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Unit 9

9.9 Cell Potential Under Non-Standard Conditions

4 min readjuly 9, 2021

sander-o

Sander Owens

fiveable-dylan

Dylan Black


AP Chemistry 🧪

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9.9: Cell Potential Under Nonstandard Conditions

For all of unit 9 we’ve discussed galvanic cells under standard conditions. For an electrochemical cell, standard conditions are 298.15K, 1 atm, and most importantly, 1M concentration of both solutions in either half cell and Q = 1. Remember that Q is the reaction quotient from unit 7. At these conditions, we can calculate E°cell for a cell using standard reduction potentials. However, sometimes we are not at standard conditions and therefore, we will have to make predictions as to whether the voltage of the nonstandard cell will be larger or smaller than E°cell. This section focuses entirely on interpreting Ecell and making connections to concentration, cell potential, and equilibrium.

Comparing Ecell and E°cell

You may remember in unit 9.5 we discussed the difference between ΔH° and ΔH and how ΔH is a driving force towards equilibrium. The same applies to Ecell and E°cell! It’s important to know that a galvanic cell that is running is not at equilibrium. By running, the cell is moving towards equilibrium. At that point, the reaction enters dynamic equilibrium and the voltage at that non-standard position will be zero. This is exactly what a dead battery is. A dead battery is nothing more than a galvanic cell that has reached equilibrium. At equilibrium, Ecell = 0. 
This is the same concept as the one we saw in 9.5 with ΔH° and ΔH. At equilibrium, ΔH = 0. Therefore we can draw a relationship between Ecell and Q similar to the relationship between ΔH and Q:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3ktuQlZPoPZh.png?alt=media&token=78c8ae31-3a83-4a51-9f80-795b17ff773f

Image From LibreTexts

In this instance, R is 8.314 J/molK (or equivalent depending on units), T is temperature, n is moles of electrons, and F is Faraday’s constant which is 96485C/ mol e-. This equation is known as the Nernst Equation and shows us the relationship between E°cell and Ecell and Q. 

Concentration and Cell Potential

An important factor in predicting cell potential at nonstandard conditions is concentration. At standard conditions, concentration is always 1M but otherwise, we can still make predictions as to what Ecell is like compared to E°cell. We want to do this by remembering that at standard conditions Q = 1 (this is because the concentrations are both 1 so [1]^n/[1]^m = 1) and that Q = [product]^n/[reactant]^m where n and m are stoichiometric coefficients. If Q > 1, we find that we have “too many products” and thus our Ecell will be less than E°cell. Similarly, if Q < 1, we find that Ecell will be greater than E°cell. Let’s look at an example:
Consider the reaction 2Al (s) + 3Mn2+ (aq) → 2Al3+ (aq) + 3Mn (s) and compare Ecell to E°cell for the following scenarios:
  1. [Al3+] = 1.5M and [Mn2+] = 1.0M
  2. [Al3+] = 1.0M and [Mn2+] = 1.5M
  3. [Al3+] = 1.5M and [Mn2+] = 1.5M
For each of these parts we will use the same method: finding Q, comparing to 1, and then drawing conclusions from that value.
In general, we can see that Q = [Al3+]^2 / [Mn2+]^3. Plugging in for problems 1-3 we find:
  1. Q = [1.5]^2 / [1.0]^2 > 1
  2. Q = [1.0]^2 / [1.5]^3 < 1
  3. Q = [1.5]^2 / [1.5]^3 < 1
For #1, we can conclude that Ecell < E°cell because Q > 1. 
For #2 and #3, we can conclude that Ecell > E°cell because Q < 1.
Let’s take a look at another example MCQ:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Yr8LmU3DvKHk.png?alt=media&token=ae0f511b-dc32-4710-afc7-2f941c2549b7

Image From Abigail Giordano

As always, let’s start with the Q expression for this reaction:
Q = [Cd2+]/[Ag+]^2
By making the silver electrode larger, neither of these concentrations change. As long as there is an electrode, Q does not change in this instance. Therefore, the answer is D: Voltage does not change. If instead the Ag electrode was removed, our answer would be C.

Using the Nernst Equation

The Nernst Equation is another important way we can make predictions on the relationship between E°cell and Ecell. For a refresher, here are a few representations of the Nernst Equation:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-7G7aLkvcpuwT.png?alt=media&token=ee79085c-8b49-48fd-b291-586631b7e2f1

Image From LibreTexts

These are the same equation except one is the natural log (log base e) and the other is log base 10. The bottom equation is also only true at . On the AP exam, you will NOT be expected to use these equations to find actual values. Instead, you’ll be expected to make predictions using the Nernst Equation. These predictions will involve how a reaction will proceed given certain conditions for Ecell, E°cell, and Q. In understanding the Nernst Equation, we can draw predictions to how changes in these values will affect the others.
Plugging in 0 for Ecell and K for Q, we can find a formula for E°cell at equilibrium:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Ok0YtZvqt6Gq.png?alt=media&token=bbf9c6a1-13e6-45a4-b701-30eaa41c85c8

Image From Abigail Giordano

Here’s a chart with these relationships laid out with delta G as well:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-s2C2mkGN84Re.png?alt=media&token=7754c99f-3957-4d16-b3c7-7a034dc4d9e0

Image From LibreTexts

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