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Balance the following oxidation-reduction equations. The reactions occur in acidic or basic aqueous solution, as indicated. a. \(\mathrm{MnO}_{4}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{MnO}_{2}+\mathrm{IO}_{3}^{-} \quad\) (basic) b. \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{Cl}^{-} \longrightarrow \mathrm{Cr}^{\frac{3}{3}+}+\mathrm{Cl}_{2} \quad\) (acidic) c. \(\mathrm{S}_{8}+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{SO}_{2}+\mathrm{NO} \quad\) (acidic) d. \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{O}_{2}+\mathrm{MnO}_{2} \quad\) (basic) e. \(\mathrm{Zn}+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{N}_{2} \quad\) (acidic)

Short Answer

Expert verified
The equations are balanced by separating into half-reactions, balancing atoms first for elements other than O and H, then O and H, balancing charges with electrons, and recombining the half-reactions.

Step by step solution

01

Identify the Redox Couples

In each reaction, identify the substances that are reduced and oxidized by writing their oxidation half-reactions. This will help in determining the electron transfer.
02

Balance Atoms Other Than Oxygen and Hydrogen

For each identified half-reaction, balance all atoms except for oxygen and hydrogen to ensure the correct stoichiometry for the redox process.
03

Balance Oxygen Atoms

For reactions in acidic solution, add water molecules to balance the oxygen atoms. For reactions in basic solution, the usage of OH鈦 might be needed after accounting for intermediate acidic conditions.
04

Balance Hydrogen Atoms

In acidic solutions, use H鈦 ions to balance hydrogen atoms. In basic solutions, first add H鈦 to balance hydrogen atoms and then neutralize them with OH鈦 ions.
05

Balance Charge

Balance the charges of each half-reaction by adding electrons. The number of electrons lost in the oxidation half must equal the electrons gained in the reduction half.
06

Combine Half-Reactions

Add the balanced half-reactions together, ensuring that the electrons cancel each other out, resulting in a balanced overall reaction.
07

Double Check Atom and Charge Balancing

Verify that all atoms, as well as the charge on both sides of the equation, are balanced.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Oxidation-Reduction
Oxidation-reduction reactions, often called redox reactions, are processes in which electrons are transferred between substances, leading to changes in oxidation states. In these reactions, one reactant loses electrons and undergoes oxidation, while another gains electrons and undergoes reduction.

- **Oxidation** involves the loss of electrons. The substance that loses electrons is called the reducing agent because it causes another substance to be reduced.- **Reduction** is the gain of electrons. The substance that gains electrons is called the oxidizing agent because it causes another substance to be oxidized.

In redox reactions, it is crucial to identify which atoms change their oxidation state. Recognizing these changes helps in balancing the chemical equation accurately. Let's say, in the provided reactions, Mn in \(MnO_4^-\) changes its oxidation state as it gains or loses electrons, determining whether it is undergoing oxidation or reduction.
Balancing Chemical Equations
Balancing chemical equations is essential in representing how atoms rearrange during a chemical reaction. This process ensures the conservation of mass, meaning the elements and their amounts remain constant throughout the reaction.

- **Balance Atoms Other Than Oxygen and Hydrogen:** Focus on elements that aren't oxygen or hydrogen initially for straightforward stoichiometry.- **Balance Oxygen:** In acidic solutions, add water \( H_2O \) to balance oxygen. In basic solutions, use hydroxide \(OH^-\) after adjusting for acidic conditions.- **Balance Hydrogen:** In acidic solutions, use hydrogen ions \( H^+ \) to balance hydrogen. For basic solutions, first balance using \( H^+ \) and then neutralize with \( OH^- \).- **Balance Charge:** Electron balance is crucial鈥攅nsure that electrons lost equals electrons gained.

Balancing involves combining these elements correctly to achieve a harmonious equation where both mass and charge are conserved, reflecting a real chemical process.
Acidic and Basic Solutions
Chemical reactions can occur in either acidic or basic environments, affecting how the equations are balanced. Understanding the solution type is integral as the method of balancing changes accordingly.

