Problem 67 - Chemistry Matter and Change

Question

Copper When solid copper pieces are put into a solution of silver nitrate, as shown in Figure 19.12, silver metal appears and blue copper(II) nitrate forms. Write the corresponding chemical equation without balancing it. Next, determine the oxidation state of each element in the equation. Write the two half-reactions, labeling which is oxidation and which is reduction. Finally, write a balanced equation for the reaction.

Step-by-Step Solution

Answer

The unbalanced chemical equation for the reaction between copper and silver nitrate is given as: Cu(s) + AgNO₃(aq) → Ag(s) + Cu(NO₃)₂(aq). The oxidation states of each element are as follows: Cu(0), Ag(+1), N(+5), and Cu(+2). The oxidation half-reaction is Cu → Cu²⁺ + 2e⁻, and the reduction half-reaction is 2Ag⁺ + 2e⁻ → 2Ag. The balanced chemical equation is Cu(s) + 2AgNO₃(aq) → 2Ag(s) + Cu(NO₃)₂(aq).

Step 1: Write the unbalanced chemical equation

Copper reacts with silver nitrate, forming silver and copper(II) nitrate. The unbalanced chemical equation can be written as: Cu(s) + AgNO₃(aq) → Ag(s) + Cu(NO₃)₂(aq)

Step 2: Determine the oxidation states of each element

There are four elements present in this reaction. Let's find the oxidation state of each element. 1. Copper (Cu) in Cu(s): In its elemental form, the oxidation state is 0. 2. Silver (Ag) in AgNO₃: In silver nitrate, the nitrate ion (NO₃⁻) has a charge of -1 and Ag has a charge of +1 to balance the negative charge on NO₃⁻. So, the oxidation state of Ag in AgNO₃ is +1. 3. Nitrogen (N) in AgNO₃ and Cu(NO₃)₂: In nitrate ion (NO₃⁻), nitrogen has an oxidation state of +5. 4. Copper (Cu) in Cu(NO₃)₂: In copper(II) nitrate, each nitrate ion has a charge of -1, and there are two such ions. To balance the total negative charge, copper carries a charge of +2. Now we have the oxidation states for each element: Cu(0) + Ag(+1)NO₃ → Ag(0) + Cu(+2)(NO₃)₂

Step 3: Write the oxidation and reduction half-reactions

Comparing the oxidation states of the elements to determine which one is being oxidized and which one is being reduced: - Copper: From oxidation state 0 to +2, therefore, it is oxidized. (Oxidation half-reaction) - Silver: From oxidation state +1 to 0, therefore, it is reduced. (Reduction half-reaction) Oxidation half-reaction: Cu → Cu²⁺ + 2e⁻ Reduction half-reaction: Ag⁺ + e⁻ → Ag

Step 4: Write the balanced chemical equation

Now let's balance the equation by making sure the electrons lost in the oxidation reaction are equal to the electrons gained in the reduction reaction. Since Cu releases 2 electrons and Ag requires only 1 electron, the reduction half-reaction should be multiplied by 2 to make sure the number of electrons is equal. Oxidation half-reaction: Cu → Cu²⁺ + 2e⁻ Reduction half-reaction: 2Ag⁺ + 2e⁻ → 2Ag Now we can combine both half-reactions: Cu + 2Ag⁺ → Cu²⁺ + 2Ag Let's replace the silver ion with silver nitrate in the balanced equation: Cu(s) + 2AgNO₃(aq) → 2Ag(s) + Cu(NO₃)₂(aq) This is the final balanced chemical equation for the reaction between copper and silver nitrate.

Key Concepts

Oxidation States

Understanding oxidation states is key to mastering redox reactions. An oxidation state represents the degree of oxidation of an atom. It indicates the number of electrons an atom has gained, lost, or shared when bonding with other atoms. In this exercise, we have several oxidation states to identify:

• Copper (Cu): In its elemental form, copper has an oxidation state of 0. However, when it forms copper(II) nitrate, its oxidation state becomes +2.
• Silver (Ag): In silver nitrate, silver has an oxidation state of +1. This changes to 0 when silver metal is formed.
• Nitrogen (N) in nitrate ion (NO₃⁻): Nitrogen maintains an oxidation state of +5 throughout the reaction, balancing the overall negative charge of the nitrate ion.

By understanding oxidation states, we can determine which substances are oxidized and which are reduced during a reaction.

Half-Reactions

Redox reactions can be broken down into two half-reactions: one for oxidation and one for reduction. Identifying these helps us track electron transfer.

• Oxidation Half-Reaction:
  Copper goes from an oxidation state of 0 to +2: \[ \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \] This shows that copper is oxidized as it loses two electrons.


• Reduction Half-Reaction:
  Silver goes from an oxidation state of +1 to 0: \[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \] This indicates that silver is reduced as it gains an electron. Each silver ion gains one electron.

Through half-reactions, we can easily see how the electrons are transferred during the reaction.

Balancing Chemical Equations

Balancing chemical equations ensures that the same number of each type of atom is present on both sides of the equation. In redox reactions, we also need to ensure that the electrons lost in the oxidation reaction balance the electrons gained in the reduction reaction.
Here, copper loses two electrons while each silver ion gains one electron, requiring the reduction reaction to be doubled:

• Oxidation: \[ \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \]
• Reduction: \[ 2\text{Ag}^+ + 2e^- \rightarrow 2\text{Ag} \]

Once the electrons are balanced, both half-reactions can be combined:\[ \text{Cu} + 2\text{AgNO}_3 \rightarrow 2\text{Ag} + \text{Cu(NO}_3)_2 \]This ensures that the chemical equation is completely balanced, reflecting the conservation of mass and charge.

Copper and Silver Nitrate Reaction

The reaction between copper and silver nitrate is a classic example of a redox reaction, where oxidation and reduction occur simultaneously.

• When copper metal is placed in a solution of silver nitrate, copper atoms lose electrons (oxidation) to form copper ions:
\[ \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \]
• These electrons are then gained by silver ions in the solution, reducing them to silver metal:
\[ 2\text{Ag}^+ + 2e^- \rightarrow 2\text{Ag} \]
• The full balanced reaction can be written as:
\[ \text{Cu} + 2\text{AgNO}_3 \rightarrow 2\text{Ag} + \text{Cu(NO}_3)_2 \]

This reaction highlights the transformation of copper from its elemental form to an oxidized state within copper(II) nitrate, while silver ions are reduced to form solid silver metal. Such reactions not only demonstrate chemical principles but also have real-world applications, such as the refining and recovery of metals.