Question

Analyze An earthen vessel was discovered in 1938 near Baghdad. This ancient vessel contained an iron bar surrounded by a copper cylinder, as shown in Figure 20.30 . When filled with an electrolyte such as vinegar, this vessel might have acted as a battery. a. Identify the cathode. b. Identify the anode. c. Calculate the standard cell potential of this battery.

Short answer

a. The cathode is the copper cylinder. b. The anode is the iron bar. c. The standard cell potential of this battery is 0.78 V.

Step-by-step solution

Identify the cathode and anode in the setup

In a galvanic cell, the anode is the electrode where oxidation occurs, and the cathode is the electrode where reduction occurs. Electrons flow from the anode to the cathode. In this specific setup, there is an iron bar (Fe) surrounded by a copper cylinder (Cu). The standard reduction potentials for both metals can be found in a table of standard potential values: - For iron: \[Fe^{2+}(aq) + 2e^- \leftrightarrow Fe(s) \:; \: E^0_{Fe} = -0.44 V\] - For copper: \[Cu^{2+}(aq) + 2e^- \leftrightarrow Cu(s) \:; \: E^0_{Cu} = +0.34 V\] Higher standard reduction potentials mean a greater tendency to be reduced. Since copper has a higher standard reduction potential (+0.34 V) than iron (-0.44 V), copper is more likely to be reduced, and iron is more likely to be oxidized. Therefore, the copper cylinder is the cathode, and the iron bar is the anode. a. The cathode is the copper cylinder. b. The anode is the iron bar.

Calculate the standard cell potential of this battery

Now that we have identified the cathode and anode, we can calculate the standard cell potential of this electrochemical cell. The standard cell potential (\(E^0_{cell}\)) can be calculated using the reduction potentials of the cathode and anode: \[E^0_{cell} = E^0_{cathode} - E^0_{anode}\] We have already found the standard reduction potentials for copper and iron: - Copper: \(E^0_{Cu} = +0.34 V\) - Iron: \(E^0_{Fe} = -0.44 V\) Plugging these values into the equation: \[E^0_{cell} = (+0.34 V) - (-0.44 V) = +0.34 V + 0.44 V = 0.78 V\] c. The standard cell potential of this battery is 0.78 V.

Key concepts

Galvanic Cell

Imagine a device that converts chemical energy directly into electrical energy - this is exactly what a galvanic cell does. It is composed of two different metals connected by a salt bridge or a porous partition. These metals, known as electrodes, are submerged in solutions containing their own ions.

Let's consider the case of the curious artifact found near Baghdad. Here, we have an iron bar and a copper cylinder, each playing a role in the electrochemical process. In such a setup, iron is the one that loses electrons (oxidation), and therefore becomes the anode. Copper, on the other hand, gains electrons (reduction) and serves as the cathode. Electrons flow from the anode to the cathode through an external circuit, providing electrical energy. This flow is driven by the different tendencies of the electrodes to lose or gain electrons – a property inherent in the metals involved.

To make this more relatable for students, think of a galvanic cell like a team sport with two players: one 'passes' the electrons (anode) and the other 'catches' them (cathode). Just like in sports, having a good 'strategy' (electrolyte solution) and 'playing field' (the salt bridge or porous partition) is essential for the 'game' (electrochemical reaction) to happen effectively.

Standard Reduction Potential

The standard reduction potential is a measure of how readily a substance gains electrons, which translates to its ability to be reduced. Every substance has a characteristic value measured under standard conditions: a solute concentration of 1 M, a gas pressure of 1 atm, and a temperature of 25°C. These values are often found in tables and act as a leaderboard for redux capabilities.

In our ancient battery example, the reduction potentials guide us to identify the roles of copper and iron. Copper has a standard reduction potential of +0.34 V, while iron lies at -0.44 V. Higher positive values indicate a stronger tendency to gain electrons and act as a cathode. This explains why, in the Baghdad battery, copper is the cathode and iron is the anode.

For students trying to remember the concept, think of standard reduction potentials like individual scores in a game. The higher your score (positive potential), the more likely you are to 'win' (be reduced). This simplified analogy can demystify the concept and make it more relatable.

Cell Potential Calculation

When it comes to calculating the cell potential, we essentially determine the electric potential difference between the two electrodes of a galvanic cell. The equation we use is:
\[E^0_\text{cell} = E^0_\text{cathode} - E^0_\text{anode}\]

This difference is the 'voltage' or 'electromotive force (emf)' that drives the electrons across the circuit. In our case, the cell potential for the Baghdad battery is the difference between the copper cathode and iron anode potentials:
\[E^0_\text{cell} = (+0.34 V) - (-0.44 V) = 0.78 V\]

This result tells us how much electrical energy is produced per charge unit transported between the two electrodes. The larger the cell potential, the greater the cell's ability to do work—that is, to power electrical devices. For students to easily understand this: imagine you have two runners – one starts ahead (+0.34 V), the other behind (-0.44 V). The difference in their positions is like the cell potential; it indicates who has more 'ground' to cover, hence showing the extent of 'work' they can do in a race to generate electricity.