound often used as a source of iron in supplements, such as vitamin tablets. It is a crystalline solid that easily dissolves in water. When dissolved, it dissociates into iron ions (\( \text{Fe}^{2+} \)) and sulfate ions (\( \text{SO}_4^{2-} \)).

Iron(II) sulfate has significant applications due to the essential role of iron in the human body, including the formation of red blood cells.

• It often appears as blue-green crystals due to the presence of water molecules.
• It's important in the industrial production of iron and steel, in water treatment, and as a coloring agent.
• Understanding the properties of Iron(II) sulfate helps in laboratory settings where its reactivity and solubility play crucial roles.

When calculating the amount of iron in a supplement that contains Iron(II) sulfate, we focus on determining the number of moles of \( \text{Fe}^{2+} \) ions that are available for reactions.

Net ionic equation

A net ionic equation is a simplified chemical equation used to show the actual chemical changes occurring in a reaction. It eliminates the spectator ions, which don't participate in the actual chemical change. In our exercise, the net ionic equation is: \[ \text{Cr}_2\text{O}_7^{2-}(aq) + 6 \text{Fe}^{2+}(aq) + 14 \text{H}^{+}(aq) \rightarrow 2 \text{Cr}^{3+}(aq) + 6 \text{Fe}^{3+}(aq) + 7 \text{H}_2\text{O}(l) \]

This equation indicates that one mole of chromate ions reacts with six moles of iron(II) ions in an acidic solution to create \( \text{Cr}^{3+} \) and \( \text{Fe}^{3+} \) ions, along with water molecules.

• The chromate ion undergoes a reduction (gains electrons) and is reduced to chromium(III) ions.
• The iron(II) ion undergoes oxidation (loses electrons) and turns into iron(III) ions.
• The hydronium ions are necessary to balance the reaction in acidic conditions and result in the formation of water.

Understanding net ionic equations is crucial as it enables chemists to focus on the most meaningful parts of complex reactions, simplifying analyses and calculations.

Molar mass calculation

Molar mass is a key concept in stoichiometry, as it allows the conversion of between moles and grams. It represents the mass of one mole of a given substance. The use of molar mass is illustrated in our example where calculating the mass of iron (\( \text{Fe} \)) is necessary. Here's how molar mass plays a role:

• The molar mass of iron (Fe) is approximately 55.85 g/mol.
• To convert moles of iron to grams, multiply the number of moles by the molar mass. For iron in the reaction, 0.0008952 moles of \( \text{Fe} \) equate to 0.050 grams.
• In practical applications, we often convert grams to milligrams (mg), especially in pharmaceutical contexts, because medications are dosed using milligrams.

Understanding how to calculate molar mass and use it in conversion is essential not only for laboratory work but also in real-life applications such as determining the contents of dietary supplements or medicines.