Question

Balance each of the following half-reactions. a. \(\mathrm{Al} \rightarrow \mathrm{Al}^{3+}\) b. \(\mathrm{I}^{-} \rightarrow \mathrm{I}_{2}\) c. \(\mathrm{C o}^{3+} \rightarrow \mathrm{C o}^{2+}\) d. \(\mathrm{P}^{3-} \rightarrow \mathrm{P}_{4}\)

Short answer

The balanced half-reactions are as follows: a. Al → Al^(3+) + 3e^- b. 2I^(-) → I₂ + 2e^- c. Co^(3+) + e^- → Co^(2+) d. 4P^(3-) → P4 + 12e^-

Step-by-step solution

Balance the aluminum atoms

Here, there is one aluminum atom on both sides, so there is no further balancing needed for the atoms.

Balance the charge

The product side has a charge of +3, while the reactant side has a charge of 0. To balance the charge, we add 3 electrons (e-) to the product side: Al → Al^(3+) + 3e^- b. Balancing the I^(-) --> I2 half-reaction:

Balance the iodine atoms

Here, the product side has two iodine atoms, so we add a stoichiometric coefficient of 2 to the iodide ion: 2I^(-) → I₂

Balance the charge

Now the reactant side has a charge of -2, while the product side has a charge of 0. To balance the charge, we add 2 electrons (e-) to the product side: 2I^(-) → I₂ + 2e^- c. Balancing the Co^(3+) --> Co^(2+) half-reaction:

Balance the cobalt atoms

Here, there is one cobalt atom on both sides, so there is no further balancing needed for the atoms.

Balance the charge

The reactant side has a charge of +3 while the product side has a charge of +2. To balance the charge, we add 1 electron (e^-) to the reactant side: Co^(3+) + e^- → Co^(2+) d. Balancing the P^(3-) --> P4 half-reaction:

Balance the phosphorus atoms

The product side has 4 phosphorus atoms, so we add a stoichiometric coefficient of 4 to the phosphide ion: 4P^(3-) → P4

Balance the charge

Now the reactant side has a charge of -12, while the product side has a charge of 0. To balance the charge, we add 12 electrons (e^-) to the product side: 4P^(3-) → P4 + 12e^-

Key concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. In the language of chemistry, it serves as a form of bookkeeping, ensuring that atoms are conserved in the processes described by chemical equations.

For instance, when balancing the reaction \(\mathrm{I}^{-} \rightarrow \mathrm{I}_{2}\), we must consider the stoichiometric coefficient – a number placed in front to indicate the quantity of molecules or ions participating in the reaction. Here, two iodide ions (\(\mathrm{I}^{-}\)) are required to produce one molecule of \(\mathrm{I}_{2}\), showcasing the ratio of 2:1. Stoichiometry plays a crucial role in chemical equations as it guarantees the mass and charge are balanced, reflecting the law of conservation of mass and charge.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are characterized by the transfer of electrons between chemical species. The species that loses electrons is oxidized, while the one that gains electrons is reduced.

This concept is exemplified in the reaction \(\mathrm{Al} \rightarrow \mathrm{Al}^{3+}\), where aluminum (\(\mathrm{Al}\)) is oxidized by losing three electrons to become \(\mathrm{Al}^{3+}\). Electron transfer is the key feature of a redox process, and understanding how electrons move can unveil much about the reaction, including its stoichiometry and the changes in oxidation states that occur.

Chemical Equations

Chemical equations are representations of chemical reactions where the reactants are shown on the left and the products on the right, with an arrow indicating the direction of the reaction.

Balancing such equations is an essential skill in chemistry; it involves ensuring that the same number of each type of atom exists on both sides of the equation, as seen in the phosphorus half-reaction \(4\mathrm{P}^{3-} \rightarrow \mathrm{P}_{4}\). Balancing also extends to charges in the case of ionic species, requiring that the overall charge is the same on both sides of the equation. A balanced chemical equation complies with the laws of conservation of mass and charge, providing a fundamental pillar in the study of chemical reactions.

Electron Transfer

Electron transfer is the movement of electrons from one atom or molecule to another, which is fundamental to the process of redox reactions. It often involves the use of electrons (e\(^-\)) in balancing half-reactions to ensure that the total charge before and after the reaction is equal.

In the half-reaction \(\mathrm{C}o^{3+} \rightarrow \mathrm{C}o^{2+}\), a single electron is transferred to the cobalt ion (\(\mathrm{C}o^{3+}\)) to reduce it to \(\mathrm{C}o^{2+}\). It emphasizes the need for balancing charge as well as mass in the detailed depiction of the chemical change, highlighting the interplay between stoichiometry, chemical equations, and the underpinning principles of electron transfer.