- **Acidic Solutions:** Preferentially use water ( \( H_2O \), hydrogen ions ( \( H^+ \), and electrons to balance oxygen, hydrogen, and charge, respectively. For instance, in the reaction involving chromate and chloride, balance with \( H^+ \) Post oxygen balance using water.- **Basic Solutions:** Adjust hydrogen and charge using hydroxide ions ( \( OH^- \) after initially balancing like it's in an acidic medium. Then neutralize excess \( H^+ \) by adding enough \( OH^- \) to form water. This method applies for the reaction where permanganate and iodide occur in a basic solution.

Whether it's acidic or basic, the prime objective is to achieve a balance that truly mirrors the chemical scenario.
Half-Reaction Method
The half-reaction method is an effective approach to balancing redox equations. This method involves breaking down the equation into two half-reactions: one for oxidation and the other for reduction.

- **Separate Half-Reactions:** Identify and write down the oxidation and reduction half-reactions separately.- **Balance Each Half-Reaction:** - Atoms other than \( O \) and \( H \) - Oxygen with \( H_2O \) - Hydrogen with \( H^+ \) - Charges with electrons- **Combine Half-Reactions:** Add the balanced half-reactions back together, ensuring that the electrons cancel out completely.

Through this method, complexity is significantly reduced as each half-reaction is independently balanced and then regathered to form the complete equation. This systematic approach makes handling redox reactions manageable and precise, ensuring clarity and distinction between oxidation and reduction processes.

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Most popular questions from this chapter

A solution of copper(II) sulfate is electrolyzed by passing a current through the solution using inert electrodes. Consequently, there is a decrease in the \(\mathrm{Cu}^{2+}\) concentration and an increase in the hydronium ion concentration. Also, one electrode increases in mass and a gas evolves at the other electrode. Write half-reactions that occur at the anode and at the cathode.

In an analytical determination of arsenic, a solution containing arsenious acid, \(\mathrm{H}_{3} \mathrm{AsO}_{3}\), potassium iodide, and a small amount of starch is electrolyzed. The electrolysis produces free iodine from iodide ion, and the iodine immediately oxidizes the arsenious acid to hydrogen arsenate ion, \(\mathrm{HAsO}_{4}{ }^{2-}\). $$ \mathrm{I}_{2}(a q)+\mathrm{H}_{3} \mathrm{AsO}_{3}(a q)+\underset{2 \mathrm{I}^{-}(a q)+\mathrm{HAsO}_{4}^{2-}(a q)+4 \mathrm{H}^{+}(a q)} $$ When the oxidation of arsenic is complete, the free iodine combines with the starch to give a deep blue color. If, during a particular run, it takes \(65.4 \mathrm{~s}\) for a current of \(10.5 \mathrm{~mA}\) to give an endpoint (indicated by the blue color), how many grams of arsenic are present in the solution?

A mercury battery, used for hearing aids and electric watches, delivers a constant voltage \((1.35 \mathrm{~V})\) for long periods. The half-reactions are $$ \begin{aligned} &\mathrm{HgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Hg}(l)+2 \mathrm{OH}^{-}(a q) \\ &\mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{e}^{-} \end{aligned} $$ Which half-reaction occurs at the anode and which occurs at the cathode? What is the overall cell reaction?

Describe the zinc-carbon, or Leclanch茅, dry cell and the lead storage battery.

A silver oxide-zinc cell maintains a fairly constant voltage during discharge \((1.60 \mathrm{~V})\). The button form of this cell is used in watches, hearing aids, and other electronic devices. The half-reactions are $$ \begin{aligned} &\mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{e}^{-} \\ &\mathrm{Ag}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Ag}(s)+2 \mathrm{OH}^{-}(a q) \end{aligned} $$ Identify the anode and the cathode reactions. What is the overall reaction in the voltaic cell?

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