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Tips for Approximating Delta G from Cell Potential
Here are some tips for approximating delta G from cell potential. So here we have the equation delta G equals -nF and then the cell potential that we have here.
So using the example one, I'll show you the calculation and how the short-cut will help you out here. So let's take a look. So if you're given the balanced redox equation already, a short cut for finding the number of electrons, here's a trick.
Take a look of the number of atoms of each thing that you have that's half size or reduced. So if you take a look at the golds, there's only one atom on gold on both sides, and 3 atoms of silver on both sides. So between the gold and the silver, the lowest common multiple between those number of atoms; 1 and 3 is 3. So you have 3 moles of electrons. That's how you figure it out. So that's the trick.
So if we plug it in, to the equation, it's a salt. So delta G equals negative and then n is the number of moles of electrons. So that's 3 moles of electrons here, times F. That's Faraday's constant. So it's 96485 Coulombs per mole of electron times. Then the cell potential is 0.70V or 0.70Joules per Coulomb because a volt is equal to J/C.
So you do the math, delta G that equals -202,618J and that's equal to, in kilo joules, -202.618kJ. So I'll show you a shortcut or a trick for how to calculate delta G or something pretty close to it. So what we'll do is we'll take the number -100, and we'll just use this as the multiplier. Times the number of moles of electrons, so that's 3. Times the voltage or the cell potential. So in this case it's 0.70, so cell potential. Then when I multiply all those, I end up with -210kJ. Then -210kJ is a pretty close approximation to what the actual delta G of that reaction is.
Since delta G is negative, it tells you that the reaction is spontaneous and that's temperature because the sign is negative for delta G amount. So let's take a look at our example here, example 2.
So the things that get oxides and reduce, probably the Manganese and probably the Fluorines. So the Manganese we have 2 atoms here. We have 10 atoms of Fluorine and the same thing on the opposite side. So the lowest common multiple between 2 and 10 is 10. So we have 10moles of electrons that's being transfered.
So let's do our delta G approximation. So we'll take a number -100 and we'll multiply it times 10 because that's the number of moles of electrons times the cell potential, so that's -1.36V. Then you multiply them out then you get -1360kJ. This is the approximation that you have here.
If you did the math, then the actual value would be +1312kJ, that's pretty close. So since Delta G is positive, then the reaction would be non-spontaneous at that particular temperature.
So hopefully these tips and these tricks will help you in approximating delta G in cell potential, and also, how to figure out the number of moles of electrons, without splitting them into half reactions. Have a good one.