Tips for Using the Nernst Equation
Here are some tips and tricks for using the Nernst equation when you’re trying to find the cell potential, given initial conditions are concentrations. So you know from your studies that, the Nernst equation equals the cell potential and that equals the standard cell potential in volts, minus 0.0591 over n times log(Q).
And just to label those variables for you; this is the standard cell potential and that’s in Volts. And then the n represents the number of electrons that’s transferred, during your redox reaction. And then Q stands for from way back when, the reaction quotient using initial concentrations.
And if you forget what Q is, then you can take a look at our equilibrium section and it will tell you what Q is. This is not Q that’s hypothermal energy, this is Q the reaction quotient. So here we have an example written for us where we’re use the Nernst equations.
So it says calculate the cell potential for the reaction. And then we have Cu2+ plus Ag yields Cu plus Ag+. And then our initial concentration of Copper2 Iron is 2.0M and for the silver iron is 4.0M.
So first thing we want to is, we want to calculate the cell potential of this reaction by splitting into half reactions. So the first one, we’ll match up the coppers with each other and then the second one, we'll match up the silvers with each other. Then notice how I lined up the yield signs. So the copper is nice and easy. I need 2 electrons on the left side, the silver I only need one electron on the right side. And now we look up the cell potentials. I have the centre of reduction potentials, and then for copper, it’s point 0.34V. And since this is reduction, we don’t have to have to change it. And then the silver, this is oxidation so the cell potential for the half reduction will be 0.80V. But since this oxidation, and we flipped the reduction potential, then I’m going to put a negative here.
And then, to make the electrons equal, we need 2 here, 2 here, and 2 here. So we have 2 electrons. So when we add up our equations, the electrons cancel out and you’re left with 2Ag plus Cu2+ yields 2Ag+ plus Cu. And then all you got to do is now add up your cell potentials from your half reactions. And so E's zero cell equals -0.46V, so that’s how much we have.
One pitfall that my students make is, don’t forget, since we flipped the silver half reaction to make it so it's oxidation, or since we wrote it that way. Don’t forget, if you look it up on the chart that you would take the negative of the centre of reduction potential. So that’s why we use -0.80 and then we add them together in the end.
Last, then we’re going to use the Nernst equation. So E is zero equals and then we’ll plug in -0.46V because that’s our standard cell potential that we calculated here, for this reaction, minus 0.0591 over. And how many electrons are transferred? Well the ones we cancelled out we had 2. So we'll write a 2 here on the bottom and then the log of Q cubed. And so to calculate Q, well Q would equal, in this case. Well remember solids don’t count. So all we have is aqueous stuff. So we have Silver ion and that’s squared because remember, the coefficient become the exponents over the concentration of [Cu2+] and remember all those are initial.
So all I have to is now plug in. So I have 4.0M and I'll square that. Don’t forget to square, over and then you put 2.0M for the copper. And so in effect, that will be the log of 16 over 2, that’s the of 8. So when we do our calculations and I get a -0.46V. And then minus and then I would have 0.027V when I do the calculation. And so our final answer for our cell potential with those concentrations would be -0.49V. Don’t forget since this is a negative, remember, this will tell you that your cell would right now be non-spontaneous, which would mean that you will need outside energy or electricity in order for that reaction to happen. Remember, if the cell potential is positive, then that means that it is spontaneous, and the electrons will flow on their own. So hopefully these tips and tricks will help you in using the Nernst equation. Sounds hard. but it’s not very. Have a good one.