00:00:00
we've looked at solvents and now we need
00:00:02
to look at the behavior of ions in
00:00:03
solution so remember we just find a few
00:00:06
basic terms without terms of our ions
00:00:08
are cations cathode anions anode but
00:00:10
fundamentally ions are what gives
00:00:12
solutions our conductivity so whenever
00:00:14
we think of a current flowing in a
00:00:16
solution we have to visualize it as a
00:00:18
flow of ions not a flow of electrons
00:00:20
whenever we make conductivity
00:00:21
measurements these can all be traced
00:00:24
back to ionic interactions to how these
00:00:26
ions behave in solution the ionic
00:00:28
mobility that we discussed is a
00:00:30
phenomenon which links the measurable
00:00:32
quantities to do with the currents that
00:00:34
we observe in solution as well as the
00:00:36
theoretical quantities in terms of the
00:00:38
limiting conductivity of an ion well
00:00:41
first introduce some basic concepts to
00:00:43
cover mobility in solutions the first of
00:00:45
these is diffusion diffusion is simply
00:00:48
motion due to concentration differences
00:00:50
so if we have a concentration of ions in
00:00:54
one part of the solution we would expect
00:00:55
these to diffuse through the solution so
00:00:58
that we get an even concentration
00:01:00
throughout this applies to all molecules
00:01:02
in that solution migration by comparison
00:01:05
is motion due to electric fields so if
00:01:07
we put an electric field across our
00:01:08
solvent we would expect our ions to move
00:01:12
in the direction of that electric field
00:01:14
relevant to their charge it only applies
00:01:16
to charged particles in solution so
00:01:18
these ions that we're talking about the
00:01:21
third motion of mobility is something
00:01:22
called convection which is motion due to
00:01:24
thermal phenomena or simply stirring a
00:01:26
solution it's not considered in this
00:01:28
course but it's something to be aware of
00:01:29
as it's something you are probably
00:01:31
already familiar with in order to make
00:01:33
measurements on electrochemical cells we
00:01:35
need to establish some basic electrical
00:01:38
concepts so this will require a little
00:01:40
bit of physics revision but it's vital
00:01:42
to understand the first of these is
00:01:43
current current is simply the flow of
00:01:45
charge and how it moves around a circuit
00:01:48
so the current can be delivered a number
00:01:50
of different ways but fundamentally it
00:01:51
is a transfer of charge voltage is
00:01:54
another one but we would tend to talk
00:01:56
about it in terms of a potential
00:01:57
difference and we'll talk about that
00:01:58
later in the course but a voltage is
00:02:00
something that can be very easily
00:02:01
measured using a voltmeter the next
00:02:03
phenomena to consider it's resistance
00:02:05
which carries the unit of ohms
00:02:07
resistance is simply the resistance to
00:02:09
carrying electrical charge the greater
00:02:10
the resistance the greater the potential
00:02:12
difference required to push
00:02:13
current through that conductor power is
00:02:15
another phenomena we need to discuss
00:02:17
power is simply the rate of transfer of
00:02:20
energy so in electrical terms it's a
00:02:23
relationship between the current and the
00:02:25
voltage the last one which is slightly
00:02:26
different is conductance G which is
00:02:29
simply the inverse of the resistance so
00:02:32
the greater the conductance the lower
00:02:34
the resistance and these are all kind of
00:02:36
fairly we're fairly comfortable with
00:02:38
these ideas but it's important to lay
00:02:41
down which ones we're going to be using
00:02:43
when we think of electrochemistry we
00:02:45
think of solution conductivity so we
00:02:46
tend not to think about what's going on
00:02:48
in the external circuit we only think
00:02:50
about what's going on in solution
00:02:51
between our two electrodes this is as we
00:02:53
said a couple times before is the result
00:02:55
of the mobility of charges it's not a
00:02:58
straightforward process so we need to be
00:03:00
aware of what it is we need to consider
00:03:02
and at this point it's worth flagging up
00:03:04
the conductivity is different to
00:03:06
conductance so I mentioned conductance
00:03:08
in the previous slide I mentioned them
00:03:10
both to avoid confusion conductivity is
00:03:13
simply the ability for a solution to
00:03:15
carry a current through motion of ions
00:03:16
where it's conductance is simply the
00:03:19
ability to pass current so conductance
00:03:21
applies to anything which carries
00:03:22
