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### Course: AP®︎/College Chemistry > Unit 9

Lesson 8: Cell potential and free energy# Standard cell potential

Standard cell potential is the potential of a cell when all reactants and products are in their standard states. The standard potential for any cell can be calculated by subtracting the standard reduction potential of the half-reaction occurring at the anode from the standard reduction potential of the half-reaction occurring at the cathode. Created by Jay.

## Want to join the conversation?

- Why do we change the sign of the reduction potential when we reverse the equation?(1 vote)
- The short answer is that cell potential is a thermodynamic property, and when we reverse the order of a reaction we switch the sign if a thermodynamic property. Similar to how enthalpy works.

The long answer involves how we define cell potential. In a spontaneous voltaic cell, electrons move from one electrode to the other naturally. Specifically it’s the electrons in one electrode which are higher in energy than the other and so desire to have lower energy by traveling from the high energy electrode to the low energy electrode. The energy levels of the two electrodes are fixed, so the electron traveling from the high energy electrode to the low energy one travels the same energy difference as an electron traveling from the low energy electrode to the high energy electrode, except that the signs are different.

Going from high to low energy, the electron naturally does this and loses energy which we interpret as a positive voltage. Going from low to high is the same energy difference, but now since the electron does want to do this naturally we have to input a certain amount of energy to essentially promote it to the higher energy electrode, which we interpret as a negative voltage. So the same energy distance is covered, but the sign of the voltage tells us which way we are traveling. If we reverse a redox reaction, we change the direction electron is moving. If it begins as a reduction reaction where an electron is gained, reversing the reaction will make it an oxidation reaction where an electron is lost.

Hope that helps.(5 votes)

- When given the value for E not of the oxidation and reduction half-reaction, is that something that needs to be given in a question?(2 votes)
- How come the Cu reduction has a positive potential whereas the Zn is negative? Isn't the sign of the potential directly related to the loss/gain of electrons?(1 vote)
- The sign has to do with how we define standard reduction potentials. When we have an electrochemical cell, any cell, set up and we want to measure the voltage, we can do so for the entire cell. So the voltage we measure is a combination of both the anode and the cathode, not of an individual half-reaction. This is because as a redox reaction, we cannot have one without the other. But this means we cannot measure half-cell potentials in isolation.

To get around this problem we measure the potentials of all half-reaction against the same reference half-reaction. The reference half-reaction is referred to as the standard hydrogen electrode, or SHE, which has a reaction: 2H^(+)(aq) + 2e^(-) ⇋ H2(g). Essentially it’s the reduction of acidic protons into hydrogen gas. When we connect other reactions to this SHE and measure the voltage, we’re still measuring the combined voltage of both the SHE and the other half-reaction. But if every reaction’s voltage is measured against the same SHE reference, then we can compare their half-reaction voltages this way.

So the signs of the standard reduction potentials are showing how strongly a half-reaction is being reduced or oxidized compared to the SHE. Positive values mean they are reduced when connected to the SHE, and negative values mean they are being oxidized when connected to the SHE. Generally, though, a more positive standard reduction potential indicates something which prefers to be reduced (stronger oxidizer), and a more negative value indicates something that likes to be oxidized (stronger reducer).

Hope that helps(2 votes)

- 03:00

So, what is the polarity of the standard cell potential? Is the positive end of the voltmeter connected to the the ions or the solid for the oxidation side?(1 vote) - Why do we calculate cell potential(0 votes)
- Because it’s one of the simplest properties in electrochemistry which helps you do further electrochemistry.(2 votes)

