Problem 26 - Chemistry The Central Science In Si Units

Question

Complete and balance the following equations, and identify the oxidizing and reducing agents. (Recall that the \(\mathrm{O}\) atoms in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), have an atypical oxidation state.) (a) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) (acidic solution) (b) \(\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)\) (acidic solution) (c) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow \mathrm{HCOOH}(a q)+\) \(\mathrm{Cr}^{3+}(a q)\) (acidic solution) (d) \(\mathrm{BrO}_{3}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)\) (acidic solution) (e) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{AlO}_{2}^{-}(a q)\) (basic solution) (f) \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

Equations are balanced by assigning oxidation states, identifying half-reactions, balancing mass and charge, and identifying oxidizing/reducing agents.

Step 1: Assign Oxidation Numbers

Identify and assign the oxidation numbers for each element in the reactants and products of the given chemical equations. This helps in identifying the changes in oxidation states to determine which species are oxidized and which are reduced.

Step 2: Separate the Half-Reactions

For each equation, split the oxidation (loss of electrons) and reduction (gain of electrons) processes into separate half-reactions. This will help in balancing each half-reaction individually.

Step 3: Balance Atoms and Charge for Half-Reactions

Begin by balancing all atoms other than oxygen and hydrogen. Next, balance the oxygen atoms by adding water molecules and hydrogen atoms by adding H⁺ ions in acidic solutions (or OH⁻ in basic solutions). Lastly, balance the charge by adding electrons.

Step 4: Equalize Electrons Transferred

Multiply each half-reaction by an appropriate integer so that the number of electrons lost in oxidation equals the number of electrons gained in reduction. This will ensure the charge is balanced when the half-reactions are recombined.

Step 5: Combine and Simplify Half-Reactions

Add the two balanced half-reactions together. Cancel out any species that appears on both sides of the equation, such as electrons, water, hydrogen, or hydroxide ions, leaving a balanced net ionic equation.

Step 6: Identify the Oxidizing and Reducing Agents

Determine the oxidizing and reducing agents by identifying which reactants contain the atoms that are reduced and oxidized, respectively. The oxidizing agent is the substance reduced, whereas the reducing agent is the substance oxidized.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry. It ensures that there are equal numbers of each type of atom on both sides of the equation. The Law of Conservation of Mass states that mass can neither be created nor destroyed in a chemical reaction. Hence, we must balance the elements to adhere to this law.

To balance an equation, start by listing the number of atoms of each element present on either side of the equation. Adjust coefficients to make sure they match. Remember:

• Start by balancing the elements that appear in only one reactant and one product first.
• Leave elements like hydrogen and oxygen for last as they frequently appear in multiple compounds.
• Check your work by recounting atoms for each element; ensure the total number remains equal on both sides.

Finally, review the equation to ensure it's balanced, and verify that the simplest possible coefficients are used.

Oxidation States

Understanding oxidation states is crucial for recognizing redox reactions. The oxidation state or number represents the total number of electrons that an atom gains or loses to form a chemical bond. It's a useful tool for keeping track of electron exchange in reactions.

Here are some guidelines for assigning oxidation states:

• An atom in its elemental state has an oxidation state of zero.
• For monoatomic ions, the oxidation state equals the charge of the ion.
• Oxygen generally has an oxidation state of -2, except in peroxides like \( ext{H}_2 ext{O}_2\), where it's -1.
• Hydrogen is typically +1 when bonded to nonmetals and -1 when bonded to metals.
• The sum of oxidation states for all atoms in a neutral molecule must be zero or equal the charge of the ion.

Understanding these rules helps identify which elements undergo oxidation or reduction in a reaction.

Half-Reaction Method

The half-reaction method is a systematic approach to balance redox reactions. It breaks down the process into manageable steps, focusing on oxidation and reduction separately.

Steps in the half-reaction method include:

• Splitting the unbalanced equation into two half-reactions, one for oxidation and one for reduction.
• Balancing all elements in each half-reaction except oxygen and hydrogen.
• Balancing oxygen by adding water molecules and hydrogen by adding hydrogen ions in acidic solutions. For basic solutions, balance hydrogen using water and hydroxide ions.
• Ensuring charge balance by adding electrons: Assign electrons to balance the charges in each half-reaction.
• Multiplying the half-reactions by suitable coefficients so that the electrons lost in oxidation are equal to those gained in reduction.

Once each half-reaction is balanced, they are combined, ensuring electrons and other species cancel out accordingly, yielding the balanced overall reaction.

Oxidizing and Reducing Agents

In redox reactions, an oxidizing agent facilitates oxidation by accepting electrons, while a reducing agent promotes reduction by donating electrons. Recognizing these agents is essential for understanding electron transfer in chemical reactions.

Key points to remember:

• The oxidizing agent is the substance that gets reduced. It gains electrons and its oxidation state decreases.
• The reducing agent gets oxidized. It loses electrons and its oxidation state increases.

For example, in hydrogen peroxide (\( ext{H}_2 ext{O}_2\)), when it decomposes, oxygen goes from an unusual -1 oxidation state to 0 in \( ext{O}_2\), meaning it acts as both an oxidizing and reducing agent in certain reactions. Knowing these roles helps predict reaction outcomes and adjust conditions for desired results.