Practice Problem: Cell Potential, Equilibrium Constants, and Free Energy Change
(SINGING) He knows a lot about the science stuff, Professor Dave explains.
NARRATOR: Let's look at a question regarding cell potential and free energy. Consider the following system at 25 degrees Celsius. We have 2AG plus ions plus solid Fe, yielding 2AG solid, plus Fe2 plus. And we also need the following data. We have the reduction potential for Fe2 plus as being equal to negative 0.447 volts. And we have the reduction potential for silver plus as being equal to 0.7996 volts.
Now number one, what is the equilibrium constant? And to answer that, we will need this expression. And two, what is the standard free energy change?
And to answer that, we will need this expression. So that's all the information we need. Go ahead and give this a try.
[MUSIC PLAYING]
So let's put our electrochemical data up top. Now, if we will recall, both of those expressions that we are going to use to get the answers we need involve E cell. So we need to calculate E cell first. Now, E cell as we recall, is E cathode minus E anode. The substance with the greater reduction potential will be reduced at the cathode, because the substance that has the greater potential to be reduced will be the one that is reduced. So that means E cell will be E cathode or the half reaction involving the silver ion being reduced, that is 0.7996 volts, minus E anode, which will be the half reaction involving iron, which means it is actually solid iron that will be oxidized. And that value is negative 0.447 volts.
Now remember, once again we do not alter these values at all. It does not matter that the number of electrons in those half reactions is not equal. It also does not matter that we flipped around that iron half reaction to become an oxidation. The minus sign in E cathode minus E anode already takes that flip into account. All we do is plug in the values exactly as they are from the table or from the given data. So that is our E cell expression, and E cell will therefore be equal to 1.247 volts.
So let's put that up here. Now we are ready to answer our two questions. So we wanted to figure out K, the equilibrium constant. And we are going to have to use this expression, which we are able to do because we are at 25 degrees Celsius. So we want to solve for K. So let's plug in what we know. E cell, as we said, is 1.247 volts.
Now, N is the moles of electrons. So if we take a look at that original equilibrium, we can see that one iron atom is giving up two electrons, one to each of two silver plus ions, to yield two silver atoms and one Fe2 plus ion. So there are 2 moles of electrons that are being transferred in this process. So that's why we put a 2 there. N is the moles of electrons.
So that's all of our data. Let's just bring two up to the other side and double that E cell value. And then let's divide by this value. And we get 42.1 equals log K. Now, if we remember a little bit about what logarithms are, if you need some review, you can check out my tutorial on logarithms. But we can solve this by saying that K is equal to 10 to the 42.1. And if we put that in the calculator, we get 1.34 times 10 to the 42. So that is an extremely large value for the equilibrium constant. This equilibrium very heavily favors the products. And that is our K value, which is what we wanted.
And then the second question asked us to calculate the standard free energy change. And that is going to be given by this expression. And so for n, once again, that is the moles of electrons. We already figured that out. So we're going to use that value again. That is two. And then F is Faraday's Constant. That is equal to the charge on 1 mole of electrons. And Faraday's constant is 96,485 joules or mole volts.
And then E cell, as we said, is 1.247 volts. So this is very handy. Volts are going to cancel, leaving us a value in joules per mole. And so the standard free energy change is going to be equal to negative 2.406 times 5 joules per mole. And then we more typically report these values in kilojoules per mole. So we can divide by 1,000, and we get negative 240.6 kilojoules per mole.
So those are the values that we got for the cell potential, the equilibrium constant, and the standard free energy change.
Thanks for watching, guys. Subscribe to my channel for more tutorials. Support me on Patreon so I can keep making content. And as always feel, free to email me, ProfessorDaveExplains@gmail.com.
[MUSIC PLAYING]