Problem 19 - Chemistry: Principles and Reactions

Question

Write a balanced equation to show (a) the reaction of chromate ion with strong acid. (b) the oxidation of water to oxygen gas by permanganate ion in basic solution. (c) the reduction half-reaction of chromate ion to chromium(III) hydroxide in basic solution.

Step-by-Step Solution

Answer

(a) Reaction of chromate ion with strong acid (b) Oxidation of water to oxygen gas by permanganate ion in basic solution (c) Reduction half-reaction of chromate ion to chromium(III) hydroxide in basic solution Answer: (a) 2 CrO_4^{2-} + 2 H^+ -> Cr_2O_7^{2-} + H_2O (b) 2 MnO_4^{-} + 3 H_2O -> 2 MnO_2 + 3 O_2 + 4 OH^- (c) 2 CrO_4^{2-} + 2 OH^- -> 2 Cr(OH)_3 + 6 e^-

Step 1: Write the unbalanced equation

Write the unbalanced equation with chromate ion (CrO_4^{2-}) reacting with a strong acid (H^+): CrO_4^{2-} + H^+ -> ?

Step 2: Determine the products

In the presence of a strong acid, chromate ion is protonated to form dichromate ion (Cr_2O_7^{2-}) and water: CrO_4^{2-} + H^+ -> Cr_2O_7^{2-} + H_2O

Step 3: Balance the equation

To balance the equation, we need to adjust the number of atoms on both sides: 2 CrO_4^{2-} + 2 H^+ -> Cr_2O_7^{2-} + H_2O (b) Oxidation of water to oxygen gas by permanganate ion in basic solution

Step 1: Write the unbalanced equation

Write the unbalanced equation with permanganate ion (MnO_4^{-}) oxidizing water (H_2O) to oxygen gas (O_2) in a basic solution: MnO_4^{-} + H_2O -> MnO_2 + O_2

Step 2: Balance the equation

Balance the equation by adjusting the number of atoms on both sides: 2 MnO_4^{-} + 3 H_2O -> 2 MnO_2 + 3 O_2 + 4 OH^- (c) Reduction half-reaction of chromate ion to chromium(III) hydroxide in basic solution

Step 1: Write the unbalanced half-reaction

Write the unbalanced reduction half-reaction, in which chromate ion (CrO_4^{2-}) is reduced to chromium(III) hydroxide (Cr(OH)_3) in a basic solution: CrO_4^{2-} -> Cr(OH)_3

Step 2: Balance the oxygen atoms

Add water (H_2O) to balance the oxygen atoms: CrO_4^{2-} + 3 H_2O -> Cr(OH)_3

Step 3: Balance the hydrogen atoms

Add hydroxide ions (OH^-) to the other side to balance the hydrogen atoms: CrO_4^{2-} + 3 H_2O -> Cr(OH)_3 + 6 OH^-

Step 4: Balance charges

Add electrons (e^-) to the appropriate side of the equation to balance the charges: 2 CrO_4^{2-} + 8 OH^- -> 2 Cr(OH)_3 + 6 OH^- + 6 e^-

Step 5: Simplify the equation

Simplify the equation by eliminating the common species: 2 CrO_4^{2-} + 2 OH^- -> 2 Cr(OH)_3 + 6 e^-

Key Concepts

Balanced Chemical Equations

Chemical reactions need to be represented by balanced chemical equations. This means that the number of each type of atom on the reactants side must equal the number on the products side. This balance is in accordance with the Law of Conservation of Mass, which states that mass cannot be created or destroyed in a chemical reaction.
Balancing equations requires some steps:

• Identify all reactants and products in the equation.
• Count the number of atoms of each element in the reactants and products.
• Add coefficients in front of compounds to balance the number of atoms of each element on both sides.
• Ensure all coefficients are the smallest set of whole numbers that balance the equation.

For example, in the given reaction of chromate ion with a strong acid, balancing involves altering coefficients so that the Cobalt atoms and other elements are equal on both sides of the equation. Balancing chemical equations is foundational for understanding more complex topics like oxidation-reduction reactions.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, or redox reactions, involve the transfer of electrons between substances. Oxidation refers to the loss of electrons, while reduction refers to the gain of electrons. These reactions are crucial because they are involved in many chemical and biological processes, such as cellular respiration and combustion.
Understanding oxidation numbers can help identify what is being oxidized and reduced:

• Oxidation number increases when a substance is oxidized.
• Oxidation number decreases when a substance is reduced.

In these reactions, oxidizing agents gain electrons and are reduced, while reducing agents lose electrons and are oxidized. For example, in the conversion of water to oxygen gas by a permanganate ion, water acts as a reducing agent and loses electrons. This process is part of the larger redox reaction, where the permanganate ion undergoes a reduction.

Chromate Ion Reactions

Chromate ions ( ext{CrO}_4^{2-}) are involved in a number of reactions, especially redox reactions. A significant chromate reaction occurs when chromate ions are introduced to an acidic environment, causing them to convert into dichromate ions ( ext{Cr}_2 ext{O}_7^{2-}). The chromate-dichromate equilibrium is an important aspect of this chemistry.
In acidic conditions, the reaction can be shown as:

• Chromate ions react with hydrogen ions ( ext{H}^+) to form dichromate ions and water.

The process also works in reverse: In basic conditions, dichromate ions can revert back to chromate ions. This chromate-dichromate interconversion is essential in many titrations and chemical analyses, as it can signal changes in acidity in solutions.

Permanganate Ion Reactions

Permanganate ions ( ext{MnO}_4^{-}) are strong oxidizing agents. In basic solutions, they play a role in a variety of oxidation reactions. The permanganate ion can oxidize water into oxygen gas while itself being reduced to manganese dioxide ( ext{MnO}_2).
Key points in permanganate ion reactions:

• Permanganate ions usually change color during the reaction, from vibrant purple to brown, indicating their reduction.
• In acidic solutions, permanganate ions are reduced to manganese ( ext{Mn}^{2+}), illustrating different behavior in varying pH contexts.
• In basic solutions, the reduction typically halts at manganese dioxide ( ext{MnO}_2).

These reactions are vital in chemical analysis and are used in titrations to quantify reducing agents in a sample. Their versatility and predictability make permanganate reactions particularly useful in academic and industrial laboratories.