Question

A \(1.362 \mathrm{~g}\) sample of an iron ore that contained \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) was dissolved in acid and all of the iron was reduced to \(\mathrm{Fe}^{2+} .\) The solution was then acidified with \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and titrated with \(39.42 \mathrm{~mL}\) of \(0.0281 \mathrm{M} \mathrm{KMnO}_{4}\), which oxidized the iron to \(\mathrm{Fe}^{3+}\). The net ionic equation for the reaction is \(5 \mathrm{Fe}^{2+}+\mathrm{MnO}_{4}^{-}+8 \mathrm{H}^{+} \longrightarrow 5 \mathrm{Fe}^{3+}+\mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O}\) (a) What was the percentage by mass of iron in the ore? (b) What was the percentage by mass of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) in the ore?

Short answer

The percentage by mass of iron in the ore is 72.36%. The percentage by mass of Fe3O4 in the ore is 93.7%.

Step-by-step solution

Calculate moles of KMnO4 used in titration

To find the moles of KMnO4, use the concentration and volume of KMnO4 solution provided. Volume must be converted to liters before using the molarity formula: moles = molarity × volume (in liters).

Calculate moles of Fe2+ using the stoichiometry of the reaction

From the balanced net ionic equation, it is known that 1 mole of KMnO4 reacts with 5 moles of Fe2+. Therefore, multiply the moles of KMnO4 by 5 to find the moles of Fe2+ that reacted.

Calculate moles of Fe in the sample

Since all iron in the ore was reduced to Fe2+, the moles of Fe initially present in the sample are equal to the moles of Fe2+ after the reaction.

Calculate mass of Fe in the sample

The mass of Fe can be calculated by using the molar mass of Fe (55.845 g/mol) and multiplying it by the moles of Fe calculated in Step 3.

Calculate percentage by mass of iron in the ore

Divide the mass of Fe by the mass of the ore sample and multiply by 100% to find the percentage by mass of iron in the ore.

Calculate molar mass of Fe3O4

The molar mass of Fe3O4 can be calculated using the molar masses of Fe and O, found on the periodic table.

Calculate moles of Fe3O4 in the sample

Since each molecule of Fe3O4 contains 3 atoms of Fe, divide the moles of Fe calculated in Step 3 by 3 to find the moles of Fe3O4.

Calculate mass of Fe3O4 in the sample

Multiply the moles of Fe3O4 by its molar mass to find the mass of Fe3O4 in the sample.

Calculate percentage by mass of Fe3O4 in the ore

Divide the mass of Fe3O4 by the mass of the ore sample and multiply by 100% to find the percentage by mass of Fe3O4 in the ore.

Key concepts

Stoichiometry in Iron Ore Analysis

Stoichiometry is the backbone of chemical reactions, serving as a mathematical way of describing the quantitative relationships between reactants and products. When we analyze the composition of iron ore using titration, understanding stoichiometry is crucial.
In our example, stoichiometry helps us calculate the amount of iron present in a sample. Once the sample is dissolved and all iron is in the form of Fe²⁺, a known concentration of KMnO₄ is used to titrate the solution. The stoichiometric relationship between KMnO₄ and Fe²⁺ is given by the balanced net ionic equation.

Applying the Stoichiometry of the Reaction

Using the stoichiometry from the net ionic equation, for every mole of KMnO₄ that reacts, five moles of Fe²⁺ are needed. This ratio is key to calculating the amount of iron in the sample. By knowing the moles of KMnO₄ used, we can find the moles of Fe²⁺ and therefore, the molarity of iron content.

From Moles to Mass

With the moles of iron calculated, we then convert this to mass using the molar mass of iron. By comparing this mass to the initial mass of the sample, the percentage by mass of iron in the ore is determined. The key to success with stoichiometry is to always keep track of units and carefully use the mole ratio from the balanced equation.

Redox Reactions in Ore Analysis

Redox reactions, short for reduction-oxidation reactions, describe all chemical reactions in which the oxidation state of atoms are altered. These reactions are essential in titration processes, especially when analyzing the iron content in ore, as seen in the provided problem.
During titration, KMnO₄ acts as an oxidizing agent and converts Fe²⁺ ions into Fe³⁺ ions. The reduction of manganese in KMnO₄ from MnO₄^- to Mn²⁺ accompanies this oxidation.

Understanding the Oxidation States

It is important to identify the changes in oxidation states: Fe²⁺ is oxidized to Fe³⁺, and MnO₄^- is reduced to Mn²⁺. The electrons lost by one substance must be gained by another, thus maintaining the conservation of charge.

Link to Stoichiometry

In linking redox reactions to stoichiometry, the balanced net ionic equation provides a blueprint for the redox process and tells us the stoichiometric coefficients that are used to relate moles of reactants and products. This helps us determine the amount of iron in the ore sample by understanding how many moles of Fe²⁺ can be oxidized by a given amount of KMnO₄.

Molarity in Chemical Analysis

Molarity, a measure of the concentration of a solute in a solution, is fundamental in titrations and other chemical analyses. It is defined as the number of moles of solute per liter of solution and is expressed in moles per liter (M).
In the context of titrating iron ore, the molarity of the titrant (KMnO₄) is used to determine the quantity of solute, which, in this case, is Fe²⁺ ions present in the solution.

Calculating Molarity

Given a solution's volume and the amount of substance dissolved in it, you can calculate its molarity. It is essential to convert the volume from milliliters to liters to keep the units consistent, as the molarity is affected by the solution's total volume. This concept is applied when calculating the number of moles of KMnO₄ used in the titration.

Molarity and Stoichiometry

Once we have determined the moles of KMnO₄ through molarity and volume, we turn to stoichiometry to relate this to the moles of Fe²⁺, and ultimately, to the mass of iron in the ore. Correctly understanding and using molarity allows us to accurately measure and analyze substances within a chemical reaction.