Problem 1 - Chemistry and Chemical Reactivity

Question

Write balanced equations for the following half-reactions. Specify whether each is an oxidation or reduction. (a) \(\mathrm{Cr}(\mathrm{s}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})\) (in acid) (b) \(\mathrm{AsH}_{3}(\mathrm{g}) \rightarrow \mathrm{As}(\mathrm{s})\) (in acid) (c) \(\mathrm{VO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{V}^{2+}(\mathrm{aq})\) (in acid) (d) \(\mathrm{Ag}(\mathrm{s}) \rightarrow \mathrm{Ag}_{2} \mathrm{O}(\mathrm{s})\) (in base)

Step-by-Step Solution

Answer

(a) Oxidation, (b) Oxidation, (c) Reduction, (d) Oxidation.

Step 1: Understand Oxidation and Reduction

Oxidation involves the loss of electrons and increase in oxidation state, while reduction involves the gain of electrons and decrease in oxidation state. In acid or base, the balancing includes atoms and charges, often involving protons (H) or hydroxide ions (OH).

Step 2: Balance Chromium Reaction (a)

Begin with the reaction \( \mathrm{Cr}(\mathrm{s}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq}) \). Chromium goes from 0 to +3 oxidation state, losing 3 electrons. The balanced equation in acidic solution is:1. Write the skeleton reaction: \( \mathrm{Cr} \rightarrow \mathrm{Cr}^{3+} \).2. Balance chromium atoms: Already balanced.3. Balance electrons: Add 3 electrons to the products side: \( \mathrm{Cr} \rightarrow \mathrm{Cr}^{3+} + 3e^- \).4. Identify: This is an oxidation reaction.

Step 3: Balance Arsenic Reaction (b)

Consider \( \mathrm{AsH}_{3}(\mathrm{g}) \rightarrow \mathrm{As}(\mathrm{s}) \). Arsenic goes from -3 to 0 oxidation state, losing 3 electrons. In acidic media:1. Write the skeleton reaction: \( \mathrm{AsH}_3 \rightarrow \mathrm{As} \).2. Balance arsenic: Already balanced.3. Balance electrons: Add 3 electrons to the products side: \( \mathrm{AsH}_3 \rightarrow \mathrm{As} + 3H^+ + 3e^- \).4. Identify: This is an oxidation reaction.

Step 4: Balance Vanadium Reaction (c)

The reaction is \( \mathrm{VO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{V}^{2+}(\mathrm{aq}) \). Vanadium goes from +5 to +2, gaining 3 electrons. Balance in acid:1. Write the skeleton reaction: \( \mathrm{VO}_{3}^{-} \rightarrow \mathrm{V}^{2+} \).2. Add 3 electrons to the reactants: \( \mathrm{VO}_{3}^{-} + 3e^- \rightarrow \mathrm{V}^{2+} \).3. Balance oxygen with water, \( 3H_2O \) added to products: \( \mathrm{VO}_{3}^{-} + 3e^- \rightarrow \mathrm{V}^{2+} + 3H_2O \).4. Balance hydrogen with protons, \( 6H^+ \) added to reactants: \( \mathrm{VO}_{3}^{-} + 3e^- + 6H^+ \rightarrow \mathrm{V}^{2+} + 3H_2O \).5. Identify: This is a reduction reaction.

Step 5: Balance Silver Reaction (d)

For \( \mathrm{Ag}(\mathrm{s}) \rightarrow \mathrm{Ag}_{2}\mathrm{O}(\mathrm{s}) \). Silver goes from 0 to +1 in \( \mathrm{Ag}_2\mathrm{O} \). Balance in basic solution:1. Write the skeleton reaction: \( 2\mathrm{Ag} \rightarrow \mathrm{Ag}_{2}\mathrm{O} \).2. Add 2 OH- to products for charge balance: \( 2\mathrm{Ag} + 2OH^- \rightarrow \mathrm{Ag}_2\mathrm{O} \).3. Add one water molecule to reactants: \( 2\mathrm{Ag} + 2OH^- \rightarrow \mathrm{Ag}_2\mathrm{O} + H_2O \).4. Identify: This is an oxidation reaction.

Key Concepts

Oxidation

Oxidation occurs when a chemical species loses electrons, leading to an increase in its oxidation state. Imagine oxidation as a process where an element gives away electrons, much like donating energy.
In chemical reactions, recognizing oxidation means identifying the species that is losing electrons. This can be seen as an element's oxidation number increasing in the reaction.
For example, in the reaction

• \( ext{Cr} ightarrow ext{Cr}^{3+} + 3e^- \)

Chromium starts with an oxidation state of 0 and ends with +3. It loses 3 electrons, evidencing oxidation.
Similarly, in the reaction

• \( ext{AsH}_3 ightarrow ext{As} + 3H^+ + 3e^- \)

Arsenic also undergoes oxidation, going from an oxidation state of -3 to 0. Remember, any decrease in negative charge or increase in positive charge often implies oxidation.

Reduction

Reduction is the opposite of oxidation. It involves the gain of electrons, leading to a decrease in oxidation state. Think of reduction as receiving electrons.
Recognizing reduction in a reaction involves identifying the species that is gaining electrons, often indicated by a decrease in oxidation number.
For instance, in the reaction:

• \( ext{VO}_{3}^{-} + 3e^- + 6H^+ ightarrow ext{V}^{2+} + 3H_2O \)

Vanadium starts with a +5 oxidation state and reduces to +2. It gains 3 electrons, embodying reduction. The environment might involve acidic or basic solutions, affecting how the reaction is balanced with water molecules or protons.

Half-Reactions

Half-reactions are used to clearly show the electron transfer process in redox reactions. They break down the overall redox reaction into two simpler parts: oxidation and reduction.

• Oxidation half-reaction: Details the loss of electrons by an element or compound.
• Reduction half-reaction: Shows the gain of electrons.

Each half-reaction must account for all changes in atom types and charges. For every electron lost in the oxidation half, it's gained in the reduction half.For example, take the following half-reaction:

• \( ext{Cr} ightarrow ext{Cr}^{3+} + 3e^- \)
• \( ext{VO}_{3}^{-} + 3e^- + 6H^+ ightarrow ext{V}^{2+} + 3H_2O \)

These steps clarify which species are oxidized and which are reduced, making it easier to balance the full equation.

Balancing Equations

Balancing redox equations ensures the conservation of mass and charge, critical for correctly representing the reaction. It involves adjusting coefficients to have the same number of each type of atom and total charge on both sides of the equation.
In acidic solutions, often

• H⁺ ions
• Water molecules

are used to balance hydrogen and oxygen atoms. While in basic solutions,

• OH⁻ ions
• Water molecules

are used to achieve the balance.
Consider balancing the silver reaction:

• \( 2 ext{Ag} + 2OH^- ightarrow ext{Ag}_2 ext{O} + H_2O \)

Here, balancing the charges and the water maintain the overall charge and number of atoms. Balancing is essential, aligning the stoichiometry of chemical reactions to real-world circumstances.