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in the last session we explored the
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thermodynamics of electric processes in
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this session we're now going to look at
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the kinetics of what goes on at the
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electrode so we looked at what happens
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when we have equilibrium established at
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the electrodes but now let's consider
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what happens when we allow a current to
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flow at the electrodes so we've
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established what happens with electro
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chemical equilibria but now what we're
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going to do is explore what happens when
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we disturb that equilibrium by applying
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an external potential fundamentally we
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want to look at what happens to the
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current as the potential varies what we
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expect to happen and what predictions
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can we make if we apply a higher
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potential difference do we get a higher
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current is there a linear relationship
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between them and should there be a
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linear relationship between them through
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exploring these questions we will start
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tricks find out what's going on at the
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electrode fundamentally in chemistry we
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want to consider rates of reaction so
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when we think of regular reactions we
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apply the principles of these rate laws
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so we're familiar with forming a rate
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equation such as this the rate of change
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of the concentration of a with respect
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to time is equal to the negative of the
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rate constant times concentration this
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is for a first order process we can
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apply similar principles to electrode
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processes so at the electrode what's
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going on well let's think first of all
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we are transferring a certain number of
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electrons if we're transferring a
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certain number electrons we can then
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consume a certain fraction a certain
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proportion of reactants so we have n
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moles of reactant being consumed this of
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course it assumes a single electron
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process so this means that we can find
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the overall charge transferred be Q as a
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number of electrons times Faraday's
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constant multiplied by the number of
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moles of reactant consumed so this is a
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simple relationship between charge and
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the amount of reaction that we're
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working with when we think of charge
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transfer we start to think of what's
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going on with the electric current
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because the current is the thing that we
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measure remember that current is simply
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the rate of charge transfer so the rate
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of transfer charge with respect to time
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this gives us the current that we can
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observe but we also have our rate of
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reaction which is the rate of change of
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our reactant as a function of time as
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well so fundamentally we are looking at
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a rate equation whether it's a rate of
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transfer of charge or a rate of
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consumption of
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reacting looking at this equation here
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between the overall charge transferred
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and the amount of reaction we have
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present all we need to do is find our
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derivative our first derivative with
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respect to time so if we differentiate
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both sides we'll get an expression the
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rate of charge transfer with respect to
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time our current can be equated to the
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rate of the reaction and the faraday
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constant so this is a fairly
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straightforward way to look at the
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current flowing through our
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electrochemical cell and the reactions
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happening at the electrode to understand
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a bit more we need to go back to the
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area considerations remember we looked
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at the areas of electrodes because this
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is quite an important aspect of it many
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considerations that we work with involve
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using conductivity and conductivity
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fundamentally is an area function so
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working with these cross-sectional areas
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becomes very very useful we apply
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similar principles to the electric
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processes and the reasoning for that
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will become clear later on but we are
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looking at the rate of a reaction per
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unit area so if we take our rate of
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reaction we simply divide it by the area
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of the electrode we get an expression
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which relates our current to the area of
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those electrodes the important thing we
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need to recognize here is that the
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current that flows is a representation
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of that rate of reaction if the reaction
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happens faster we would expect to get a
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faster rate of transfer of electrons
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which would lead to a higher current
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observed in the circuit around the cell
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why is the area important well let's
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look at what's going on at the electrode
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so if we think about what's going on at
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this electrode let's consider the
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cathode at first so cations these A plus
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ions will gather at the surface of that
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electrode and they'll just deposit in a
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layer remember we saw this when we were
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looking at the inner Helmholtz plane and
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the diffuse double there in one of our
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earlier sessions so electrons will
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transfer from our electrode to our
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caffeine reducing it and it will deposit
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this atomic a at the surface so what
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happens to the surface so as each layer
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of cations is deposit at the surface and
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fundamentally reduced this surface will
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advance so as each layer gets there we
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extend the electrode surface and we get
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a similar process happening in Reverse
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at the anode so when we consider the
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overall area of the electrode the
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greater the area the more cations can
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access the electrode and deposit metal
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atoms at the surface
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the rate expression therefore has to
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include an element of the area and we
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see that that rate expression
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demonstrates the area deposition the
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overall area of that electrode we want
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to think of the rate of this reaction
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the reaction that we consider is
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first-order all that needs to happen is
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the cation just needs to get to the
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surface what that means for our rate
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equation is that it becomes the amount
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of material produced per unit area per
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unit time so the bigger the electrode
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the faster the rate the smaller the
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electrode the slower the rate so if we
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have a larger electrode area we get more
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sites and larger area as we've said
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gives us a higher rate this means
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overall our rate equation which we're
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familiar with becomes this rate whatever
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that might be is a rate constant times
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the concentration of X the more of X we
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have in solution the faster rate it's
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going to go it's worth considering the
