Video Transcript
Using the standard electrode potentials shown in the table, calculate, to three decimal places, the cell potential for the following electrochemical cell.
In an electrochemical cell, electrons are generated in a redox reaction. The redox reaction can occur spontaneously or nonspontaneously. If it occurs spontaneously, the cell is a galvanic cell. The cell in this question is a galvanic cell. For now, we can take this as fact, but we’ll be able to confirm this by calculating the cell potential, as the cell potential is positive if the reaction occurs spontaneously.
Galvanic cells are made of two half-cells that are connected by a wire and a salt bridge. In one half-cell, oxidation occurs. This will produce electrons in the cell, making this the negative electrode. We call this electrode the anode. Electrons produced at the anode travel through the external circuit to the other half-cell. These electrons will be used in the reduction reaction. As electrons are being used up in this half-cell, this is the positive electrode, which we call the cathode.
To conveniently represent an electrochemical cell, we can use cell notation. In cell notation, we have the anode information on the left and the cathode information on the right. The double vertical line represents the salt bridge. The single line represents a phase boundary, in this case between the solid metal electrodes and a solution containing ions. So, the cell might look something like this. As cadmium is the anode, the cadmium metal will be oxidized, losing two electrons to form cadmium two plus ions. Nickel is the cathode. So, nickel two plus ions will be reduced, gaining two electrons to form solid nickel.
We need to calculate the cell potential for this cell using standard electrode potentials. Standard electrode potentials tell us the potential difference between the standard hydrogen electrode and a half-cell under set standard conditions, which are solution concentrations of one molar, gas pressures of one atmosphere, and temperatures of 25 degrees Celsius. Standard electrode potentials tell us the tendency of a half-cell to accept electrons. A more positive standard electrode potential indicates a greater tendency to accept electrons.
Since reduction involves gaining electrons, half-cells with a higher standard electrode potential are more likely to be reduced. We can see the nickel half-cell has a more positive standard electrode potential compared to the standard electrode potential of the cadmium half-cell. So, it makes sense that nickel is the cathode in this cell and cadmium is the anode.
We can calculate the cell potential if we subtract the standard electrode potential for the anode from the standard electrode potential for the cathode. To use this formula, both of the standard electrode potentials should be written in terms of reduction for the half-equation, which these standard electrode potentials are. We might also see this equation for the cell potential written this way, where we add the standard electrode potential for the anode, which is in terms of oxidation. But these two equations are equal since the standard electrode potential for reduction is the same as the standard electrode potential for oxidation, just with the opposite sign.
Now, let’s calculate the cell potential for the cell in this question. As we’ve discussed, nickel is the cathode. The standard electrode potential for the nickel half-cell is negative 0.257 volts. Cadmium is the anode; its standard electrode potential is negative 0.4030 volts. Performing the calculation gives us positive 0.146 volts, which already has three decimal places as the question asked for. As we can see, the cell potential is positive. So, the redox reaction in this electrochemical cell would occur spontaneously.
So, using the standard electrode potentials for the cadmium and nickel cell, we calculated the cell potential to be positive 0.146 volts.
