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19.6 Cell Potential, Delta G, and the Equilibrium Constant | General Chemistry - YouTube
Channel: Chad's Prep
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e cell delta g and the equilibrium
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constant we'll be taking a look at the
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mathematical relationship between these
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three in this lesson my name is chad and
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welcome to chad's prep where my goal is
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this lesson's part of my new general
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to the channel click the bell
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notification
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all right so it turns out that your
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standard e cell your standard value for
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delta g and your equilibrium constant
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are all mathematically related they're
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all mathematically interdependent in
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fact so if you know one you actually can
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calculate the other two and you could be
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on the hook for just such an occasion
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and we're going to do an example
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of exactly this so
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we're going to take a look at this
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lovely reaction and we're first going to
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calculate the standard value for the
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cell potential e cell
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and then we're going to use that to
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calculate delta g and keq now we hinted
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towards this in the last lesson but the
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relationship between delta g and e cell
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so is given by this lovely equation so
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it turns out
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n here's the number of moles of
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electrons transferred in either the half
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reaction or complete reaction so f is
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faraday's constant same one we saw 96
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500 coulombs per mole of electrons so
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then you got your e cell and notice uh
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we use delta g and e cell to figure out
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if a reaction is spontaneous we've
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already said that if delta g is negative
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reaction's spontaneous if e cell is
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positive reaction spontaneous and here's
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the mathematical relationship that shows
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you that if e cell is positive then
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because of that negative sign delta g is
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going to come out negative f here is a
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positive constant n is a positive number
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of moles of electrons and so if e cell
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is positive because of that negative
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sign delta g has to come out negative
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they're mathematically interdependent
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now back in the thermodynamics chapter
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we saw a relationship between delta g
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and the standard value for delta g
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and we found out that at equilibrium
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delta g went to zero and q
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equaled the equilibrium constant and we
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got another relationship out of that
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that delta g standard equal negative rt
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ln of that equilibrium constant
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on the last lesson we saw that from that
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lovely relationship between the
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non-standard standard values for delta g
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we derived the nernst equation relating
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the non-standard and standard values for
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the cell potential the e cell so in a
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similar fashion at equilibrium this e
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cell value under non center conditions
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goes to zero and q
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equals k and we get another relationship
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in very similar fashion out of this
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where e cell standard
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equals r t over n f
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natural log
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of the equilibrium constant
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and so notice that this first one up
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here relates delta g standard
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to the equilibrium constant you know one
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you can calculate the other assuming you
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know what temperature it applies to same
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thing now with your standard e cell
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value in your equilibrium constant you
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know one you can calculate the other as
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well again assuming you know what
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temperature you're uh referring to
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cool and so if you know any one of these
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three your standard value for e cell
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your standard value for delta g or your
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equilibrium constant any one of those
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three you should be able to calculate
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the other two and as i said again that's
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exactly what we're going to do so we're
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going to calculate e cell standard for
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this given some reduction potentials and
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i'm just taking out the two that we need
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here so but typically you'd have a whole
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table of them at your disposal so when
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you use that to calculate your standard
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value for e cell here and we can see
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that
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zinc is exactly backwards what you see
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here here it's getting oxidized this is
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the reduction potential so instead of
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negative 0.76 volts it's positive 0.76
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volts is one way to look at that and
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then copper two plus two copper exactly
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what we see here so positive 0.34 volts
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and so positive 0.34 and positive 0.76
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means that our standard cell potential
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is going to equal positive
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1.10 volts notice you could have also
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done cathode minus anode 0.34 minus a
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negative 0.76 so whether you change the
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sign on the anode to make an oxidation
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potential or whether you subtract to
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change the sign for you both leave you
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the same answer again that your standard
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cell potential is 1.10 volts okay so now
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we can find both delta g and keq and we
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can use this one to get delta g standard
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from the standard value of e cell so and
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then we got a couple of different
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options once we get delta g standard we
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could use this relationship to get the
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equilibrium constant we've done that in
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the past or we could use this one as
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well and we'll do it that way since it's
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new
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so let's get delta g first so in this
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case
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delta g standard equals negative n f
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times your e-cell standard and so in
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this case that's going to be
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negative and in this case this is a
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two-electron transfer whether we're
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looking at it
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copper two plus go into copper that's
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two electrons being gained or zinc going
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to zinc two plus that's two electrons
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being lost overall it is balanced to a
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two electron transfer that's what gets
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plugged in right here so two moles of
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electrons faraday's constant 96
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500
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coulombs per mole of electrons and then
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times your standard cell potential here
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of 1.10 volts
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all right now instead of writing a volt
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here i'm going to write what a volt
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actually is equal to and that is a joule
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per coulomb so you can see how the units
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work out a volt equals a joule per
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coulomb but you can see how the moles of
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electrons part is going to cancel here
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the coulomb's going to cancel here and
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delta g is going to come out in joules i
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just want to make sure you realize that
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because if you're doing this as like a
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part of a multiple choice calculation
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odds are the delta g's are probably
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going to be listed in kilojoules instead
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you might have to convert
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at the end so but using volts this comes
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out in joules so we've got 2 times 96
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500
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times 1.1 and we're going to get 212
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300.
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uh
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i must have lost the negative side i
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lost my negative sign on the front well
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let's try that again so negative 212 300
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notice we should have expected it to
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come out negative and if we divide by a
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thousand to convert to kilojoules then
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negative 212.3
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kilojoules
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so there's your delta g standard
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and like i said if we want to calculate
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keq from here we could use that delta g
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standard to get it so let's go the new
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route here and let's do one other thing
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so
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a lot of you will have this abbreviated
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again at 298 kelvin
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so r times t divided by f
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is going to be .0257
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and then divided by that n value
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times the natural log of keq so there's
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a version of this one as well that used
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that same combination of constants as
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long as you're at 298 kelvin that we saw
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in that last lesson
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and so let's go ahead and calculate that
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equilibrium constant now rearrange this
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a little bit and so in this case we're
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going to have n
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times e cell
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all over 0.0257
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equals ln of k
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and then to get rid of that ln you might
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recall it's e
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exponential their inverse function so
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here they cancel
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so we're left with k
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equals n times e cell and n here in this
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case was again two
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moles of electrons we'll go from there
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in fact i guess i should plug in all my
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numbers so we got two moles of electrons
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times 1.10 volts all over 0.0257
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e to the power of my bad
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i suddenly realized this was not going
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to come out large enough and notice i'm
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expecting it to come out very large you
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notice we got a positive voltage
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reaction is definitely spontaneous under
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standard conditions that's why i knew
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delta g standard should come out
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negative and fairly negative at that and
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we should expect the equilibrium
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constant this reaction being spontaneous
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understanding conditions is going to
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favor the products and in this case it's
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very spontaneous so favor them heavily
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which is why we should expect the
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equilibrium constant to come out much
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much larger than 1.
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all right so 2 times 1.1 divided by
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0.0257
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and then we're going to do e to the 85.6
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here that's going to be a big number
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1.5 times 10 to the 37.
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so reaction that heavily favors the
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products at equilibrium
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cool and that's exactly how this works
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again we started off with the table of
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reduction potentials we used it to
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calculate the standard value for e cell
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we then use that standard value for e
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cell to calculate the standard value for
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delta g
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so and then we use the standard value
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for e cell to calculate the equilibrium
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constant as well and again you can start
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out with any one of those three this
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last one was the worst part of the
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calculation for solving something under
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a natural log but i can give you the
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standard value for your cell potential
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standard value for your gibbs free
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energy or your equilibrium constant and
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you should be able to calculate the
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other two
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now if you found this lesson helpful
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