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in this session we're going to be
00:00:02
exploring what happens with
00:00:03
electrochemical equilibrium in
00:00:05
electrochemical environments so thinking
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about electrochemistry at equilibrium
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our general method for exploring
00:00:12
electrochemistry
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is to consider what happens at these
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equilibria so firstly we established
00:00:17
this electrochemical equilibrium and
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then we disturb this equilibrium by
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applying an external potential now an
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electrochemical equilibrium is not the
00:00:26
same as a chemical equilibrium but the
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definition is we're looking at no net
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current flowing across the interface so
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if we look at what's going on in this
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interface here there will be a
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continuous exchange a constant exchange
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of electrons but there is no net current
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flowing so this is a dynamic equilibrium
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so this is different from a chemical
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equilibrium it is an electrochemical
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equilibrium so let's think about the
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different types of cells that we have
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that make use of this equilibrium so the
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first thing we're looking at is a
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galvanic cell so a galvanic cell has a
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spontaneous reaction which converts
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chemical potential to electrical energy
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when the switch for this galvanic cell
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is open no current can flow so there's
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an electrochemical equilibrium at the
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electrode surfaces we have this
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continual exchange of electrons that one
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and a continual exchange of electrons at
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the other but there is no net current
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flowing however each electrode is at a
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different potential when we close the
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switch current is allowed to flow we get
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spontaneous oxidation happening at the
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anode spontaneous reduction happening at
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the cathode and this difference in
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potential allows the current to flow
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lighting the bulb this particular cell
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I've drawn is an example of a cell known
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as a Daniell cell it is a standard cell
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for electro chemical equilibria it's
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well recognized and well understood so a
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galvanic cell relies on a spontaneous
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chemical process to convert to
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electrical energy so what other types of
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cell do we have well the electrolytic
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cell is the second type these ones have
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a non spontaneous reaction and these
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ones rely on putting electrical energy
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into the cell and it drives a non
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spontaneous process the example I've put
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here is electrolysis of water so we have
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a power supply which applies a potential
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difference which forces those fair
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to change which creates a reaction at
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each surface it raises the potential of
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one lowers the potential the other and
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drives the reaction forward rechargeable
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batteries are an example of something
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that behaves as both types of cell so a
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rechargeable battery is galvanic on
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discharging so it's supplying electrical
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energy to the appliance using that
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chemical energy to generate the
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electrical potential but when we want to
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put energy back into it for storage it
