Problem 110 - General Chemistry: Principles and Modern Applications

Question

In the equation \(\begin{aligned} ? \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+4 \mathrm{H}^{+}(\mathrm{aq}) & \longrightarrow ? \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1) \end{aligned}\) the missing coefficients (a) are each \(2 ;\) (b) are each 4; (c) can have any values as long as they are the same; (d) must be determined by experiment.

Step-by-Step Solution

Answer

The correct coefficients that balance the equation are 2 for \(Fe^{2+}(aq)\) and \(Fe^{3+}(aq)\), 1 for \(O_{2}(g)\) and \(4H^{+}(aq)\), and 4 for \(H2O(l)\). Therefore, the option (a) 'each 2' is correct.

Step 1: Identifying Atom Counts

Initially, consider the counts of Iron (Fe), Oxygen (O), and Hydrogen (H) ions on either side of the reaction. On the left side, we have one atom of Fe, two atoms of O, and four atoms of H. On the right side of the reaction, we have one atom of Fe, two atoms of O, and two atoms of H.

Step 2: Balancing Hydrogen and Iron Atoms

The Fe counts are already balanced, so we have to balance Hydrogen (H) first. As the equation contains four Hydrogen atoms on the left side and only two on the right, a coefficient of 2 before H2O should balance the number of Hydrogen atoms in the equation. Now, the equation becomes \(Fe^{2+}(aq) + O2(g) + 4H^{+}(aq) \longrightarrow Fe^{3+}(aq) + 2*2H2O(l)\). Therefore, it will appear as \(Fe^{2+}(aq) + O2(g) + 4H^{+}(aq) \longrightarrow Fe^{3+}(aq) + 4H2O(l)\). Now we have four Hydrogen atoms on both sides.

Step 3: Balancing Oxygen Atoms

Currently, our equation has two Oxygen atoms on the left and four on the right (because of 4 molecules of H2O). To balance Oxygen atoms, we have to put the coefficient 2 before \(Fe^{2+}(aq)\) and \(Fe^{3+}(aq)\). Finally, the balanced equation appears as \(2Fe^{2+}(aq) + O2(g) + 4H^{+}(aq) \longrightarrow 2Fe^{3+}(aq) + 4H2O(l)\).

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It acts like a recipe, showing how much of each substance is needed or produced. Using stoichiometry, we can precisely determine the proportions needed to balance a chemical equation. For example, in the given reaction, understanding stoichiometry allows us to balance it by adding appropriate coefficients.

The process entails:

• Identifying and listing reactants and products in the equation.
• Counting the number of atoms of each element on both sides.
• Adding coefficients to satisfy the law of conservation of mass, ensuring atoms are neither gained nor lost.

By accurately applying stoichiometry, we can ascertain the balanced form of a reaction, as demonstrated by transforming:\[\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+4\mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1)\] into:\[2 \mathrm{Fe}^{2+}(\mathrm{aq}) + \mathrm{O}_2(\mathrm{g}) + 4\mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Fe}^{3+}(\mathrm{aq}) + 4 \mathrm{H}_2\mathrm{O}(l)\] highlighting that stoichiometry not only aids in equation balancing but also in understanding chemical reactions in depth.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes where oxidation and reduction occur simultaneously. Oxidation refers to the loss of electrons, while reduction involves the gain of electrons. Redox reactions are essential in various chemical processes, from energy production within cells to the functioning of batteries.

In the aforementioned reaction:\[2 \mathrm{Fe}^{2+}(\mathrm{aq}) + \mathrm{O}_2(\mathrm{g}) + 4\mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Fe}^{3+}(\mathrm{aq}) + 4 \mathrm{H}_2\mathrm{O}(l)\]we can observe that iron (\(\mathrm{Fe}\)) transitions from a +2 to a +3 oxidation state, indicating it is oxidized as it loses an electron.

• Oxygen involves in the reduction as it gains electrons from iron.
• Hydrogen participates as a proton donor, balancing charge shifts.

Understanding the redox context of reactions provides insight into how electron exchanges occur during chemical interactions, a core aspect of chemical processes and a central theme in balancing equations successfully.

Oxidation States

Oxidation state, or oxidation number, is a concept used to track the transfer of electrons in a chemical reaction. It is defined as a theoretical charge that an atom would have if all bonds were ionic. The oxidation number helps determine which atoms are oxidized and which are reduced in redox reactions.

In the given reaction, tracking oxidation states is essential:

• Iron (\(\mathrm{Fe}\)) transitions from +2 in \(\mathrm{Fe}^{2+}\) to +3 in \(\mathrm{Fe}^{3+}\), showing a loss of one electron, hence being oxidized.
• The oxidation state of Oxygen starts at 0 in \(\mathrm{O}_{2}\) and changes as it participates in creating \(\mathrm{H}_2\mathrm{O}\).
• Hydrogen's role remains as +1, facilitating the movement of electrons without changing its oxidation state.

Identifying oxidation states ensures clarity in the electron flow, crucial for comprehensively understanding and balancing redox reactions. This clarity reinforces the significance of correctly determining how elements change during reactions and provides a structured approach to studying chemical interactions more deeply.