Question

Make a sketch of a concentration cell employing two \(Z \mathrm{n} / \mathrm{Zn}^{2+}\) half-cells. The concentration of \(\mathrm{Zn}^{2+}\) in one of the half-cells is \(2.0 \mathrm{M},\) and the concentration in the other half-cell is \(1.0 \times 10^{-3} \mathrm{M}\) . Label the anode and the cathode and indicate the half-reaction occurring at each electrode. Also indicate the direction of electron flow.

Short answer

Sketch two half-cells with zinc electrodes, one in a 2.0 M \(Zn^{2+}\) solution (cathode), the other in a \(1.0 \times 10^{-3} M\) \(Zn^{2+}\) solution (anode). Connect with a salt bridge and external wire; electrons flow from anode to cathode.

Step-by-step solution

Understanding Concentration Cells

A concentration cell consists of two half-cells with the same electrodes and the same electrolytes but at different concentrations. The half-cell with the higher concentration will act as the cathode (reduction occurs here), and the half-cell with the lower concentration will act as the anode (oxidation occurs).

Sketching the Concentration Cell

Draw two half-cells, each with a Zn electrode submerged in an aqueous solution of \(Zn^{2+}\). In one half-cell, label the concentration of \(Zn^{2+}\) as \(2.0 M\), and in the other, label it as \(1.0 \times 10^{-3} M\). Connect the two half-cells with a salt bridge and place an external wire between the two electrodes.

Labeling the Electrodes

Label the electrode in the half-cell with \(2.0 M\) concentration of \(Zn^{2+}\) as the cathode, where the reduction half-reaction \(Zn^{2+} + 2e^- \rightarrow Zn(s)\) will occur. Label the electrode in the half-cell with \(1.0 \times 10^{-3} M\) concentration of \(Zn^{2+}\) as the anode, where the oxidation half-reaction \(Zn(s) \rightarrow Zn^{2+} + 2e^-\) will occur.

Indicating the Direction of Electron Flow

Show the direction of electron flow in the external circuit from the anode to the cathode (from the lower concentration half-cell to the higher concentration half-cell).

Indicating the Direction of Ion Flow in the Salt Bridge

In the salt bridge, show the direction of ion flow: cations flow towards the cathode, and anions flow towards the anode to maintain electrical neutrality.

Key concepts

Electrochemical Cells

Electrochemical cells are fundamental components of batteries and various types of sensors. They convert chemical energy into electrical energy through chemical reactions. Essentially, these cells consist of two electrodes immersed in an electrolyte, and they facilitate the flow of electrons from one electrode to another, creating an electric current.

Each cell has two half-cells, often represented by metal strips or rods, known as electrodes, which are made of different materials. These electrodes are connected by an external circuit that allows electrons to flow from one electrode to another. Additionally, there's a salt bridge, which is a pathway that allows ions to move between the half-cells to balance the charge as electrons move through the external circuit.

This movement of charges is harnessed as electrical energy, which can be used to power electrical devices. It's a dazzling interplay of chemistry and physics that shows us how energy transformation can be harnessed in practical applications.

Galvanic Cells

Galvanic cells, also known as voltaic cells, are a type of electrochemical cell that spontaneously converts chemical energy into electrical energy through redox reactions. These cells are the foundation of batteries, whereby the chemical reaction produces electrons at one electrode, the anode, which then flow to the other electrode, the cathode, through an external circuit, producing electric current.

Anatomy of a Galvanic Cell

In a galvanic cell, the anode is where oxidation occurs (loss of electrons), while the cathode is the site of reduction (gain of electrons). The chemical reaction is driven by the difference in potential energy between the reactants and products, leading to a flow of electrons as the cell reaches an equilibrium.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions are the heart of electrochemical cells, including galvanic and concentration cells. During redox reactions, electrons are transferred from one substance to another, leading to a change in oxidation state for both reactants.

In the context of a concentration cell, the cell operates based on the principle of redox reactions occurring at different rates due to the differing concentrations of ions. Oxidation occurs at the anode where a substance loses electrons, and reduction takes place at the cathode where a substance gains electrons. The overall cell's spontaneous reaction drives the electrons through the external circuit from the anode to the cathode, generating an electric current that can be harnessed for work.

Anode and Cathode Identification

Knowing how to accurately identify the anode and cathode is crucial in understanding electrochemical cells. The anode is the electrode where oxidation occurs, meaning it's where the material loses electrons. Conversely, the cathode is the electrode where reduction happens, where the material gains electrons.

In concentration cells, the anode and cathode are determined by the concentration of the ions in the half-cells. The half-cell with the lower concentration of ions will be the anode, as electrons are oxidized (released) from the material. The half-cell with the higher ion concentration will be the cathode since it will gain electrons through reduction. This distinction allows for the flow of electrons from the anode to the cathode when the external circuit is completed.