Question

Balance the following equations for reactions occurring in an acidic solution. (a) \(\mathrm{NO}_{3}^{-}+\mathrm{Zn} \longrightarrow \mathrm{NH}_{4}^{+}+\mathrm{Zn}^{2+}\) (b) \(\mathrm{Cr}^{3+}+\mathrm{BiO}_{3}^{-} \longrightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{Bi}^{3+}\) (c) \(\mathrm{I}_{2}+\mathrm{OCl}^{-} \longrightarrow \mathrm{IO}_{3}^{-}+\mathrm{Cl}^{-}\) (d) \(\mathrm{Mn}^{2+}+\mathrm{BiO}_{3}^{-} \longrightarrow \mathrm{MnO}_{4}^{-}+\mathrm{Bi}^{3+}\)

Short answer

Balanced equations: (a) \(4\mathrm{NO}_{3}^{-} + 10\mathrm{Zn} + 40\mathrm{H}^{+} \rightarrow 4\mathrm{NH}_{4}^{+} + 10\mathrm{Zn}^{2+} + 3\mathrm{H}_{2}\mathrm{O}\), (b) \(2\mathrm{Cr}^{3+} + 6\mathrm{BiO}_{3}^{-} + 30\mathrm{H}^{+} \rightarrow \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 6\mathrm{Bi}^{3+} + 15\mathrm{H}_{2}\mathrm{O}\), (c) \(\mathrm{I}_{2} + 6\mathrm{OCl}^{-} + 12\mathrm{H}^{+} \rightarrow 2\mathrm{IO}_{3}^{-} + 6\mathrm{Cl}^{-} + 6\mathrm{H}_{2}\mathrm{O}\), (d) \(2\mathrm{Mn}^{2+} + 5\mathrm{BiO}_{3}^{-} + 14\mathrm{H}^{+} \rightarrow 2\mathrm{MnO}_{4}^{-} + 5\mathrm{Bi}^{3+} + 7\mathrm{H}_{2}\mathrm{O}\). Each reaction is balanced with respect to both atoms and charge.

Step-by-step solution

Balance elements other than O and H

For each reaction, start by balancing all elements except for oxygen and hydrogen. Adjust coefficients to ensure the same number of each type of atom on both sides.

Balance the oxygens by adding water molecules

Next, for oxygen balance, add H2O molecules on the side which has less oxygen.

Balance the hydrogens by adding protons (H+)

To balance hydrogen, add H+ ions on the side which requires more hydrogen.

Balance the charges by adding electrons

Reactions in an acidic solution may require adding electrons (e-) to balance the overall charge on both sides of the equation.

Simplify if necessary

If there are the same number of a particular molecule on both sides, reduce them for simplicity.

Verify the Balance

Check that atoms and charge are balanced on both sides for each equation.

Key concepts

Chemical Equation Balancing

The art of chemical equation balancing lies in ensuring that the number of atoms for each element is the same on both sides of the equation. This adheres to the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction.
For instance, when balancing the reaction \(\mathrm{NO}_{3}^{-}+\mathrm{Zn} \longrightarrow \mathrm{NH}_{4}^{+}+\mathrm{Zn}^{2+}\), one begins by balancing atoms of zinc and nitrogen first. It's analogous to solving a puzzle where each piece must find its exact place to complete the picture, except the picture should mirror itself perfectly on either side.

Redox Reactions in Acidic Solution

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between substances. In an acidic solution, these reactions also include the participation of \(\mathrm{H}^{+}\) ions. When balancing redox reactions in acid, after balancing the atoms, you would add water molecules to balance the oxygen atoms and then add protons \(\mathrm{H}^{+}\) to balance the hydrogen atoms.
This process ensures that the transfer of electrons does not disrupt the pH of the solution. For example, after adjusting the atoms in our previous zinc reaction, additional water molecules or protons may be needed to account for any changes in oxygen or hydrogen atoms.

Stoichiometry

Stoichiometry is the quantitative aspect of chemistry that forms the backbone of balancing equations. Using stoichiometry, chemists calculate the precise amounts of reactants and products involved in a chemical reaction.
In a balanced chemical equation, stoichiometric coefficients indicate the ratio of moles of each substance. Correct stoichiometry is critical when scaling reactions for practical applications, such as industrial synthesis or titrations in a lab, ensuring the reactants are used efficiently without wastage.

Oxidation-Reduction Chemistry

Oxidation-reduction chemistry is the study of reactions where electrons are transferred, leading to changes in the oxidation states of the elements involved. Oxidation refers to the loss of electrons, while reduction refers to the gain of electrons. Each reaction has an oxidizing agent that accepts electrons and a reducing agent that donates electrons.
Recognizing the agent roles is crucial for balancing the equation, as seen in the reaction \(\mathrm{Cr}^{3+}+\mathrm{BiO}_{3}^{-} \longrightarrow \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}+\mathrm{Bi}^{3+}\); chromium is being oxidized, and bismuth is being reduced. The balanced equation will reflect the conservation of electrons, highlighting the intrinsic link between the stoichiometry and the redox processes.