electricity but conductivity is specific
00:03:25
to the solution and it's conductivity
00:03:26
that we're going to be looking at in
00:03:28
this course measuring conductivity is a
00:03:32
slightly tricky but it's a fairly
00:03:34
straightforward procedure once we see
00:03:36
what's going on to do it we need to take
00:03:38
two equally sized electrodes so we have
00:03:40
our cathode of a given area and we have
00:03:42
an anode of equal area we make sure that
00:03:44
these are parallel and we separate them
00:03:46
by a fixed distance we can then apply a
00:03:48
potential difference across them and
00:03:50
measure the current that goes through
00:03:51
the solution this allows us to determine
00:03:53
the resistance via this V equals IR
00:03:56
relationship so just rearrange this
00:03:58
divide both sides by AI and we get a
00:04:00
value for the resistance this gives us a
00:04:02
value for that solution conductivity
00:04:04
which carries a symbol Kappa which Greek
00:04:07
letter K and it has the units of per ohm
00:04:11
per meter and we simply use this
00:04:12
equation to determine our solution
00:04:14
conductivity a solution conductivity is
00:04:16
measured but it only relates that
00:04:18
particular solution that we've measured
00:04:19
at the time a more useful measurement is
00:04:21
the molar conductivity so looking at how
00:04:23
the conductivity of a solution varies
00:04:25
with its concentration this is known as
00:04:27
the
00:04:27
molar conductivity encouraged this
00:04:28
symbol lambda so this is a capital
00:04:31
lambda with subscript M for molar
00:04:33
conductivity and this eliminates the
00:04:35
effect of concentration so this will
00:04:37
give us the molar conductivity for any
00:04:39
solution of a particular analyte that
00:04:41
we're interested in now the units of the
00:04:43
molar conductivity can be complex so
00:04:45
Kappa is in Peron per meter the
00:04:48
concentration C is in moles per cubic
00:04:50
meter we're trying to keep an SI units
00:04:52
remember we're normally used to diem per
00:04:55
diem cubed here we're interested in
00:04:57
meter cubed while limiting molar
00:04:59
conductivity in ohms per square meter
00:05:01
ohm square meter per mole these units
00:05:03
can be complex but it's important you're
00:05:05
able to move between them when we look
00:05:06
at the actual formula itself when we see
00:05:08
these units written down we normally see
00:05:10
them in the square centimeter unit so
00:05:13
it's important that you're happy with
00:05:15
this particular conversion because the
00:05:17
conversion is absolutely vital
00:05:19
remember we're stressing how to convert
00:05:21
units all the way through your course so
00:05:23
make sure you're happy with this unit
00:05:24
conversion when we think of conductivity
00:05:27
we want to look at the concentration so
00:05:29
concentration as I'm sure is no surprise
00:05:31
greatly affects the conductivity of a
00:05:33
solution and the common way of thinking
00:05:35
about it is that higher concentration
00:05:37
gives higher conductivity because the
00:05:39
reasoning is that we have more ions in
00:05:41
solution so there are more current
00:05:42
carriers this seems a perfectly logical
00:05:44
way to think however as is always the
00:05:48
case it's never quite as simple and when
00:05:50
we measure our conductivity we find that
00:05:52
actually as the concentration increases
00:05:54
we get a decrease in the molar
00:05:56
conductivity so it does vary with
00:05:59
concentration but in the opposite way
00:06:02
that we would predict so this seems
00:06:03
extremely strange so we need to under
00:06:05
unravel why that's the case we also see
00:06:08
here we've got two electrolytes we've
00:06:09
got a strong electrolyte potassium
00:06:11
chloride I've got a weak electrolyte of
00:06:13
ethanoic acid so we need to unravel this
00:06:17
a little bit because again not only does
00:06:19
it depend on concentration but it also
00:06:21
depends on the type of electrolyte
00:06:23
although in this case the fact that the
00:06:26
weak electrolyte has a lower
00:06:27
conductivity should probably doesn't
00:06:29
surprise us because we would expect
00:06:30
fewer current carriers but this is in
00:06:33
contravention with what we see it
00:06:35
increasing concentrations so let's start
00:06:37
looking at these phenomena the
00:06:39
electrolyte itself is extremely
00:06:41
important so when we think of strong
00:06:43
electrolytes we assume them to be 100%
00:06:46
dissociated into ions so HCl KCl and so
00:06:50
on and so forth we have 100%
00:06:52
