Learn about Advanced Placement Chemistry, Thermodynamics 5, in this comprehensive video by bannanaiscool.
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Rob Lederer: Free energy and the equilibrium constant for a reaction, you know what that is, remember equilibrium constants are concentrations of products divided by concentrations of reactants. They are related to one another. You can go through a bunch of manipulations to find out how but this is what you end up within the end. The 'delta-G-naught', which is the delta-G at standard conditions for a reaction, which can be calculated from our back table that has delta-G for all kinds of different compounds and elements. If you find the delta-G-naught for a reaction of the standard conditions, it equal negative RT natural log of K; equilibrium constant, where R again is 8.314 joules per kelvin mole. So if you can calculate the delta-G-naught for a reaction under standard conditions, and then this number, you know what, temperature that you are at, you can take those, divided into this side and then take the anti-natural log of that number to get the equilibrium constant K. Those redox reactions that we've seen before, redox reactions sometimes are quite spontaneous, right, that the reaction happens instantaneously. Well, those have very, very large equilibrium constants for K. So a very large number - if you take the natural log of a very large number, it's a positive number, times this, times this, with a negative, the delta-G will be a negative number, and that means it's going to be spontaneous; that makes sense. If a reaction has a very, very small K value, then it just might have a K value that's negative. when you take the natural log of it, not in negative K value, but natural log of that small value might be negative, times of negative, gives you a delta-G that would be ending up to be non-spontaneous. That's how that works. Delta-G can be related to the equilibrium constant K. Remember in the redox unit, we were always talking about spontaneous and non-spontaneous. Well, then that means then that those things that we calculate in that unit like the voltage values or the E-naught values can actually be related to gives free energy G. So with a bunch of derivations, here is what you can come up with. Delta-G equals negative nFE. Now that means that the number of moles that you have exchange in a reaction times Faraday's constant, where Faraday's constant is in coulombs per mole. Those two multiply and you get coulombs. E, which is voltage, is actually joules per coulomb. When you multiply joules per coulombs times coulombs, you get yourself joules; delta-G is in joules. If a cell, remember redox cell, remember putting together a voltaic cell, if that's spontaneous, it is going to have a positive E value. The positive here times this times this, but it's a negative here gives you a negative delta-G, which means spontaneous. You can take that formula and perform some magic on it to be able to come up with this one here, and this formula is for this reason. You know how the E-naught are specific to a certain temperature, pressure sort of thing under standard conditions. What happens if you mess with the standard conditions and you change the concentrations inside of each of the half cells that they are no longer one mole per liter but they are actually varied and different. What happens if you change the temperature? Oh man, then you actually come up with new values for the E. So how do we actually calculate the new voltage of a cell? This right here we just call that Nernst equation. This is from Nernst. I don't know what the Nernst was, what nationality, but this is the Nernst equation, okay. One of the new value for E is actually the old E-naught, that you would normally get on a chart, minus 0.0592 over the number of moles of electrons exchange in a reaction. So you look at this reaction here. It was two electrons that are actually gained by the copper-2 ion, two electrons lost by the zinc. So they exchange two. If you have two half reactions, you multiply it together one by - one had three electrons in it, one had two,