Question

The uranyl ion \(\left(\mathrm{UO}_{2}^{2+}\right)\) is a fairly stable ion of uranium that requires strong reducers to reduce the oxidation number of uranium further. Balance this redox reaction using the half reaction method by assuming an acidic solution. $$ \mathrm{UO}_{2}^{2+}+\mathrm{HN}_{3} \rightarrow \mathrm{U}+\mathrm{N}_{2} $$

Short answer

\(\mathrm{UO}_{2}^{2+} + \mathrm{HN}_{3} + 3\mathrm{H}^{+} \rightarrow \mathrm{U} + 2\mathrm{H}_{2}\mathrm{O} + \mathrm{N}_{2}\).

Step-by-step solution

Break Down the Reaction

First, we identify the oxidation and reduction processes. The uranyl ion (\(\mathrm{UO}_{2}^{2+}\)) is being reduced to uranium (\(\mathrm{U}\)), while the hydrazoic acid (\(\mathrm{HN}_{3}\)) decomposes to produce nitrogen gas (\(\mathrm{N}_{2}\)).

Write the Half-Reactions

For the oxidation half-reaction: \(\mathrm{HN}_{3} \rightarrow \mathrm{N}_{2}\). For the reduction half-reaction: \(\mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}\).

Balance Atoms Except Oxygen and Hydrogen

In the reduction half-reaction, uranium is already balanced. For the oxidation half-reaction, balance nitrogen: \(\mathrm{HN}_{3} \rightarrow \mathrm{N}_{2}\).

Balance Oxygen Atoms

Add water molecules to balance oxygen in the reduction half-reaction: \(\mathrm{UO}_{2}^{2+} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{U}\).

Balance Hydrogen Atoms

Balance hydrogen by adding protons (\(\mathrm{H}^{+}\)) where needed. The reduction reaction becomes: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{U} + 2\mathrm{H}_{2}\mathrm{O}\).

Balance Charges with Electrons

Add electrons to balance the charges. For the reduction half-reaction, two electrons are added on the left: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{U} + 2\mathrm{H}_{2}\mathrm{O}\).

Balance the Oxidation Half-Reaction

Add electrons to the oxidation half-reaction to balance charge: \(\mathrm{HN}_{3} + 2\mathrm{e}^{-} \rightarrow \mathrm{N}_{2} + 1\mathrm{H}^{+}\).

Combine the Half-Reactions

Ensure the number of electrons lost in oxidation equals those gained in reduction. Combine: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^{+} + \mathrm{HN}_{3} \rightarrow \mathrm{U} + 2\mathrm{H}_{2}\mathrm{O} + \mathrm{N}_{2} + 1\mathrm{H}^{+}\). Balance hydrogen by modifying \(\mathrm{H}^{+}\).

Final Balanced Equation

The balanced reaction is: \(\mathrm{UO}_{2}^{2+} + \mathrm{HN}_{3} + 3\mathrm{H}^{+} \rightarrow \mathrm{U} + 2\mathrm{H}_{2}\mathrm{O} + \mathrm{N}_{2}\).

Key concepts

Half Reaction Method

The half reaction method is a systematic way to balance redox reactions. It involves separating the oxidation and reduction parts of the reaction into two distinct processes, known as half-reactions. This method is particularly useful when dealing with complex reactions, as it simplifies the balancing by focusing on one process at a time.
To use the half reaction method:

• First, identify the species that undergo oxidation and reduction. This involves looking at how electrons are transferred between atoms in the reactants and products.
• Next, write separate equations for the oxidation and reduction reactions, known as half-reactions. Each half-reaction will illustrate the electron transfer process for one of the reacting species.
• Balance each half-reaction separately, ensuring that both mass and charge are balanced. This typically involves adding water, hydrogen ions, and electrons as needed.
• Finally, combine the balanced half-reactions to form a complete redox equation, ensuring that the electrons cancel out to maintain charge balance in the overall equation.

This structured approach helps ensure accuracy by dealing with each change separately before putting everything back together.

Oxidation and Reduction

Oxidation and reduction are key concepts in chemistry relating to the transfer of electrons. An easy way to remember this is the term 'OIL RIG': Oxidation Is Loss, Reduction Is Gain – referring to the loss or gain of electrons respectively.

• In a redox reaction, oxidation refers to the process where a substance loses electrons. As a result, the oxidation state of that entity increases.
• Conversely, reduction is the process where a substance gains electrons, and its oxidation state decreases.
• When balancing redox reactions, it's essential to account for both processes, as they are complementary; one cannot occur without the other. Therefore, in a balanced redox equation, the number of electrons lost by one substance must be equal to the number of electrons gained by another.

Identifying which species undergo oxidation and which undergo reduction is the first step towards balancing redox equations using the half reaction method.

Acidic Solutions

Acidic solutions play a crucial role in balancing redox reactions, especially when oxygen and hydrogen atoms need to be balanced. Redox reactions in acidic solutions often involve the use of hydrogen ions (\(H^+\)) to balance hydrogen atoms, which is essential for maintaining charge and mass balance.

• In an acidic environment, you can add \(H^+\) ions to one side of a half-reaction to balance the hydrogen atoms. Balancing these atoms often goes hand-in-hand with balancing oxygen atoms.
• Additionally, water molecules (\(H_2O\)) may be added as needed to ensure the oxygen atoms are balanced. When a redox reaction is carried out in an acidic medium, this approach simplifies balancing both the proton and electron exchanges.

By using these balancing tools, any discrepancies in oxygen and hydrogen atom numbers can be corrected. This helps in achieving a properly balanced chemical equation.

Balancing Chemical Equations

Balancing chemical equations is a foundational skill in chemistry, ensuring that the same amount of each element is present on both sides of the equation, reflecting the conservation of mass. In redox reactions, this process must also consider the charge and electron count.

• Begin by writing the unbalanced chemical equation, identifying the substances undergoing redox changes.
• Utilize the half reaction method to separately balance the oxidation and reduction reactions. This ensures that the electrons lost and gained are equal, maintaining charge constancy.
• Combine these balanced half-reactions, adjusting stoichiometric coefficients as necessary to ensure that both mass and charge are conserved in the overall balanced equation.

Balancing chemical equations requires careful attention, as each element must be accounted for, both in terms of atoms and charges. This process ensures that chemical reactions comply with the law of conservation of matter and energy, which is essential for predicting the quantities of reactants and products involved in chemical processes.