Worked example: Calculating E° using standard reduction potentials

- [Instructor] Let's do a worked example where we calculate the standard potential at 25 degrees Celsius for this reaction. In this redox reaction, silver cations are reduced to form solid silver and solid chromium is oxidized to form the Cr3+ ion. The first step is to write down the half reactions that make up the overall redox reaction. So we said that silver cations are reduced, therefore we need to gain the electron to turn into solid silver and solid chromium to turn into chromium 3+ ions must lose three electrons. Next, we need to find the standard voltages for our two half reactions. And to do that, we could consult a standard reduction potential table, and here's our table that shows standard reduction potentials for some reduction half reactions at 25 degrees Celsius. The standard reduction potentials or standard reduction voltages for these half reactions are all compared to the reduction of H+ ion. So two H+ plus two electrons forming hydrogen gas has a standard reduction potential of exactly zero volts. For our particular redox reaction, we need to know the reduction potential for the reduction of silver cations to form solid silver. The standard reduction potential for this half reaction is equal to positive 0.80 volts. The other half reaction that we need to know about involves the oxidation of solid chromium to chromium 3+ cations. But since this is a standard reduction potential table, the half reaction is written as a reduction half reaction. The standard reduction potential for this half reaction is negative 0.74 volts. But since we need this half reaction written as an oxidation half reaction, if we were to reverse this half reaction, how it's written, we would need to change the sign of the voltage. So the standard oxidation potential would be positive 0.74 volts. So I've gone ahead and written in the voltages for our half reactions. The standard reduction potential for our half reaction was positive 0.80 volts, and the standard oxidation potential for our half reaction is positive 0.74 volts. Our next step is to make the number of electrons equal for our two half reactions and add them together. For our oxidation half reaction, we're losing three electrons, but for our reduction half reaction, we're only gaining one electron. Therefore we need to multiply everything through in our reduction half reaction by three, that gives us 3Ag+ plus three electrons goes to 3Ag. Notice that even though we multiplied everything through in our reduction half reaction by a factor of three, we did not multiply the standard reduction potential by a factor of three. And that's because voltage is an intensive property and doesn't depend on the amount of substance. So it doesn't matter if we're talking about the reduction of one mole of silver cations, or three moles of silver cations. The standard reduction potential is the same for both half reactions. And when we add our two half reactions together, so here are all of the reactants and then over here would be all of the products. The three electrons would cancel out on both sides and give us 3Ag+ plus solid chromium goes to 3Ag plus Cr3+, which gives us back our original redox reaction. And since we were able to add our two half reactions together and get our overall redox reaction, to find the standard voltage for this reaction, we should be able to add together the voltages for the two half reactions. So positive 0.8 plus 0.74 is equal to positive 1.54 volts. So the standard potential for this redox reaction at 25 degrees Celsius is equal to positive 1.54 volts. There's another way to calculate the standard potential for this redox reaction, and this way only uses standard reduction potentials. So to calculate the standard potential for the redox reaction, we take the standard reduction potential for the reduction process and from that we subtract the standard reduction potential for the oxidation process. So for our reduction half reaction the standard reduction potential is equal to positive 0.80 volts. So we'd plug that into our equation for the reduction process. And for our oxidation half reaction, the standard reduction potential, if you remember from the standard reduction potential table is equal to negative 0.74 volts. So that would get plugged into our equation for the oxidation process. And when we plug in our voltages, we get the same answer that we got before. So the standard potential for our reaction is equal to positive 1.54 volts at 25 degrees Celsius.