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becomes electrolytic as we charge it so
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it stores that electrical energy as
00:02:46
chemical potential the next phase of
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equilibria we want to look at is the
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Nernst equation so just a quick recap on
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this you covered this in year one I've
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linked the video below
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this relates electrode potentials to
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free energies and there are several ways
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to represent this but the main way that
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we're most familiar with is this form of
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the Nernst equation where we're looking
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at how the electrode potential varies
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according to the number of electrons
00:03:12
exchanged and the reaction quotient so
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it modifies the standard potential for
00:03:16
our real reaction conditions so remember
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the reaction quotient whenever we're
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looking at equilibria is a product of
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the activity to the right hand side
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divided by the products the activity to
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the left hand side you remember doing
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this as a products over reactants but
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when we're dealing with equilibria we
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don't really have products and reactants
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so we need to look at the different
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sides of the equation we normally use
00:03:40
concentrations rather than activities
00:03:41
assuming that the standard activity is
00:03:43
unity this only applies at very low
00:03:45
concentrations however but it means that
00:03:47
we end up with Q being unitless which
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makes life a lot easier
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so let's think about our reaction
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quotient here if we have our general
00:03:56
reaction remember we have the products
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of the right hand side divided by the
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products of the left hand side and at
00:04:02
low concentrations activities are
00:04:04
approximately equal to concentration so
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we can use this approximation this
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doesn't tell the whole story of course
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we need to look at the half equations
00:04:12
there's reduction half equations to find
00:04:14
the number of electrons that are being
00:04:15
transferred this allows us to establish
00:04:17
the value of n and therefore use the
00:04:19
Nernst equation
00:04:22
whenever we're thinking of using these
00:04:25
reactions we need to consider what
00:04:26
phases were working within so we're what
00:04:29
wondering whether we're looking at
00:04:30
solids liquids or gases so the first
00:04:33
thing to do is start with the half-cell
00:04:35
reactions so by convention we always
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write these as reductions so if we
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consider the phenomenon of the
00:04:41
electrolysis of water to release oxygen
00:04:43
gas we have liquid and gas present so
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have liquid water we have gaseous oxygen
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and we have aqueous hydrogen so how do
00:04:52
we treat the reaction quotient how do we
00:04:55
consider a concentration when we have
00:04:57
bulk liquid and bulk gas but whenever
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we're thinking of the solvent remember
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we're thinking about activities the
00:05:03
activity can be taken as a unity because
00:05:05
it is the solvent and the activity
00:05:07
doesn't change significantly as part of
00:05:09
the reaction so because it's not
00:05:11
changing we can accept it cancels out as
00:05:13
one for the gas we want to consider the
00:05:17
partial pressure so the partial pressure
00:05:19
of oxygen since the gases were almost
00:05:21
always working with atmospheric pressure
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and there are being evolved at
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atmospheric pressure and they are pure
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gases at the point of evolution we can
00:05:30
also take these as being unity so this
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allows us to simply consider this in
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terms of the aqueous terms now we need
00:05:37
to make sure we look at our pressures
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look at our concentrations to make sure
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that that still applies but almost
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always our gases and our solvents will
00:05:45
be considered under standard conditions
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so let's apply the Nernst equation to a
00:05:51
full cell so using this we can predict
00:05:54
the variation of cell potentials the
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spontaneous direction of reaction free
00:05:57
energy change okay this is a recap from