## Video transcript

- [Instructor] Standard Cell Potential, which is also called
Standard Cell Voltage, refers to the voltage of
an electrochemical cell when reactants and products
are in their standard states, at a particular temperature. For a zinc copper galvanic cell, solid zinc reacts with
copper two plus ions, to form solid copper,
and zinc two plus ions. Standard Cell Potential
is symbolized by E naught of the cell, where the superscript naught refers to the fact that
reactants and products are in their standard states. For a solid, standard state
refers to the pure solid under a pressure of one atmosphere. So we're talking about pure solid zinc, and pure solid copper. And for a solution, standard state refers to
a one molar concentration. So our concentration of copper two plus ions in solution is one molar, and so is our concentration
of zinc two plus ions. And for this zinc copper
cell, at 25 degrees Celsius, the Standard Cell Potential is
equal to positive 1.10 volts. Now that we've talked about
the Standard Cell Potential for a zinc copper cell, let's look at a diagram
of this galvanic cell. For this cell, the anode
compartment contains solid zinc metal, and
one molar concentration of zinc two plus ions,
in aqueous solution. The anode is where oxidation takes place. So at the zinc electrode, the solid zinc is converted
into zinc two plus ions, and two electrons are lost. So this is the oxidation
half reaction for this cell. The electrons that are lost
in the oxidation half reaction travel through the wire. So there's a flow of electrons,
from the zinc electrode, toward the copper electrode. The cathode compartment contains the solid copper
electrode and in solution, one molar concentration
of copper two plus ions. And the cathode is where
reduction takes place. So at the surface of the copper electrode, the copper two plus ions in solution gain two electrons and
turn into solid copper. So this is the reduction
half reaction for this cell. If we were to attach a volt
meter to our two electrodes, the volt meter would read 1.10 volts. And this voltage is the
Standard Cell Potential. So E naught of the cell is equal to positive 1.10 volts. And the Standard Cell Potential
depends on the potentials for the two half reactions
that make up the cell. So if we know the potentials
for the half reactions that make up the cell, we can calculate the standard potential of any galvanic cell. And let's see how we could do
that for this particular cell. To calculate these standard cell potential for our zinc copper cell, we're going to use what are called Standard Reduction Potentials. Standard Reduction
Potentials are symbolized by E naught of reduction. And these refer to the voltages for half reactions that are written as reduction half reactions. For example, if copper two plus
is reduced by two electrons to form solid copper, the voltage for this half reaction, or the Standard Reduction Potential, is equal to positive 0.34 volts. And for the reduction
of zinc two plus ions by two electrons to form solid zinc, the Standard Reduction Potential is equal to negative 0.76 volts. We just saw from our
zinc copper cell diagram, that copper two plus ions are reduced to form solid copper. So, we're going to leave this
half reaction as it's written. However, in our diagram
for our zinc copper cell, we saw that solid zinc was
actually being oxidized to form zinc two plus ions. So we need to rewrite
the second half reaction as an oxidation half reaction. And that just means reversing everything. And if we're reversing our half reaction, we have to change the sign on the voltage. So if the potential is negative 0.76 volts for the reduction half reaction, it would be positive 0.76 volts for the oxidation half reaction. So now I've changed it to show
the oxidation half reaction, solid zinc turning into zinc
two plus ions in solution, and the loss of two electrons. The Standard Oxidation
Potential for this half reaction is positive 0.76 volts. The next step is to add the
two half reactions together. So here are all of our reactants, and here are all of the products. Notice how two electrons would cancel out, and that gives us copper two
plus ions in aqueous solution, plus solid zinc forms solid copper, and zinc two plus ions in solution. Since we were able to
get the overall equation by adding the two half reactions together, we should be able to get the
overall Standard Cell Potential E naught of the cell,
by adding together the standard potentials for
our two half reactions. So E naught of the cell is equal to E naught of the reduction half reaction, plus E naught of the
oxidation half reaction, which is equal to 0.34 plus 0.76, or positive 1.10 volts. So, the Standard Cell Potential
of our zinc copper cell is equal to positive 1.10
volts at 25 degrees Celsius. We can also calculate
Standard Cell Potential using a slightly different form of the equation that we just learned. Remember that we flipped the sign of the Standard Reduction Potential to get the Standard Oxidation Potential, which we plugged into this equation, and were able to calculate the standard potential of the cell. Instead of flipping the sign ourselves, and getting a Standard
Oxidation Potential, we could use this new equation to just use reduction potentials to calculate the standard potential of the cell. Notice that this new
equation has a negative sign that essentially flips the sign of the Standard Reduction Potential
for the oxidation process. So, it accomplishes the same
thing that we did ourselves in the first equation. So to find the standard
potential of the cell, we take the Standard Reduction Potential for the reduction process, and from that, we subtract the
Standard Reduction Potential for the oxidation process. So, this equation is a bit of a shortcut. So when we plug in our
Standard Reduction Potentials of positive 0.34 volts
and negative 0.76 volts, the negative sign means we
end up with the same answer we got before, a positive 1.10 volts.