Problem 87
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.
Step-by-Step Solution
Verified Answer
Add 8 electrons to the left side: \( \mathrm{NO}_{3}^{-} + 8e^{-} \rightarrow \mathrm{NH}_{4}^{+} \).
1Step 1: Determine Oxidation States
First, identify the oxidation states of nitrogen in \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{NH}_{4}^{+}\). In \(\mathrm{NO}_{3}^{-}\), nitrogen has an oxidation state of +5. In \(\mathrm{NH}_{4}^{+}\), nitrogen has an oxidation state of -3.
2Step 2: Calculate the Change in Oxidation State
Calculate the change in the oxidation state of nitrogen: from +5 in \(\mathrm{NO}_{3}^{-}\) to -3 in \(\mathrm{NH}_{4}^{+}\). The change is \(+5 - (-3) = +8\).
3Step 3: Identify Electron Transfer Requirement
Electrons must be added to the side where oxidation occurs to balance the increase in oxidation state. Since the oxidation state of nitrogen decreases from +5 to -3, electrons are added to the left side (reduction).
4Step 4: Add Electrons to the Half-Reaction
To reduce the oxidation state from +5 to -3, 8 electrons are added to the left side: \[ \mathrm{NO}_{3}^{-} + 8e^{-} \rightarrow \mathrm{NH}_{4}^{+} \]
5Step 5: Rewrite and Verify the Equation
Ensure the equation is balanced in terms of both mass and charge. The equation \( \mathrm{NO}_{3}^{-} + 8e^{-} \rightarrow \mathrm{NH}_{4}^{+} \) correctly reflects the transfer of electrons to achieve the required reduction in oxidation state.
Key Concepts
Understanding Oxidation StatesElectron Transfer in Redox ReactionsBalancing Half-Reactions
Understanding Oxidation States
Oxidation states are numerical values that indicate the degree of oxidation or reduction of an element in a chemical compound. They help us identify how electrons are distributed around an atom. Each atom could have different oxidation states, depending on the chemical environment it is in.
For example, in the ion \(\mathrm{NO}_3^-\), nitrogen is bonded to three oxygen atoms, creating an environment where it carries a +5 oxidation state. Conversely, in \(\mathrm{NH}_4^+\), nitrogen is bonded to hydrogen atoms, resulting in a -3 oxidation state. This shift in oxidation states from +5 to -3 indicates a gaining of electrons, which in turn suggests a reduction has occurred.
Understanding the concept of oxidation states is crucial, as it allows you to track the flow of electrons in reactions, especially those involving redox (reduction-oxidation) processes. This knowledge sets the stage for identifying electron transfer requirements in any given redox reaction.
For example, in the ion \(\mathrm{NO}_3^-\), nitrogen is bonded to three oxygen atoms, creating an environment where it carries a +5 oxidation state. Conversely, in \(\mathrm{NH}_4^+\), nitrogen is bonded to hydrogen atoms, resulting in a -3 oxidation state. This shift in oxidation states from +5 to -3 indicates a gaining of electrons, which in turn suggests a reduction has occurred.
Understanding the concept of oxidation states is crucial, as it allows you to track the flow of electrons in reactions, especially those involving redox (reduction-oxidation) processes. This knowledge sets the stage for identifying electron transfer requirements in any given redox reaction.
Electron Transfer in Redox Reactions
The core of any redox reaction is the transfer of electrons. In redox processes, one substance gets oxidized (loses electrons) while another gets reduced (gains electrons). This electron exchange is central to understanding how redox reactions work.
When analyzing the reaction \(\mathrm{NO}_3^- \rightarrow \mathrm{NH}_4^+\), you notice that nitrogen changes its oxidation state from +5 to -3. This reduction signifies the gain of electrons. For the reduction process to happen, electrons have to be added to the nitrogen atom, and this addition occurs on the side of the equation where reduction is required, which in this case is the left side of the equation. This highlights the delicate balance needed to maintain charge equilibrium in the reaction.
Recognizing where and how electrons must be transferred ensures the reaction conforms to conservation laws, crucial for balancing redox equations.
When analyzing the reaction \(\mathrm{NO}_3^- \rightarrow \mathrm{NH}_4^+\), you notice that nitrogen changes its oxidation state from +5 to -3. This reduction signifies the gain of electrons. For the reduction process to happen, electrons have to be added to the nitrogen atom, and this addition occurs on the side of the equation where reduction is required, which in this case is the left side of the equation. This highlights the delicate balance needed to maintain charge equilibrium in the reaction.
Recognizing where and how electrons must be transferred ensures the reaction conforms to conservation laws, crucial for balancing redox equations.
Balancing Half-Reactions
Half-reaction balancing is a method used to ensure both mass and charge are properly managed in a redox reaction. Each redox reaction can be split into two half-reactions: one representing oxidation and the other reduction.
For the half-reaction \(\mathrm{NO}_3^- \rightarrow \mathrm{NH}_4^+\), we focus on balancing the reduction process. We first calculated the change in oxidation state and determined electrons must be added to achieve the appropriate state change. By adding 8 electrons to the left side of the equation, we ensure nitrogen’s oxidation state transitions correctly from +5 to -3. Thus, the balanced equation becomes \(\mathrm{NO}_3^- + 8e^- \rightarrow \mathrm{NH}_4^+\).
Balancing half-reactions not only requires the correct accounting of electrons but also must take into account the charges of the reacting species. By doing this methodically, chemists can confidently manipulate reactions for various applications, ranging from industrial chemical processes to biological systems.
For the half-reaction \(\mathrm{NO}_3^- \rightarrow \mathrm{NH}_4^+\), we focus on balancing the reduction process. We first calculated the change in oxidation state and determined electrons must be added to achieve the appropriate state change. By adding 8 electrons to the left side of the equation, we ensure nitrogen’s oxidation state transitions correctly from +5 to -3. Thus, the balanced equation becomes \(\mathrm{NO}_3^- + 8e^- \rightarrow \mathrm{NH}_4^+\).
Balancing half-reactions not only requires the correct accounting of electrons but also must take into account the charges of the reacting species. By doing this methodically, chemists can confidently manipulate reactions for various applications, ranging from industrial chemical processes to biological systems.
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