Problem 1 - Chemical Principles in the Laboratory

Question

A student measures the potential of a cell made up with \(1.0 \mathrm{M}\) CuSO, in one solution reservoir and 1.0 \(\mathrm{M} \mathrm{Ag}_{2} \mathrm{SO}_{4}\) in the other. There is a metallic copper (Cu) electrode in the CuSO, and a metallic silver (Ag) electrode in the \(A g_{2} S O_{4}\), and the cell is set up as shown in Figure \(32.1 .\) She finds that the potential, or voltage, of the cell, \(E_{\text {call }}^{0}\), is \(0.45 \mathrm{V}\), and that the copper electrode is negative. a. At which electrode is oxidation occurring? b. Write the equation for the oxidation half-reaction in this cell. c. Write the equation for the reduction half-reaction in this cell. d. Write the net ionic equation for the spontaneous oxidation-reduction reaction that occurs in this cell.

Step-by-Step Solution

Answer

a. Oxidation occurs at the copper electrode. b. Cu → Cu²⁺ + 2e⁻ c. 2Ag⁺ + 2e⁻ → 2Ag d. Cu + 2Ag⁺ → Cu²⁺ + 2Ag

Step 1: Identify the Electrodes

The cell is composed of a copper (Cu) electrode in CuSO₄ solution and a silver (Ag) electrode in Ag₂SO₄ solution. The copper electrode is negative, indicating it is the anode and where oxidation occurs as electrons flow from the anode to the cathode.

Step 2: Determine the Oxidation Half-Reaction

Oxidation occurs at the copper electrode. The oxidation half-reaction for copper is \[ \text{Cu} \rightarrow \text{Cu}^{2+} + 2\text{e}^- \]Copper is oxidized to copper ions, releasing two electrons.

Step 3: Determine the Reduction Half-Reaction

Reduction occurs at the silver electrode, as it is the cathode. The standard reduction reaction is\[ \text{Ag}^+ + \text{e}^- \rightarrow \text{Ag} \]However, because the solution is Ag₂SO₄, two silver ions are reduced to deposit solid silver:\[ 2\text{Ag}^+ + 2\text{e}^- \rightarrow 2\text{Ag} \]

Step 4: Write the Net Ionic Equation

Combine the oxidation and reduction half-reactions to get the net ionic equation:\[ \text{Cu} + 2\text{Ag}^+ \rightarrow \text{Cu}^{2+} + 2\text{Ag} \]This shows copper atoms oxidizing to copper ions, and silver ions reducing to form silver metal.

Key Concepts

Oxidation-Reduction Reaction

In electrochemistry, an oxidation-reduction (redox) reaction is a chemical reaction in which electrons are transferred between two substances. This electron transfer results in changes in oxidation states of the involved substances. Oxidation refers to the loss of electrons, whereas reduction is the gain of electrons.

These reactions are fundamental in electrochemical cells where chemical energy is converted to electrical energy. The process of one substance losing electrons (oxidation) and another gaining electrons (reduction) ensures energy flow, measurable as voltage and used to do work or drive other chemical reactions.

• Oxidation: Loss of electrons, increase in oxidation state.
• Reduction: Gain of electrons, decrease in oxidation state.

Understanding redox reactions is key in studying electrochemical cells, such as galvanic cells, where these reactions occur at the electrodes.

Half Reactions

Half reactions are a way to represent the two parts of a redox reaction separately - the oxidation half-reaction and the reduction half-reaction. Each half-reaction explicitly shows either the oxidation or reduction process, including the electrons involved. This separation allows for easier balancing of redox reactions and analysis of the electron flow.

The oxidation half-reaction occurs at the anode, where a metal atom, such as copper, loses electrons and is oxidized to metal ions. The reduction half-reaction takes place at the cathode, where ions in solution gain electrons and are reduced to metal atoms, such as silver.

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

Both half-reactions must be balanced not only in terms of atoms but also in terms of charge, ensuring the number of electrons lost equals the number gained.

Electrode Potential

Electrode potential refers to the ability of an electrode to drive an electric current in a cell. It represents the tendency of a chemical species to be reduced or oxidized and is measured in volts. Each half-reaction has an associated standard electrode potential, which allows us to predict the direction of electrons flow.

Standard Electrode Potential (\(E^0\)) is determined under standard conditions and is used to determine the feasibility of a redox reaction. In a galvanic cell, the electrode with a higher reduction potential will act as the cathode, while the one with a lower reduction potential becomes the anode.

• A positive cell potential indicates a spontaneous reaction.
• Electrode potential affects the overall cell potential, which is the energy available to do electrical work.

Understanding electrode potentials helps in identifying which redox reactions will occur in a given setup and allows predictions of cell voltage based on the known potentials of the electrodes involved.

Galvanic Cell

A Galvanic cell is a type of electrochemical cell that generates electrical energy from spontaneous redox reactions occurring in separate compartments, known as half-cells. Each half-cell contains an electrode and an electrolyte, which participates in either oxidation or reduction.

In a Galvanic cell:

• Anode: The electrode where oxidation occurs, and electrons are released.
• Cathode: The electrode where reduction happens, and electrons are gained.

The two half-cells are connected by a salt bridge or porous membrane that allows ion flow, maintaining electrical neutrality while preventing the solutions from mixing. The flow of electrons from the anode to the cathode through an external circuit produces electricity that can be harnessed to power devices.

Galvanic cells form the foundation for batteries and require careful selection of electrode materials to achieve desired voltages and conduct energy efficiently.