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what you've done before so let's think
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about the technique that we're going to
00:06:02
use so the first thing we need to do is
00:06:04
we need to write down the cell so we're
00:06:06
going to use the copper hydrogen cell
00:06:09
that I've detailed here the first thing
00:06:12
we need to do is you need to write down
00:06:13
the cell remembering to balance our half
00:06:15
cells so if we look at our two half
00:06:17
cells we can see that we don't have an
00:06:21
equal number of electrons so firstly we
00:06:23
need to balance the electron term we now
00:06:25
need to consider what we mean when we
00:06:26
say electrochemical versus chemical
00:06:28
equilibria electrochemical equilibria as
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we said has no net current and are the
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conditions for measuring cell potential
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but electrochemical equilibrium has to
00:06:37
be present otherwise we're not able to
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measure a cell potential when we set up
00:06:41
our cell like this our voltmeter has
00:06:42
have a very high internal resistance
00:06:44
that we don't get any current flowing so
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we don't allow current to flow therefore
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we've got electrochemical equilibria at
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both electrodes that allows us to
00:06:52
measure that cell potential chemical
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equilibrium however requires in a
00:06:57
slightly different definition it
00:06:59
requires that the Delta G for the entire
00:07:01
process is zero so remember that Delta G
00:07:04
is minus NFE that means that the cell
00:07:08
potential overall has to be zero but if
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we allow current to flow the cell
00:07:12
potential is clearly not zero so we need
00:07:14
to reach a different state so a galvanic
00:07:17
cell at equilibrium remember galvanic
00:07:19
cell is where we have a spontaneous
00:07:20
current flowing a chemical equilibrium
00:07:23
the cell potential will be zero which
00:07:26
means Q equals K so the reaction
00:07:28
quotient is the equilibrium constant we
00:07:30
can use this equilibrium constant
00:07:33
because it's related to the standard
00:07:35
cell potential anyway what this allows
00:07:37
us to do is it allows us to predict an
00:07:39
equilibrium constant from a measured
00:07:41
standard potential so we can get at the
00:07:43
equilibrium constant by using the cell
00:07:46
potential which is not measured at
00:07:47
chemical equilibrium so what does this
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mean what we can find
00:07:52
okay let's consider an equilibrium such
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as this one where we have the solvation
00:07:56
of silver bromide
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it's a sparingly soluble salt so be a
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minute being able to measure this
00:08:02
solubility product so essentially the
00:08:05
equilibrium product for this dissolution
00:08:06
becomes very tricky because we have a
00:08:09
very low solubility so how do we predict
00:08:11
it well once again we can use
00:08:13
electrochemistry so we need
00:08:15
electrochemical potentials to generate a
00:08:18
reaction and we can work backwards from
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that to determine our equilibria
00:08:22
constant for this dissolution so these
00:08:25
are the two cells that we're interested
00:08:26
in and we just apply the same rules as
00:08:29
we did before we combine needs to make
00:08:31
the original equation and identify that
00:08:33
the standard electrode potential for
00:08:35
that reaction now the key thing is that
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the overall reaction is not a redox
00:08:39
process this cell is purely hypothetical
00:08:42
so the cell isn't actually real but we
00:08:45
use it for the purposes of this
00:08:47
investigation
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so once again let's revisit the copper
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hydrogen cell we spoke a little bit
00:08:54
about what's the sound of one hand
00:08:55
clapping remember we can't measure these
00:08:57
things in isolation so every half cell
00:08:59
is measured relative to that standard
00:09:01
hydrogen electrode but what does the
00:09:04
standard electrode potential actually
00:09:06
mean for a half cell you know what what
00:09:08
meaning do we ascribe it well
00:09:10
fundamentally it's a balance point it's
00:09:12
not saying that it is not 0.34 volts to
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drive copper in this direction it's
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saying that the copper 1/2 cell is 0.34
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volts more positive than the standard
00:09:25
hydrogen electrode it's just a relative
00:09:27
measurement so it shows the potential
00:09:30
that we would need to apply to switch
00:09:32
from galvanic to electrolytic cell
00:09:34
behavior if we want to look at how other
00:09:38
half cells compare we need to think
00:09:40
about free energies we can pretty much
00:09:42
measure anything we wish but it's
00:09:45
important that we consider free energies
00:09:47
it's not always possible to directly
00:09:49
compare electrode potentials remember
00:09:52
that not all half cells can be directly
00:09:53
measured so we use this relative
00:09:55
comparison between half cells to
00:09:57
determine the standard electrode
00:09:58
potential for hypothetical half cells
00:10:01
because not all of them could be
00:10:02
directly measured so let's think about
00:10:04
the direct reduction of our iron 3 to
00:10:06
learn most electron processes our single
00:10:09
electron or pair of electrons if we
00:10:11
think about iron three-plus well we can
00:10:13
either add one electron to become iron
00:10:15
two-plus or four iron to plus we can add
