Video Transcript
Find, to three decimal places, the standard cell potential for the galvanic cell with the following overall reaction: Two Ag+ aqueous plus Fe solid in equilibrium with two Ag solid plus Fe2+ aqueous.
We have been given the standard electrode potentials for two half-equations. A galvanic cell is a type of electrochemical cell where electrons are spontaneously generated through a redox reaction. A galvanic cell is made of two half-cells that are connected by a wire and a salt bridge. An oxidation half-reaction occurs in one half-cell. The half-cell where oxidation occurs is called the anode. Electrons produced in the oxidation half-reaction travel through the wire to the other electrode. Here they are used up in the reduction half-reaction. The electrode that is the site of reduction is called the cathode.
In the reaction in this question, silver plus ions form solid silver metal. So silver accepts an electron and is reduced, making silver the cathode of this galvanic cell. Meanwhile, iron loses two electrons to form iron two plus ions. So iron is oxidized. This reaction occurs at the anode of the galvanic cell. We need to calculate the standard cell potential for the cell with silver and iron. We’ll be able to do this using the standard electrode potentials that are provided. The standard electrode potential is the potential difference between the standard hydrogen electrode and a half-cell under set standard conditions.
Standard conditions are solution concentrations of one molar, pressures of one bar or approximately one atmosphere, and temperatures of 25 degrees Celsius. The standard electrode potential tells us the tendency of a half-cell to accept electrons. A more positive standard electrode potential indicates that half-cell has a greater tendency to accept electrons. The standard electrode potential for silver is more positive than the standard electrode potential for iron. So silver plus ions have a greater tendency to accept electrons. So it makes sense that silver plus ions accept electrons and are reduced in this reaction, while the iron is oxidized.
We can calculate the standard cell potential by subtracting the standard electrode potential at the anode from the standard electrode potential at the cathode. This equation specifies that the electrode potentials must be reduction potentials, which matches the electrode potentials in the table, which are indeed reduction potentials and not oxidation potentials. We could also write this equation using the standard electrode potential in terms of oxidation. These equations are equivalent as the standard electrode potential for reduction is the same as the standard oxidation potential but with the opposite sign. So the standard oxidation potential for iron would be positive 0.447 volts.
So let’s calculate the standard cell potential for the cell. Silver is the chemical species at the cathode. Silver has a standard electrode potential of positive 0.7996 volts. Notice that although there is a two in front of silver in the reaction equation, this doesn’t affect the standard electrode potential we plug into the equation. The chemical species at the anode is iron. Iron has a standard electrode potential of negative 0.447 volts. This gives us positive 1.2466 volts. The question told us to round to three decimal places, so our final answer is positive 1.247 volts. The standard cell potential for the galvanic cell with silver and iron is positive 1.247 volts.
