Question

For each requested step, use the half-reaction method to balance the oxidation-reduction equation below. (Hint: See Sample Problem A.) \({K}+{H}_{2} {O} \longrightarrow {KOH}+{H}_{2}\) a. Write the ionic equation, and assign oxidation numbers to all atoms to determine what is oxidized and what is reduced. b. Write the equation for the reduction, and balance it for both atoms and charge. c. Write the equation for the oxidation, and balance it for both atoms and charge. d. Multiply the coefficients of the oxidation and reduction equations so that the number of electrons lost equals the number of electrons gained. Add the two equations. e. Add species as necessary to balance the overall formula equation.

Short answer

2K + 2H2O → 2KOH + H2.

Step-by-step solution

Write the Ionic Equation and Assign Oxidation Numbers

Start by converting the molecular equation into an ionic equation. Split water into its ions: K + H2O → KOH + H2 becomes: K + H2O → K⁺ + OH⁻ + H2. Assign oxidation numbers: K (0), H in H2O (+1), O (-2), K in KOH (+1), O in OH⁻ (-2), H in OH⁻ (+1) and H2 (0). Now identify which elements are oxidized and reduced. Potassium (K) goes from 0 to +1 (oxidation), and Hydrogen (H) goes from +1 in H2O to 0 in H2 (reduction).

Write the Reduction Half-Reaction

The reduction half-reaction involves the hydrogen in water. H2O is reduced to H2. Write this reaction: H2O + 2e⁻ → H2. Now balance the atoms and charges. For H2O → H2, you need 2 electrons to balance the hydrogens: H2O + 2e⁻ → H2 + 2OH⁻.

Write the Oxidation Half-Reaction

The oxidation half-reaction involves potassium. Write this reaction: K → K⁺ + e⁻. The potassium atom loses one electron. The oxidation half-reaction is: K → K⁺ + e⁻.

Balance Electrons Between Half-Reactions

Ensure the number of electrons lost in oxidation equals the number of electrons gained in reduction. Multiply the oxidation half-reaction by 2 to achieve this: 2(K → K⁺ + e⁻) becomes 2K → 2K⁺ + 2e⁻.

Add Half-Reactions Together

Combine the balanced half-reactions. Add the reduction and oxidation reactions: H2O + 2e⁻ → H2 + 2OH⁻ 2K → 2K⁺ + 2e⁻, When added, the electrons cancel out: H2O + 2K → H2 + 2K⁺ + 2OH⁻.

Balance the Overall Equation

Combine ions to write the overall balanced equation and add back any necessary species to form the final balanced molecular equation from the ionic equation: 2K + 2H2O → 2KOH + H2.

Key concepts

Oxidation-Reduction Basics

Oxidation-reduction (redox) reactions are chemical processes where electrons are transferred between substances. In these reactions:

• Oxidation is the loss of electrons.
• Reduction is the gain of electrons.

These processes always occur together. When one substance is oxidized, another must be reduced. Understanding who gains and loses electrons is key to mastering redox reactions.

Half-Reaction Method Explained

Balancing redox reactions can be complex, so chemists use the half-reaction method to simplify the process. This method involves:

• Writing separate half-reactions for oxidation and reduction.
• Balancing each half-reaction for atoms and charges.
• Combining the half-reactions, ensuring the electrons lost and gained are equal.

This step-by-step approach makes it easier to ensure the equation is correctly balanced.

Understanding Oxidation Numbers

Oxidation numbers are a way to track how many electrons are lost or gained in a reaction. They help identify which atoms are oxidized and which are reduced.
Assigning oxidation numbers involves:

• Knowing the standard rules, such as oxygen typically having an oxidation number of -2.
• Applying these rules to each element in the compound.

This helps determine the changes in oxidation states during the reaction.

Writing and Balancing Ionic Equations

An ionic equation focuses on the ions involved in a reaction rather than the compound as a whole. This can simplify the balancing process.
Steps to write an ionic equation include:

• Separating compounds into their constituent ions.
• Writing the ionic form of the reaction.
• Balancing the ionic equation for both mass and charge.

This approach highlights the actual participants in the redox process, making it clearer and easier to balance.