00:10:17
two electrons to become iron metal now
00:10:19
we can't combine these because the
00:10:21
electrons don't counsel we can't equate
00:10:24
these we can't multiply them up nothing
00:10:26
is going to cancel out because the
00:10:27
electron terms don't work we can't
00:10:30
double this first one then we end up
00:10:31
with two Fe three-plus and two Fe 2 plus
00:10:33
we would just end up with 3 iron species
00:10:36
in our final equation so because the
00:10:39
electrons don't cancel we have to use
00:10:40
free energies we convert these electrode
00:10:42
potentials into free energies for each
00:10:44
process so what we do is we simply add
00:10:47
both of them together to obtain the
00:10:48
overall equation and then we add the
00:10:51
free energies together so you can see if
00:10:53
we add these together the iron two terms
00:10:55
cancel out we gain an electron and that
00:10:57
gives us the overall cell equation here
00:11:00
okay but
00:11:02
we do in terms of free energies well we
00:11:04
just simply work out the free energy for
00:11:05
each of them so the free energy for the
00:11:09
first equation simply becomes one one
00:11:11
electron times the faraday constant
00:11:12
times 0.77 one the second one becomes
00:11:15
two times - 0.44 times the Faraday
00:11:19
constant which gives us our final value
00:11:22
of + naught point 109 times the faraday
00:11:25
constant which gives a final cell
00:11:27
potential when we work backwards we
00:11:30
simply apply this equation in Reverse
00:11:32
and we end up with a cell potential of
00:11:33
negative naught point naught 3 6 so this
00:11:36
allows us to determine the cell
00:11:37
potential of any electrode provided we
00:11:39
can establish how we can put it together
00:11:42
from the existing measurable electrodes
00:11:44
this is similar to the process I spoke
00:11:46
about before with the law of independent
00:11:48
migration and the similar principle
00:11:50
you've applied with Hess's law and any
00:11:52
other situation where you use a number
00:11:54
of known quantities to find the unknown
00:11:55
to close the loop so we have all these
00:11:58
electrode potentials that we can
00:11:59
determine remember we said that a
00:12:02
standard electrode potential is simply a
00:12:03
relative measurement it's saying that
00:12:05
something is however much more positive
00:12:08
or negative than the hydrogen electrode
00:12:10
but this means it can be helpful to have
00:12:12
a visual aid whenever we think of visual
00:12:14
aids we think of drawing a graph the way
00:12:16
that we typically visualize electrode
00:12:18
potentials is to plot current against
00:12:20
potential and think about where we're
00:12:21
starting where we're going from so when
00:12:23
we're thinking about electrochemical
00:12:25
equilibrium if you've got a current
00:12:26
potential graph is zero so everything
00:12:29
becomes single dimension in this
00:12:31
particular visualization so we're going
00:12:33
to plot our standard electrode
00:12:34
potentials at I equals 0 our standard
00:12:37
hydrogen electrode by definition is at
00:12:39
zero so this is assuming standard
00:12:41
conditions where the activity of
00:12:42
hydrogen is 1 the partial pressure of
00:12:44
hydrogen is 1 let's look at the copper
00:12:47
electrode that we spoke about so once
00:12:49
again let's say we've got an activity of
00:12:51
1 this is standard conditions remember
00:12:53
and we have our standard potential marks
00:12:57
at 0.34 volts our silver electrode again
00:13:02
standard conditions has a more positive
00:13:05
potential so what we're saying is that
00:13:08
both of these are positive relative to
00:13:11
the standard hydrogen electrode but
00:13:12
we're saying now
00:13:14
that our silver chloride is 0.46 volts
00:13:17
more positive than our copper likewise
00:13:21
our copper is 0.46 volts more negative
00:13:23
than our silver electrode these are
00:13:26
simply just relative measures and this
00:13:29
graph helps us visualize them if we
00:13:32
change our concentration from standard
00:13:33
conditions we'll get a different
00:13:35
potential so if we take the silver
00:13:37
chloride and we reduce the concentration
00:13:40
we find we reduce it to 1 millimolar we
00:13:44
find that applying the Nernst equation
00:13:46
we end up with a drop in our cell
00:13:48
potential to 0.62 volts this is still
00:13:51
more positive than our copper electrode
00:13:53
so our overall cell potential we would
00:13:56
find by simply finding the difference
00:13:58
between the two in terms of trying to
00:14:00
predict what's going on here if we draw
00:14:03
a graph like this one way to remember it
00:14:05
is that whatever is on the right is the
00:14:08
species being reduced so in this cell we
00:14:10
would expect the silver cation to be
00:14:12
reduced while the species on the left we
00:14:15
would expect copper methyl to be
00:14:17
oxidized to copper two-plus and this
00:14:21
gives us a simple way of picturing
00:14:23
what's going on if we then allow a
00:14:26
current to flow we can then apply an
00:14:28
external voltage to drive a reaction in
00:14:30
a particular direction that we wish so
00:14:33
if we apply a higher voltage remember
00:14:36
this raises and lowers the electrode
00:14:38
potentials and drives the reaction a
00:14:40
different way to summarize electrode
00:14:43
potentials it's always helpful to have a
00:14:45
visual aid our standard cell potential
00:14:48
for any system will never change it's
00:14:49
measured under standard conditions and
00:14:52
fundamentally free energy still govern
00:14:54
all processes only the free energy can
00:14:57
be used to predict the direction of
00:14:58
spontaneity so whenever we have our cell
00:15:00
we would need to formally convert to a
00:15:02
free energy to determine the direction
00:15:04
of spontaneous change and concentration
00:15:07
has a big effect on cell potentials so
00:15:09
everything's under standard conditions
00:15:10
but the minute we change that
00:15:11
concentration we get a different cell
00:15:13
potential these visual representations
00:15:16
can be really helpful to work out what's
00:15:18
going on because sometimes a quick
00:15:19
sketch can allow us to just
00:15:21
discombobulated the mathematics going on