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units of the rate constant of
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centimeters per second make sure that
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you can rationalize this given that the
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concentration could be considered as
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moles per cubic centimeter slightly
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different to the moles per decimeter
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that you're used to but it is a
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congruent unit once we've considered
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both processes we can now start to look
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at the overall rate of reaction at any
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electrode we need to consider both
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processes we need to consider the
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oxidative process and the reductive
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process happening at that electrode at
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equilibrium at that electric and that
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electrochemical equilibrium these
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processes are equal because there's no
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net flow of charge but as we change the
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potential one of them begins to dominate
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whether we raise the potential or
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whether we lower the potential so we can
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consider this equilibrium in this manner
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so the overall rate is a balance of each
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process the cathodic process where the
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oxidated species is reduced and becomes
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the reduced species so the rate of this
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the forward reaction is what's happening
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in a cathodic process while the analytic
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process the reduced species goes
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backwards to the oxidized species and
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gives us an alternative rate constant so
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looking at these rates at a single
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electrode remember we can consider that
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the overall rate is the sum of the
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forward and back processes so we have
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our forward process and our back process
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which all add up to give us an overall
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rate of reaction which we
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earlier defined as this derivative
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because we have this area function this
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I over a it's easier to think of a
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current density rather than the current
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itself
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remember back in session three we talked
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about charge flux and how that passes
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through a particular area of solution if
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we consider it if we now substitute this
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J term in our current density this makes
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our overall equation for a single
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electric process where N equals one is
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simply the Faraday constant times the
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rates that we've disturbed there are a
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number of factors which affect our rate
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constant the main one we're going to be
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looking at is the effect the applied
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potential but there are a number of
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things that can affect it whether it's
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looking at temperature effects or
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potential effects remember also that
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your rate constant depends on the
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energies of activation so this is
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something you're familiar with from your
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Arrhenius relationship this Delta G
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dagger is the energy of activation you
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previously knew as EA but you'll find
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that in textbooks much as Delta G dagger
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a fraction of this free energy helps the
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oxidation so one proportion of it
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enhances the oxidative process but the
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remaining fraction of that Delta G
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inhibits the reduction so it's blocks
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reduction from happening this leads us
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to the butler-volmer relation which
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simply relates our observed current
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density to the oxidative process and the
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reductive process where we have this
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enhancement of oxidation due to alpha
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while the remaining is their inhibition
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of the reductive process it's worth
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briefly drawing your attention to the
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fact that we have introduced another
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symbol so we've introduced this ETA term
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which we've seen already to represent a
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viscosity but in this case it represents
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an over potential if you're ever in any
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doubt as to what the symbol might mean
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look at the units remember that the
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overall units of this expression have to
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go to zero so the over potential here is
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measured in volts and that will allow
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your units to cancel so what is this
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over potential well put simply the over
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potential is the difference between the
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elec were Librium potential and the
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actual potential of an electrode so if
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you think of your equilibrium cell
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potential you
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calculate that remember we did that in
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part two but the difference once we find
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our equilibrium cell potential we simply
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subtract that from the applied potential
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what we're applying to that particular
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electrochemical cell we can apply that
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potential from a voltage source whether
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it's a battery or a potential stat and
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this has an effect on the Fermi level as
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we spoke about in the last session if we
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have a positive over potential that
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creates a higher potential which has the
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effect of lowering the electron energy
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so the Fermi level decreases and that
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reduces the free energy barrier for
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oxidation so our species then can easily
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be oxidized at the electrode and that's
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our reaction proceeds however if we
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create a negative over potential it
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creates a lower potential which
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increases the electron energy it has the
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effect of raising the Fermi level once
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we have raised the Fermi level it
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reduces the free energy barrier for
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reduction so our material is then
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reduced at the electrode to summarize
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our overview of the kinetics of
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electrodes we have to consider the fact
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that the rates of oxidation and
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reduction depend on the available
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surface area we manage this by using our
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current density this J term which is
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simply the current flowing divided by
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the area available in the electrodes
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Ritz our first order of that electrode
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service this allows us to very easily
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and simply qualify what's going on at
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the electrode at equilibrium no current
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flows around our cell so we have this
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constant exchange of charge at an
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electrode interface where the rate of
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reduction is equal to the rate of
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oxidation so the charge transfer cancels
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out on both sides once we start applying
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potential we start to change the rate of
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what's going on at that electrode if we
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have a positive over potential ie we
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have a more positive potential than the
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equilibrium State we will get oxidation
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of the species favored at that electrode
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while if we lower the potential if you
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have a negative over potential it will
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favour the reduction of what's going on
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once we've applied that potential if we
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then complete the circuit we then
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satisfy the conditions and the current
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will flow from the anode to the cathode
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and will
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do electrical work as it does so
