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## Cell potential and free energy

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# Worked example: Calculating E° using standard reduction potentials

AP.Chem:

ENE‑6 (EU)

, ENE‑6.B (LO)

, ENE‑6.B.2 (EK)

## Video transcript

- [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.

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