Question

Balance each of the following equations using the change-inoxidation-number method: (a) \(\mathrm{Cu}+\mathrm{O}_{2} \rightarrow \mathrm{CuO}\) (b) \(\mathrm{KClO}_{2} \rightarrow \mathrm{KCl}+\mathrm{O}_{2}\) (c) \(\mathrm{Ca}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{H}_{2}\) (d) \(\mathrm{PbS}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{PbSO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{CH}_{4}+\mathrm{NO}_{2} \rightarrow \mathrm{N}_{2}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

Equations balanced using the change-in-oxidation-number method: (a) 2Cu + O2 -> 2CuO, (b) 2KClO2 -> 2KCl + O2, (c) Ca + 2H2O -> Ca(OH)2 + H2, (d) PbS + 4H2O2 -> PbSO4 + 4H2O, (e) 16CH4 + 22NO2 -> 11N2 + 16CO2 + 22H2O.

Step-by-step solution

Write Oxidation States and Changes

Identify the oxidation states of each element in the reactants and products. Calculate the change in oxidation numbers for all elements.

Balance Elements with Change in Oxidation Numbers

Adjust the coefficients to equalize the increase and decrease in oxidation numbers.

Balance Remaining Atoms

Balance all other atoms as usual by adjusting coefficients, ensuring the equation is balanced according to the Law of Conservation of Mass.

Verify the Balanced Equation

Check that the total number of atoms for each element and the charge are balanced on both sides of the equation.

Key concepts

balancing chemical equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the principle of the conservation of mass is satisfied. It involves making sure that the number of atoms of each element is the same on both sides of the equation. Here's how you can balance chemical equations effectively:
Identify each element in the reactants and products.
Count the number of atoms of each element in the reactants and products.
Adjust the coefficients to balance the elements one at a time.
Always start with the element that appears in the least amount of compounds.
Check your work to ensure all elements are balanced.
For example, to balance Cu + O₂ → CuO using the oxidation number method, we identify the oxidation states and adjust coefficients accordingly, ensuring conservation of mass and charge.

oxidation states

Oxidation states (or numbers) represent the degree of oxidation of an atom in a chemical compound. They help us track electron transfer during chemical reactions. The oxidation number can be positive, negative, or zero, depending on the atom's gain or loss of electrons.
Key rules for finding oxidation states include:
The oxidation state of an element in its standard state is zero (e.g., O₂, H₂).
Oxygen typically has an oxidation state of -2, except in peroxides where it is -1.
Hydrogen usually has an oxidation state of +1, except when bonded to metals in binary compounds where it is -1.
For ions, the oxidation state equals the ion’s charge (e.g., Na⁺ is +1).
In a compound, the sum of the oxidation states for all atoms must equal the compound's overall charge. Using these rules helps balance the equation by ensuring electron loss equals electron gain.

conservation of mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction. This principle is fundamental for balancing chemical equations. When we balance an equation, we ensure that the total mass of the reactants equals the total mass of the products.
This involves:
Counting the number of atoms for each element on both sides of the equation.
Regardless of the reaction, the number of each type of atom remains constant.
Adjusting the coefficients in the equation ensures that the mass is conserved.
For instance, in the reaction PbS + H₂O₂ → PbSO₄ + H₂O, we balance the lead, sulfur, oxygen, and hydrogen atoms by adjusting coefficients, keeping the mass equivalent.

chemical reaction

A chemical reaction involves the transformation of reactants into products through the breaking and forming of chemical bonds. This process involves several key concepts:
Reactants: The starting substances in a reaction.
Products: The new substances formed as a result of the reaction.
Chemical equations: Representations of chemical reactions with reactants on the left and products on the right.
In the context of oxidation-reduction (redox) reactions, such as the ones in the exercise, tracking oxidation states helps us understand how electrons are transferred during the reaction.
For instance, in the reaction CH₄ + NO₂ → N₂ + CO₂ + H₂O, identifying and balancing oxidation states helps ensure mass and charge balance, illustrating the conservation principles clearly.