Problem 90 - Introductory Chemistry Atoms First

Question

Identify the oxidizing and reducing agents in the reaction \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

In the reaction \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\), the reducing agent is \(\mathrm{NH}_{4}\) and the oxidizing agent is \(\mathrm{Cr}_{2}\mathrm{O}_{7}\).

Step 1: Assign oxidation numbers to each element

Before identifying the oxidizing and reducing agents, we need to assign oxidation numbers to each element in the reaction. Use the rules for determining oxidation numbers to do this: \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\) Oxidation numbers: \(\mathrm{N} = -3\), \(\mathrm{H} = +1\), \(\mathrm{Cr} = +6\) in \(\mathrm{Cr}_{2}\mathrm{O}_{7}\), \(\mathrm{Cr} = +3\) in \(\mathrm{Cr}_{2}\mathrm{O}_{3}\), \(\mathrm{O} = -2\)

Step 2: Determine the change in oxidation state

Now that we have assigned oxidation numbers, we can determine which elements undergo a change in oxidation state during the reaction: N goes from -3 to 0 (increases by 3), Cr goes from +6 to +3 (decreases by 3).

Step 3: Identify the oxidizing and reducing agents

The element that loses electrons (increase in oxidation state) is the reducing agent, while the element that gains electrons (decrease in oxidation state) is the oxidizing agent. In our reaction, N loses electrons (oxidation state increases by 3), making it the reducing agent. Cr gains electrons (oxidation state decreases by 3), making it the oxidizing agent. It is important to note that the entire compound containing the element should be considered as the oxidizing or reducing agent. Thus, the reducing agent is \(\mathrm{NH}_{4}\), and the oxidizing agent is \(\mathrm{Cr}_{2}\mathrm{O}_{7}\). Finally, we can write our conclusion: The reducing agent in the given reaction is \(\mathrm{NH}_{4}\), and the oxidizing agent is \(\mathrm{Cr}_{2}\mathrm{O}_{7}\).

Key Concepts

Oxidation Numbers

Understanding oxidation numbers is key to grasping oxidation-reduction reactions. These numbers help us track how many electrons an atom gains or loses during a reaction.

• Definition: An oxidation number is a book-keeping tool that tells us the effective charge on an atom in a compound.
• Rules to Assign:
  • For an atom in its elemental state, the oxidation number is zero. For example, \(N_2\) has an oxidation number of zero.
  • For a monatomic ion, the oxidation number is the same as its charge, such as \(Cl^-\) with an oxidation number of -1.
  • In compounds, hydrogen is generally assigned +1 (except in hydrides) and oxygen typically -2 (unless in peroxides).
  • For metals like chromium in \((NH_4)_2 Cr_2 O_7\), calculating oxidation numbers involves balancing those of more definite values like \(-2\) for oxygen and \(+1\) for hydrogen.
• Importance: Grasping how oxidation numbers change in a reaction tells us which elements are involved in electron transfer, guiding us to identify the oxidizing and reducing agents.

Oxidizing Agents

Once we have oxidation numbers, identifying the oxidizing agent becomes easier. The oxidizing agent is the substance that gets reduced by gaining electrons. Hence, it causes another substance to be oxidized.

• Role in Reaction: The oxidizing agent undergoes a decrease in oxidation state because it accepts electrons. For example, in the given reaction, the chromium in \(Cr_2O_7^{2-}\) has an oxidation state change from +6 to +3, indicating that it gains electrons.
• Recognizing Oxidizing Agents: Typically, these agents contain elements in their highest oxidation states and have a significant electron deficiency. Common examples include oxygen, halogens like chlorine, and certain metal oxides.
• Understanding Function: By identifying the oxidizing agent, you note which species is reduced as it gains electrons from the reducing agent.

Recognizing the oxidizing agent will enhance your overall understanding of redox reactions as it plays an essential role in the balance of electron exchange during these reactions.

Reducing Agents

Reducing agents are just as crucial in oxidation-reduction reactions and are essentially the opposite of oxidizing agents. The reducing agent is the substance that gets oxidized and loses electrons, thus causing another substance to be reduced.

• Functionality: A reducing agent undergoes an increase in oxidation state as it donates electrons. In the reaction provided, nitrogen from \(NH_4^+\) moves from -3 to 0, revealing its role in electron donation.
• Typical Characteristics: Reducing agents are usually composed of elements in low oxidation states with excess electrons, such as hydrogen, carbon, and metals like zinc and iron.
• Application: Identifying the reducing agent helps you understand which element or compound provides electrons for the reduction of another species. This information is key when balancing redox reactions and predicting product formation.

Comprehending the actions of reducing agents allows better insight into the entire electron transfer process, especially in complex reactions.