Question

From the following \(E^{\circ}\) values for the half-cells: (i) \(\mathrm{D} \rightarrow \mathrm{D}^{2+}+2 \mathrm{e}^{-} ; E^{\circ}=-1.5 \mathrm{~V}\) (ii) \(\mathrm{B}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{B} ; E^{\circ}=-0.5 \mathrm{~V}\) (iii) \(\mathrm{A}^{3-} \rightarrow \mathrm{A}^{2-}+\mathrm{e}^{-} ; E^{\circ}=1.5 \mathrm{~V}\) (iv) \(\mathrm{C}^{2+}+\mathrm{e}^{-} \rightarrow \mathrm{C}^{+} ; E^{\circ}=+0.5 \mathrm{~V}\) Which combination of two half-cells would result in a cell with largest potential? (a) \(\mathrm{i}\) and iii (b) \(\mathrm{i}\) and iv (c) iii and iv (d) ii and iv

Short answer

The largest cell potential is produced by the combination of half-cells (a) i and iii.

Step-by-step solution

Identify the Cell Potential

The potential for the galvanic cell is determined by the difference in the reduction potentials of the two half-cells. The cell with the largest potential will have the largest difference in reduction potential between its cathode and anode.

Compare Reduction Potentials for Pair (a)

For pair (a), calculate the potential difference: Cathode (iii) has a potential of +1.5 V, and Anode (i) has a potential of -1.5 V. The difference is (1.5 - (-1.5)) = 3.0 V.

Compare Reduction Potentials for Pair (b)

For pair (b), calculate the potential difference: Cathode (iv) has a potential of +0.5 V, and Anode (i) has a potential of -1.5 V. The difference is (0.5 - (-1.5)) = 2.0 V.

Compare Reduction Potentials for Pair (c)

For pair (c), calculate the potential difference: Cathode (iii) has a potential of +1.5 V, and Anode (iv) has a potential of +0.5 V. The difference is (1.5 - 0.5) = 1.0 V, noting that the anode potential needs to be reversed since it’s being used as an anode.

Compare Reduction Potentials for Pair (d)

For pair (d), calculate the potential difference: Cathode (iv) has a potential of +0.5 V, and Anode (ii) has a potential of -0.5 V. The difference is (0.5 - (-0.5)) = 1.0 V.

Determine the Largest Cell Potential

The largest potential difference is found in pair (a) with 3.0 V.

Key concepts

Electrochemical Cell

Electrochemical cells are the fundamental units of batteries and are crucial for a plethora of modern technology. Essentially, an electrochemical cell is a device capable of either generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy.

In the context of a galvanic cell, or voltaic cell, an electrochemical cell spontaneously converts chemical energy into electrical energy. This occurs via redox reactions where oxidation occurs in one half-cell and reduction in the other, creating a flow of electrons from the anode to the cathode through an external circuit, generating electric current.

A significant point to understand is that each half-cell consists of an electrode and an electrolyte. The potential difference between these two half-cells leads to the overall voltage of the electrochemical cell. The cell potential is influenced by factors like temperature, pressure, and the concentration of reactants and products. An important aspect when connecting the half-cells is ensuring that the electron flow is balanced by the flow of ions through a salt bridge, maintaining overall charge neutrality.

Reduction Potentials

The reduction potential, often expressed as standard electrode potential (\( E^\text{0} \)), is a measure of the tendency of a chemical species to acquire electrons and thus be reduced. Each half-cell in an electrochemical cell has its own unique reduction potential.

These potentials are measured under standard conditions: a 1 M solution at 25°C with a pressure of 1 atmosphere for gases. The standard reference point is the hydrogen electrode whose potential is defined as 0 volts. By comparing the reduction potentials of different half-cells, we can predict the direction of electron flow when they are connected, as electrons will move from the half-cell with lower reduction potential (anode) to the one with higher reduction potential (cathode).

The difference between the cathode's and anode's reduction potentials gives us the cell potential. When studying different combinations of half-cells, one can use these standard reduction potentials to calculate which pair will result in the highest voltage for the cell, thereby determining its capability to do electrical work.

Half-Cell Reactions

Half-cell reactions are the individual oxidation or reduction reactions that occur in their respective half-cells within an electrochemical cell. These reactions are fundamental because they generate the ions and electrons necessary for the cell's operation.

In a half-cell reaction, either reduction or oxidation will take place. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. Each half-cell contains electrodes where these reactions occur; the anode is where oxidation happens, and the cathode sees reduction. The electrodes are usually made of metals or other conductive materials immersed in an electrolyte solution that contains ions.

For a successful electrochemical reaction, it is crucial that the electrons lost in the oxidation half-cell travel through an external circuit to the reduction half-cell. This provides the electrical energy harnessed in batteries. Additionally, ensuring that the reduction potentials are correctly paired is essential for an electrochemical cell to function efficiently, as seen in the exercise provided where the largest potential dictates the most effective pairing of half-cells.