Problem 98 - General Chemistry: Principles and Modern Applications

Question

A sulfide of iron, containing \(36.5 \%\) S by mass, is heated in \(\mathrm{O}_{2}(\mathrm{g}),\) and the products are sulfur dioxide and an oxide of iron containing \(27.6 \%\) O, by mass. Write a balanced chemical equation for this reaction.

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction is \(3 FeS + 4 O_{2} \rightarrow Fe_{3}O_{4} + 3 SO_{2}\)

Step 1: Finding empirical formula of iron sulfide

The mass percentage of S in the sulfide of iron is given as \(36.5\% \). This means that the mass of S in \(100 g\) of compound is \(36.5 g\). Since the compound only contains iron and sulfur, the remaining mass must be attributed to iron: \(100 g - 36.5 g = 63.5 g\). Then, convert these masses to moles: use \(55.845 g/mol\) for iron (Fe) and \(32.06 g/mol\) for sulfur (S). \( \frac{63.5 g}{55.845 g/mol} = 1.14 mol\) (for Fe), \( \frac{36.5 g}{32.06 g/mol} = 1.14 mol\) (for S). The mole ratio of Fe to S is 1:1, thus, the empirical formula of the iron sulfide is \(FeS\).

Step 2: Finding empirical formula of iron oxide

The mass percentage of O in the oxide of iron is given as \(27.6\% \). This means that the mass of O in \(100 g\) of compound is \(27.6 g\). The remaining mass is iron: \(100 g - 27.6 g = 72.4 g\). Convert these masses to moles: \( \frac{72.4 g}{55.845 g/mol} = 1.30 mol\) (for Fe), \( \frac{27.6 g}{16.00 g/mol} = 1.73 mol\) (for O). The mole ratio of Fe to O can be approximated as 3:4, therefore, the empirical formula of the iron oxide is \(Fe_{3}O_{4}\).

Step 3: Balancing the chemical equation

Given the empirical formulas of the compounds and knowing that sulfur dioxide (\(SO_{2}\)) is also a product, we can write the unbalanced equation: \( FeS + O_{2} \rightarrow Fe_{3}O_{4} + SO_{2}\) Now balance for each element. Start with iron, there are 3 Fe in \(Fe_{3}O_{4}\) and 1 Fe in \(FeS\). So, multiply \(FeS\) by 3. To balance sulfur, multiply \(SO_{2}\) by 3. Now only oxygen left. There are total 8 O in the products, while there are 2 O in \(O_{2}\). So, multiply \(O_{2}\) by 4. The balanced chemical reaction becomes: \(3 FeS + 4 O_{2} \rightarrow Fe_{3}O_{4} + 3 SO_{2}\).

Key Concepts

Empirical Formulas

Understanding empirical formulas is key to analyzing chemical compounds. An empirical formula gives the simplest whole-number ratio of atoms in a compound. It's all about finding that basic "recipe." For example, in the given exercise, we determine the formula for iron sulfide.

• First, calculate the mass of each element based on percentage composition.
• Convert these masses into moles using their respective atomic weights: 55.845 g/mol for iron and 32.06 g/mol for sulfur.
• Divide each element’s moles by the smallest number of moles to find the simplest ratio.
• Here, the empirical formula for iron sulfide is found to be \(FeS\), meaning one atom of iron pairs with one atom of sulfur.

With empirical formulas, you strip down a compound to its most basic ratio, providing a cornerstone for further chemical understanding.

Mole Ratio

Mole ratios connect the dots between chemical substances in reactions. They are derived from the coefficients of a balanced equation, linking atoms, molecules, and moles seamlessly.

• In the context of the given task, mole ratios help determine the simplest form of the compounds, as seen with the 1:1 ratio of Fe to S.
• They also help balance chemical reactions since the number of atoms must be the same on both sides of the equation.
• Using mole ratios can also indicate how much reactant is needed for complete reactions and/or how much product can be expected.

Ultimately, mole ratios are like the language of the equation, telling us how different substances prefer to "join hands." They guide the transformation of reactants into products smoothly.

Iron Sulfide

Iron sulfide, often simply represented as \(FeS\), is a compound that marries iron and sulfur in equal mole proportions. It is a naturally occurring mineral but can also be synthesized by direct combination of iron and sulfur.

• In the exercise, iron sulfide is the starting material that's heated to interact with oxygen.
• This results in the conversion into iron oxide and sulfur dioxide, showcasing a chemical transformation.
• In balanced equations, knowing the chemical makeup of iron sulfide is essential for determining reactant and product necessities.

Iron sulfide serves as a great example of a binary compound formed directly from its elemental parents, iron and sulfur.

Iron Oxide

Iron oxide is a classic compound resulting from iron reacting with oxygen. The type we see here is \(Fe_3O_4\), known as magnetite, which holds a unique mix of Fe and O atoms.

• This exercise involves transforming iron sulfide into iron oxide, pinpointing a chemical reaction facilitated by oxygen's presence.
• The key to identifying the empirical formula of iron oxide is understanding mole ratios for the involved elements.
• The "3:4" ratio reflects the number of atoms interacting, leading to the specific formula \(Fe_3O_4\).

Gaining insight into iron oxide demonstrates how oxygen’s role shifts iron into a new form, evident in numerous naturally occurring and synthesized chemical reactions.