Question

Balance the following redox equations by the halfreaction method: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (b) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (c) \(\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}\) (in basic solution) (d) \(\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}\) (in basic solution) (e) \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}\) (in acidic solution)

Short answer

Steps include identifying half-reactions, balancing them for mass and charge, and combining them to form fully balanced equations.

Step-by-step solution

Identify the oxidation and reduction reactions

For each given redox equation, identify which species are being oxidized and which are being reduced by examining the change in oxidation states.

Write the half-reactions

For each equation, divide the reaction into oxidation and reduction half-reactions by writing down the species involved and their respective charges.

Balance atoms other than O and H

In each half-reaction, balance all the atoms other than oxygen and hydrogen, usually by inspection.

Balance oxygen atoms with water

Add \( ext{H}_2 ext{O}\) molecules to the side needing more oxygen for each half-reaction.

Balance hydrogen atoms with H⁺ or OH⁻ ions

Add \( ext{H}^+\) ions in acidic solutions or \( ext{OH}^-\) ions in basic solutions to balance hydrogen atoms in the half-reactions.

Balance charges with electrons

Add electrons (\(e^-\)) to one side of each half-reaction to balance the overall charge.

Scale the half-reactions

Multiply the half-reactions by appropriate coefficients so that the electrons lost in the oxidation process equal the electrons gained in the reduction process.

Combine and simplify reactions

Add the corrected half-reactions together, canceling out electrons and any other species that appear on both sides of the equation to give a balanced chemical equation.

Verify the balanced equation

Check that all atoms and charges balance to ensure the final redox equation is correct.

Key concepts

Half-Reaction Method

The half-reaction method is a systematic way to balance redox reactions. Redox reactions encompass two simultaneous processes: oxidation and reduction. By separating these into half-reactions, we can manage and balance the change in electron count and ensure mass and charge conservation.

This approach begins with identifying all the species involved and ascertaining changes in their oxidation states. Once that's sorted, each species undergoes either oxidation or reduction, leading us to write two separate processes or half-reactions.

• Oxidation half-reaction: shows the loss of electrons.
• Reduction half-reaction: depicts the gain of electrons.

The focus is then on balancing each half-reaction independently in terms of mass and charge before combining them back into a balanced redox equation. This ensures that the electrons lost in the oxidation half always match the electrons gained in the reduction half.

Oxidation and Reduction

At the heart of redox reactions are the processes of oxidation and reduction. Oxidation involves the loss of electrons from a molecule, atom, or ion, increasing its oxidation state, while reduction involves gaining electrons, thus reducing its oxidation state.

It’s important to remember the handy mnemonic: OIL RIG - Oxidation Is Loss, Reduction Is Gain. This reflects the electron flow and helps in recognizing what each substance is doing in a chemical reaction.

• Oxidation: Increase in oxidation number, often involves adding oxygen or removing hydrogen.
• Reduction: Decrease in oxidation number, often involves removing oxygen or adding hydrogen.

Determining the oxidation states of elements allows us to identify which atoms are oxidized or reduced. For students, becoming adept at assigning oxidation states to elements in a reaction is crucial.

Balancing Chemical Equations

Balancing chemical equations ensures that the same number of each type of atom exists on both sides of the equation, complying with the principles of conservation of mass and charge. In the context of redox reactions, it becomes slightly more intricate due to electron transfer between species.

Start by determining all the reactants and products. Then, focus on balancing all atoms except hydrogen and oxygen first. Once those are balanced, move on to oxygen atoms by adding water ( H_2O ) and then balance hydrogen by adding hydrogen ions ( H^+ ) in acidic solutions or hydroxide ions ( OH^- ) in basic solutions.

• Always follow the order: balance atoms first, then balance charge with electrons.
• Ensure that added coefficients result in the same number of electrons transferred in both half-reactions.

The trick is ensuring the number of electrons lost in oxidation equals the number gained in reductions when you total the half-reactions together.

Acidic and Basic Solutions

Redox reactions often occur in acidic or basic solutions, which affects how we balance them. The type of solution determines how atoms, especially hydrogen and oxygen, are balanced using water, hydrogen ions, or hydroxide ions.

In acidic solutions, hydrogen atoms are balanced using H^+ ions, and any imbalance in charge is corrected later using electrons. Typically, if oxygen atoms need fulfillment, water is added.

• Acidic: Use H_2O for oxygen, and H^+ for hydrogen.

In basic solutions, hydroxide ions ( OH^- ) are used instead of H^+ ions to balance hydrogen. For oxygen balance, water is still added, but additional steps ensure neutrality by often times neutralizing excess H^+ with OH^- . Remember, combining H^+ and OH^- forms water, which is essential for maintaining balance.

• Basic: Use OH^- ions for hydrogen, and H_2O remains useful for oxygen.

Recognizing these adjustments helps successfully balance redox reactions in different pH environments.