dissociation so we would expect there to
00:06:54
be a commensurate effect on the
00:06:55
conductivity but the degree of
00:06:57
dissociation depends on the solvent we
00:06:59
almost always consider water but what
00:07:01
happens if we deal with a completely
00:07:02
nonpolar solvent if we consider
00:07:04
something like dry HCl in benzene so
00:07:08
this is a very very weak electrolyte and
00:07:10
HCl will tend to clump together as ion
00:07:12
pairs by in pairs have a net charge of
00:07:15
zero and when we apply a potential
00:07:16
difference across this no current flows
00:07:19
so we need to consider what's going on
00:07:21
there we saw that the conductivity
00:07:22
decreases with concentrations so to
00:07:24
understand that we need to look into
00:07:26
these ion-ion interactions and ions
00:07:28
solvent interactions the more the ions
00:07:30
interact with themselves the less
00:07:32
current will flow but the more it
00:07:33
interacts with the solvent we'll get
00:07:35
more of an effect on the conductivity so
00:07:37
at these very low concentrations we see
00:07:39
we have an increase in the conductivity
00:07:40
which seems completely counteract
00:07:42
counter intuitive at this point we're
00:07:45
going to introduce the phenomenon of
00:07:46
infinite dilution this seems like a very
00:07:48
strange one to think of but it's a way
00:07:50
of unifying molar conductivity and
00:07:52
allows us to study it in more detail the
00:07:55
method has come up by Friedrich Kohl
00:07:56
rush who proposed our limiting molar
00:07:59
conductivity at zero this is simply an
00:08:01
extrapolation to zero concentration
00:08:03
what is our conductivity at zero
00:08:06
concentration so at zero concentration
00:08:08
we have no ion-ion interactions almost
00:08:11
by definition and our molar conductivity
00:08:13
is highest at infinite dilution because
00:08:15
there are no ion-ion interactions are
00:08:17
slowed down in migration the limiting
00:08:18
molar conductivity is simply defined as
00:08:20
the sum of the limiting molar
00:08:22
conductivity of each of the ions so that
00:08:24
the positive ion and the negative ion so
00:08:27
let's unravel this a little bit because
00:08:28
it seems a bit odd how can we measure a
00:08:30
conductivity at effectively zero
00:08:32
concentration so let's explore this a
00:08:34
bit firstly let's consider the ionic
00:08:37
atmosphere remember that we said this
00:08:38
was the surrounding atmosphere of ions
00:08:40
around a central charge it's spherical
00:08:43
and symmetric in the absence of an
00:08:45
electric field
00:08:45
now I'm not going to put all the other
00:08:47
counter ions in here but assume there
00:08:49
they are present as soon as we apply an
00:08:51
electric field so as soon as this goes
00:08:53
into
00:08:54
an electric field between two electrodes
00:08:56
this ionic atmosphere starts to be
00:08:59
distorted so think about the shape the
00:09:01
overall shape of it
00:09:02
remember the ionic caps here will have
00:09:04
an opposite charge to the central line
00:09:06
which means it's attracted to the other
00:09:07
electrode this causes drag on the eye
00:09:10
and it slows the ions migration down
00:09:12
this is something known as the
00:09:14
relaxation or the asymmetric effect but
00:09:16
when we get to low concentration to
00:09:18
remember that ionic atmosphere increases
00:09:20
in size and becomes more diffuse so the
00:09:22
more diffuse it is the less drag it
00:09:24
causes so lower concentrations get less
00:09:26
drag we get less of an effect on the
00:09:28
mobility of the ion which increases the
00:09:31
molar conductivity the next thing we're
00:09:33
going to look at is the solvent so
00:09:35
remember solvation shells so around a
00:09:37
central ion the solvent will organize
00:09:38
itself and be tied into a solvation
00:09:40
shell so whenever an ion in solution is
00:09:42
solvated and it migrates it's going to
00:09:45
be carrying the solvent molecules with
00:09:46
it
00:09:46
which gives it more mass which also
00:09:49
increases the drag in solution so as it
00:09:52
migrates towards the opposite charged
00:09:54
electrode it's dragged more it's held
00:09:57
back more by the solvent in solution
00:09:59
this is something called the electro
00:10:01
phoretic effect and it's in informally
00:10:04
termed solvent drag at lower
00:10:07
concentrations we get less drag well why
00:10:09
is this well if we think about lots of
00:10:11
these solvated ions moving together they
00:10:15
have to push past each other they have
00:10:16
to jiggle past each other but at lower
00:10:19
