Problem 40 - Chemistry Matter and Change

Question

Write the balanced chemical equation for the standard cell notations listed below. $$ \begin{array}{l}{\text { a. } \mathrm{I}^{-}\left|\mathrm{I}_{2} \| \mathrm{Fe}^{3+}\right| \mathrm{Fe}^{2+}} \\ {\text { b. } \mathrm{Sn}\left|\mathrm{Sn}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}} \\\ {\text { c. } \mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cd}^{2+}\right| \mathrm{Cd}}\end{array} $$

Step-by-Step Solution

Answer

a: \(2\text{Fe}^{3+} + 2\text{I}^- \rightarrow 2\text{Fe}^{2+} + \text{I}_2\); b: \(\text{Sn} + 2\text{Ag}^{+} \rightarrow \text{Sn}^{2+} + 2\text{Ag}\); c: \(\text{Zn} + \text{Cd}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cd}\)."

Step 1: Understand Standard Cell Notation

Standard cell notation is written in the format of anode|anode solution||cathode solution|cathode, where the anode (oxidation half-reaction) is on the left and the cathode (reduction half-reaction) is on the right. Double vertical lines represent the salt bridge.

Step 2: Analyze Cell a Notation

The cell notation \( ext{I}^{-}| ext{I}_{2}|| ext{Fe}^{3+}| ext{Fe}^{2+}\) suggests iodine is involved in the anode half-reaction and iron in the cathode half-reaction. The oxidation half-reaction is \(2 ext{I}^- ightarrow ext{I}_2 + 2e^-\), and the reduction half-reaction is \( ext{Fe}^{3+} + e^- ightarrow ext{Fe}^{2+}\). Balance electrons in the full equation, obtaining: \(2 ext{Fe}^{3+} + 2 ext{I}^- ightarrow 2 ext{Fe}^{2+} + ext{I}_2\).

Step 3: Analyze Cell b Notation

For cell \( ext{Sn}| ext{Sn}^{2+}|| ext{Ag}^{+}| ext{Ag}\), tin is the anode and silver is the cathode. The oxidation half-reaction is \( ext{Sn} ightarrow ext{Sn}^{2+} + 2e^-\), and the reduction half-reaction is \( ext{Ag}^{+} + e^- ightarrow ext{Ag}\). Balance electrons in the full equation: \( ext{Sn} + 2 ext{Ag}^{+} ightarrow ext{Sn}^{2+} + 2 ext{Ag}\).

Step 4: Analyze Cell c Notation

The cell \( ext{Zn}| ext{Zn}^{2+}|| ext{Cd}^{2+}| ext{Cd}\) indicates zinc as the anode and cadmium as the cathode. The oxidation half-reaction is \( ext{Zn} ightarrow ext{Zn}^{2+} + 2e^-\), and the reduction half-reaction is \( ext{Cd}^{2+} + 2e^- ightarrow ext{Cd}\). Balance the reaction: \( ext{Zn} + ext{Cd}^{2+} ightarrow ext{Zn}^{2+} + ext{Cd}\).

Key Concepts

Redox Reactions

Redox reactions are essential processes in electrochemistry that involve the transfer of electrons between two substances. They are a combination of two types of reactions: oxidation and reduction. In oxidation, a substance loses electrons, whereas, in reduction, a substance gains electrons. Redox reactions are crucial in various applications, such as batteries and corrosion prevention.

In electrochemical cells, redox reactions drive the flow of electrons from the anode (where oxidation occurs) to the cathode (where reduction happens). For instance, if we have a cell involving zinc and cadmium, zinc would undergo oxidation, losing electrons, while cadmium ions in solution accept these electrons to get reduced. Understanding these reactions allows us to predict and balance chemical equations that represent the overall cell reaction.

• **Oxidation**: Loss of electrons, occurs at the anode.
• **Reduction**: Gain of electrons, occurs at the cathode.
• **Electrochemical Cell**: Device that converts chemical energy into electrical energy through redox reactions.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants transforming into products. Balancing these equations ensures that there is the same number of each type of atom on both sides of the equation, maintaining the law of conservation of mass.

In the context of electrochemical cells, balancing chemical equations is crucial for predicting the outcomes of redox reactions and designing cells that function efficiently. For instance, in a cell where tin is oxidized and silver is reduced:
The balanced equation is \( \text{Sn} + 2\text{Ag}^{+} \rightarrow \text{Sn}^{2+} + 2\text{Ag} \). This equation illustrates both the transfer of electrons and the consumption and production of species in the reaction. Balancing involves ensuring that the number of electrons lost in oxidation matches the number gained in reduction to maintain charge neutrality.

• **Reactants**: Substances consumed in the reaction.
• **Products**: Substances formed as a result of the reaction.
• **Balancing**: Adjusting coefficients to have equal atoms of each element on both sides.

Standard Cell Notation

Standard cell notation is a shorthand representation of electrochemical cells and their reactions. It summarizes the information about the chemical reactions taking place at the anode and cathode. The standard format is \( \text{Anode} | \text{Anode Solution} || \text{Cathode Solution} | \text{Cathode} \), where the single vertical line \( | \) separates different phases, and the double vertical line \( || \) represents the salt bridge or separator between the two half-cells.

For example, consider the notation \( \text{Zn}|\text{Zn}^{2+}||\text{Cd}^{2+}|\text{Cd} \). This indicates zinc is oxidized at the anode, and cadmium ions are reduced at the cathode. The notation helps in writing and balancing the chemical equations of the cell reactions by clearly highlighting what gets oxidized and reduced.

• **Single Line \( | \)**: Separates different phases in a half-cell.
• **Double Line \( || \)**: Represents the salt bridge, facilitating ion flow between half-cells.
• **Half-Cell**: Each part of the cell where either oxidation or reduction occurs.
• **Anode/Cathode**: Anode is the site of oxidation, cathode is the site of reduction.