Problem 13 - General Chemistry: Principles and Modern Applications

Question

Write balanced chemical equations for the following reactions described in the chapter. (a) the reaction of \(\operatorname{Sc}(\text { OH })_{3}(\text { s) with } \mathrm{HCl}(\text { aq })\) (b) oxidation of \(\mathrm{Fe}^{2+}(\mathrm{aq})\) by \(\mathrm{MnO}_{4}^{-}(\text {aq })\) in basic solution to give \(\mathrm{Fe}^{3+}(\mathrm{aq})\) and \(\mathrm{MnO}_{2}(\mathrm{s})\) (c) the reaction of \(\mathrm{TiO}_{2}(\mathrm{s})\) with molten \(\mathrm{KOH}\) to form \(\mathrm{K}_{2} \mathrm{TiO}_{3}\). (d) oxidation of \(\mathrm{Cu}(\mathrm{s})\) to \(\mathrm{Cu}^{2+}(\mathrm{aq})\) with \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (concd aq) to form \(\mathrm{SO}_{2}(\mathrm{g})\).

Step-by-Step Solution

Answer

The balanced chemical equations are: (a) Sc(OH)3(s) + 3HCl(aq) → ScCl3(aq) + 3H2O(l), (b) 5Fe2+(aq) + MnO4-(aq) + 8H2O(l) → 5Fe3+(aq) + MnO2(s) + 20OH-(aq), (c) TiO2(s) + 2KOH → K2TiO3, (d) Cu(s) + 2H2SO4(aq) → CuSO4(aq) + SO2(g) + 2H2O(l).

Step 1: Balancing the Reaction of Sc(OH)3 with HCl

Consider the reaction in which Sc(OH)3 reacts with HCl. In the first stage, replace the formulas of substances with their structural equivalents and obtain the equation of the chemical reaction: \nSc(OH)3(s) + HCl(aq) → ScCl3(aq) + H2O(l). \nThe equation is balanced as it is, as both sides of the equation have the same number of atoms for each element.

Step 2: Balancing the Oxidation of Fe2+ by MnO4- in Basic Solution

Oxidation-reduction reactions (redox reactions) involve the transfer of electrons from one molecule to another. In this case, Fe2+ is oxidized to Fe3+ by MnO4-. The half-reactions are: \nFe2+(aq) → Fe3+(aq) + e- (Oxidation half-reaction) \nMnO4-(aq) + 2H2O(l) + 3e- → MnO2(s) + 4OH-(aq) (Reduction half-reaction) \nAdd these half-reactions together, making sure that the electrons cancel: 5Fe2+(aq) + MnO4-(aq) + 8H2O(l) → 5Fe3+(aq) + MnO2(s) + 20OH-(aq).

Step 3: Balancing the Reaction of TiO2 with Molten KOH

For this reaction, we would have TiO2(s) + 2KOH → K2TiO3. The reaction is already balanced as the number of atoms of each element is the same on both sides of the equation.

Step 4: Balancing the Oxidation of Cu with H2SO4

The balanced chemical equation for the reaction of copper with concentrated sulfuric acid is Cu(s) + 2H2SO4(aq) → CuSO4(aq) + SO2(g) + 2H2O(l). This reaction illustrates the oxidation of copper metal to copper ion with the formation of sulfur dioxide gas and water.

Step 5: Review of the Equations

Ensure that each equation is balanced correctly. In other words, make sure the number of atoms of each individual element is the same on each side of the equation. A review of the equations confirms that this is the case.

Key Concepts

Redox Reactions

A redox reaction, an abbreviation for reduction-oxidation reaction, is a type of chemical process where the oxidation states of atoms are changed. It's important to understand that redox reactions encompass two simultaneous events: reduction, where a substance gains electrons, and oxidation, where a substance loses electrons. When these electron transfers occur, the oxidation states of the substances involved change to reflect the gain or loss of electrons.

For example, when iron (\text{Fe}^{2+}) is oxidized to iron (\text{Fe}^{3+}), it loses an electron, and this change can be represented by an oxidation half-reaction: \[ \text{Fe}^{2+} (\text{aq}) \rightarrow \text{Fe}^{3+} (\text{aq}) + e^{-} \]. On the other hand, the manganese in \text{MnO}_{4}^{-} gains electrons in its reduction half-reaction. As these half-reactions occur, their combination ensures that the electrons lost and gained balance, resulting in a conserved charge throughout the reaction.

Understanding and identifying the half-reactions is crucial for balancing redox equations. Once you've done this, the overall chemical equation can be balanced, often requiring the use of coefficients to ensure that the same number of electrons is exchanged in both half-reactions. This skill is fundamental when looking to comprehend redox reactions fully.

Chemical Reaction Notation

Chemical reaction notation is a system that uses chemical formulas to represent substances and arrows to indicate the direction of a chemical reaction. It's a shorthand notation that provides a clear and concise way of conveying which reactants are transformed into which products. Each chemical in an equation is represented by its formula, which provides information about the elements and the number of atoms involved in the compounds.

For instance, the reaction of \text{Sc(OH)}_{3} with HCl is written as: \[ \text{Sc(OH)}_{3} (\text{s}) + \text{HCl} (\text{aq}) \rightarrow \text{ScCl}_{3} (\text{aq}) + \text{H}_{2}\text{O} (\text{l}) \]. This notation indicates that solid scandium hydroxide reacts with aqueous hydrochloric acid to form aqueous scandium chloride and liquid water. It also suggests the reaction's physical states with symbols like (s) for solids, (g) for gases, (l) for liquids, and (aq) for aqueous solutions. The details provided through chemical reaction notation are instrumental in understanding the transformation that occurs during a chemical process.

Oxidation States

The concept of oxidation states describes the degree of oxidation or reduction of an atom within a compound. It's essentially a bookkeeping method to keep track of electrons during chemical reactions, especially redox reactions. The oxidation state is represented by an integer, which can be positive, negative, or zero, indicating the number of electrons an atom would gain or lose if the compound was to be transformed into its constituent atoms.

For example, in the equation where copper metal (\text{Cu}) is oxidized to \text{Cu}^{2+}, the copper starts with an oxidation state of 0 (because it's an element) and ends with an oxidation state of +2. This indicates that it loses two electrons: \[ \text{Cu} (\text{s}) \rightarrow \text{Cu}^{2+} (\text{aq}) + 2e^{-} \]. Accurately determining the oxidation states of the elements in a reaction is pivotal to balancing equations where redox reactions occur. Changes in oxidation states can help articulate the flow of electrons and thus are fundamental in understanding the nature of the chemical changes taking place.