Question

In the half-reaction \(\mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+},\) on which side of the equation should electrons be added? Add the correct number of electrons to the side on which they are needed, and rewrite the equation.

Short answer

The electrons should be added to the left side of the equation, as the nitrogen atom gains 8 electrons during the reaction. The balanced half-reaction equation is: \[8\; e^{-} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+}\]

Step-by-step solution

Determine the oxidation states of nitrogen in the reactants and products

To determine the side to which electrons should be added, first, we need to determine the oxidation states of the nitrogen atoms in both the reactant and product of the half-reaction. In \(\mathrm{NO}_{3}^{-}\), the oxidation state of nitrogen is +5, while in \(\mathrm{NH}_{4}^{+}\), the oxidation state of nitrogen is -3.

Calculate the change in oxidation states

Now that we have determined the oxidation states of nitrogen in both the reactant and product, we can find the change in oxidation states. The change in oxidation states is given by: Change in oxidation state = final oxidation state - initial oxidation state In this case, the change in oxidation state is -3 - (+5) = -8.

Add electrons to balance the equation

Since the change in oxidation state is -8, it means that 8 electrons were gained during the reaction (reduction process). To balance the half-reaction equation, we need to add 8 electrons to the left side of the equation (to represent the gain of electrons due to reduction) which will result in: \(8\; e^{-} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+}\).

Rewrite the balanced half-reaction equation

Now, we can rewrite the balanced half-reaction equation as follows: \[8\; e^{-} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+}\]

Key concepts

Oxidation State

The oxidation state, or oxidation number, of an element in a compound provides insight into the electron distribution within the compound. It helps us understand which atoms are gaining or losing electrons in a chemical reaction.
In essence, it reflects the degree of oxidation of an atom.
Here's how you can think about oxidation states:

• The oxidation state of an atom in its elemental form is always 0. For example, O₂ or N₂, each have oxidation states of 0.
• In a molecule like \( ext{NO}_{3}^{-}\), the sum of the oxidation states must equal the overall charge of the molecule.
• For our half-reaction, nitrogen's oxidation state in \( ext{NO}_{3}^{-}\) is +5, which means nitrogen "gains" electrons during the oxidation to reach \( ext{NH}_{4}^{+}\) where the oxidation state is -3.

To solve redox reactions, determining the change in oxidation states is essential, as it dictates where and how many electrons transfer occurs.

Half-Reaction

A half-reaction simplifies the process of balancing redox reactions. This concept allows us to separately address the oxidation and reduction processes, focusing individually on each.
The idea is simple: break down a full chemical equation into two parts, each dedicated to one of these processes.
For instance, the half-reaction \( ext{NO}_3^{-} \rightarrow ext{NH}_4^{+}\) is specific to the reduction process.

• Reduction involves the gain of electrons, reflected through a decrease in oxidation state. Here, nitrogen goes from +5 in \( ext{NO}_3^{-}\) to -3 in \( ext{NH}_4^{+}\).
• This shows the number of electrons involved in the reduction, enabling one to precisely balance electron transfer by adding electrons to one side of the equation.

Establishing half-reactions makes it easier to identify the nature of changes in each segment of the chemical reaction.

Electron Balancing

Electron balancing is critical in ensuring that a redox reaction obeys the law of conservation of mass and charge. It involves adding the correct number of electrons to one side of a half-reaction, equalizing the electron loss and gain.

Here's how electron balancing works:

• Identify which side of the reaction loses or gains electrons. For reduction reactions, like \( ext{NO}_3^- \rightarrow ext{NH}_4^+\), electrons are gained. That is why electrons are added to the left side.
• The gain of 8 electrons is calculated based on the change in the nitrogen oxidation state from +5 to -3, equating to a gain of 8 electrons.
• Write the balanced half-reaction: \[8\; e^{-} + ext{NO}_3^{-} \rightarrow ext{NH}_4^{+} \]

Balancing electrons ensures that both mass and charge are preserved in the equation, crucial for accurate portrayal of the chemical change.