Problem 75 - Chemistry and Chemical Reactivity

Question

To analyze an iron-containing compound, you convert all the iron to \(\mathrm{Fe}^{2+}\) in aqueous solution and then titrate the solution with standardized \(\mathrm{KMnO}_{4}\). The balanced, net ionic equation is \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+5 \mathrm{Fe}^{2+}(\mathrm{aq})+8 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Mn}^{2+}(\mathrm{aq})+5 \mathrm{Fe}^{3+}(\mathrm{aq})+4 \mathrm{H}_{2} \mathrm{O}(\ell) $$ A \(0.598-\mathrm{g}\) sample of the iron-containing compound requires \(22.25 \mathrm{mL}\) of \(0.0123 \mathrm{M} \mathrm{KMnO}_{4}\) for titration to the equivalence point. What is the mass percent of iron in the sample?

Step-by-Step Solution

Answer

The mass percent of iron is approximately 12.75%.

Step 1: Identify Moles of KMnO4 Used

First, find the moles of \mathrm{KMnO4} used in the titration. Use the molarity and volume of the solution: \(moles = Molarity \times Volume\). The volume must be in liters.\[\text{Moles of } \mathrm{KMnO_4} = 0.0123 \ ext{mol/L} \times 0.02225 \ ext{L} \approx 0.000273075 \ ext{ moles of } \mathrm{KMnO_4}\].

Step 2: Use Stoichiometry to Find Moles of Fe2+

According to the balanced equation, \(1 \text{ mole of } \mathrm{MnO_4}^- \text{ reacts with } 5 \text{ moles of } \mathrm{Fe^{2+}}\). Thus, the moles of \mathrm{Fe^{2+}} are: \[\text{Moles of } \mathrm{Fe^{2+}} = 5 \times 0.000273075 \approx 0.001365375 \text{ moles}\].

Step 3: Calculate Mass of Iron in the Compound

The molar mass of iron (Fe) is approximately 55.85 g/mol. Use this to find the mass of iron that was titrated:\[\text{Mass of } \mathrm{Fe} = 0.001365375 \text{ moles} \times 55.85 \text{ g/mol} \approx 0.076247 \text{ g}\].

Step 4: Calculate the Mass Percent of Iron

The mass percent of iron in the sample is calculated using the mass of iron and the initial mass of the compound sample:\[\text{Mass percent of iron} = \left( \frac{0.076247\text{ g}}{0.598\text{ g}} \right) \times 100 \approx 12.75\%\].

Key Concepts

Stoichiometry

Stoichiometry relates to the quantitative aspects of chemical reactions. It allows you to determine the relationships between reactants and products in a chemical equation. In the context of titration, stoichiometry is vital for figuring out exactly how much of each substance is involved in a reaction.
Using the balanced chemical equation, as given in the exercise, each mole of \( \mathrm{KMnO}_4 \) reacts with five moles of \( \mathrm{Fe}^{2+} \). This ratio is essential for answering how much iron is in the sample. Once the moles of \( \mathrm{KMnO}_4 \) used in the reaction are known, the stoichiometry allows calculating the moles of \( \mathrm{Fe}^{2+} \) involved.

• This forms the backbone of figuring out the quantity of each reactant and product, ensuring the law of conservation of mass is met in the reaction.

By leveraging stoichiometry, you can navigate through complex chemical reactions and obtain precise quantitative results.

Molarity

Molarity is a measure of concentration and is expressed in moles of solute per liter of solution. It's a critical part of any chemical analysis involving solutions, as it helps quantify how much solute is present within a specific volume of solvent.
In the titration problem, the molarity of \( \mathrm{KMnO}_4 \) solution is given as 0.0123 M. By multiplying this concentration by the volume of the solution used (22.25 mL, converted to liters), we calculated the moles of \( \mathrm{KMnO}_4 \) that reacted.

• Understanding molarity allows you to accurately determine the amount of reactant involved in a chemical reaction.
• Molarity is inversely proportional to the dilution of a solution; as dilution increases, molarity decreases.

Molarity is crucial because it directly relates the amount of substance to the space it occupies and forms the basis of stoichiometric calculations in titrations.

Redox Reactions

Redox reactions involve the transfer of electrons between substances. They're fundamental to many chemical processes, including the titration of iron in this exercise.
In this context, iron is oxidized from \( \mathrm{Fe}^{2+} \) to \( \mathrm{Fe}^{3+} \), while \( \mathrm{MnO}_4^- \) is reduced to \( \mathrm{Mn}^{2+} \). This exchange is what makes the reaction proceed.

• The terms 'oxidation' and 'reduction' are crucial here—oxidation involves losing electrons, while reduction involves gaining them.
• Redox reactions can be split into two half-reactions, a technique often used to balance complex reactions.

Recognizing the role of redox reactions in titration allows you to understand how the reaction proceeds and how the analyte's form changes during the process.

Mass Percent Calculation

Mass percent calculation is a common way to express the composition of a compound. It represents the mass of a component divided by the total mass of the mixture, multiplied by 100.
In the exercise, the mass percent of iron in the sample is calculated to understand what portion of the entire sample is made up of iron.

• The calculation starts by finding the mass of iron from the moles, using its molar mass (55.85 g/mol).
• The mass percent formula is then applied: \[ \text{Mass percent} = \left( \frac{\text{mass of component}}{\text{total mass of sample}} \right) \times 100 \]

Mass percent provides an essential glimpse into the composition of the sample, showing the proportion of iron relative to the overall sample mass.
This technique is vital for obtaining basic compositional insights into a sample's makeup, serving as a foundational analysis in chemistry.