concentrations there is more free
00:10:21
solvent which means there is more space
00:10:23
between the ions and it's easier for
00:10:25
those salvation' shells to slip past
00:10:26
each other the next thing we're looking
00:10:28
at is the effect of ion pairing so
00:10:30
remember that direct ion ion pairs
00:10:33
occur when we don't get salvation so if
00:10:36
we imagine this ion ion pair forming
00:10:38
here but we also have some ions free in
00:10:40
solution as well the ion pair carries no
00:10:43
charge
00:10:43
so when we put it into an electric field
00:10:45
count free counter ions move but the ion
00:10:48
pair stays locked together when we have
00:10:51
low concentrations we get less pairing
00:10:53
happening so they're proportionally
00:10:55
fewer uncharged ion pairs consequently
00:10:57
if you have fewer ion pairs the net
00:10:59
mobility of ions in solution increases
00:11:01
as well so we have all of these
00:11:03
different effects happening we have the
00:11:05
ionic atmosphere becomes more diffuse at
00:11:07
low concentrate
00:11:08
increasing mobility the solvent
00:11:11
salvation shells interact less with each
00:11:13
other so there's increased mobility at
00:11:15
low concentrations and we get less iron
00:11:17
pairing at low concentration which
00:11:19
increases the mobility of the ions so
00:11:21
all these effects serve to increase the
00:11:24
mobility which increases the molar
00:11:26
conductivity when we think about weak
00:11:28
electrolytes they are different the
00:11:30
strong electrolytes but
00:11:31
electrochemically it's important to
00:11:33
consider what they're doing as well so
00:11:35
let's consider our acetic acid
00:11:37
dissociation so we have a seating acid
00:11:39
plus water dissociates into the
00:11:41
hydronium ion and the acetate r9 these
00:11:44
have lower conductivity and strong
00:11:46
electrolytes this shouldn't be a
00:11:47
surprise to us there are fewer charge
00:11:49
carriers due to the lower dissociation
00:11:50
and consequently we can ignore the ion
00:11:52
ion interactions but as the
00:11:55
concentration drops the dissociation
00:11:58
constant remains a constant at a given
00:12:00
temperature but the proportion of the
00:12:03
acid dissociated changes
00:12:05
this may seem slightly odd but if we
00:12:07
look at this particular equation here
00:12:08
we're looking at the only thing we're
00:12:10
interested in the concentration of water
00:12:11
we're going to assume as constant will
00:12:13
eliminate that we have our dissociation
00:12:16
constant but it takes the form of x
00:12:19
squared over Y so we've got two values
00:12:21
that are squared remember the hydronium
00:12:23
ion and the acetate ion are an equal
00:12:27
concentration so x squared divided by
00:12:29
the concentration of our acetic acid
00:12:31
what happens as each thing varies
00:12:34
well let's rearrange this equation let's
00:12:36
make the concentration of the acetic
00:12:38
acid the subject so this varies with x
00:12:41
squared if we increase the stock
00:12:43
concentration by 4 this means the
00:12:46
hydroxo nehemiah the thing we're
00:12:48
interested in one of the charge carriers
00:12:50
only increases by two whereas let's go
00:12:53
the other way if we decrease the
00:12:55
concentration of this by a hundred the
00:12:57
concentration of the kept charge
00:12:59
carriers only decreases by 10 so because
00:13:02
of this we get this greater and greater
00:13:05
dissociation at lower and lower
00:13:07
dilutions to a point where at infinite
00:13:09
dilution we have 100% dissociation we
00:13:12
get the same behavior as for strong
00:13:14
electrolytes however measuring the
00:13:16
conductivity of weak electrolytes
00:13:17
becomes a challenge in order to overcome
00:13:20
this we need to consider the
00:13:21
of independent migration this describes
00:13:24
how ions behave and its core assumption
00:13:27
is that electrolyte behavior an infinite
00:13:30
dilution is identical so remember that
00:13:32
we had these definitions for the sums of
00:13:34
it for infinite dilutions so at infinite
00:13:37
dilution we would have for HCl we would
00:13:40
say that the overall molar conductivity
00:13:43
at infinite dilution is equal to the sum
00:13:45
of each of the molar conductivity of
00:13:47
each of the constituent ions so that
00:13:50
seems fairly straightforward that's
00:13:52
absolutely fine we're okay with that but
00:13:54
a thing to remember with the independent
00:13:55
migration is that whatever we're working
00:13:57
the conductivity of the proton is the
00:14:00
same regardless of where it comes from
00:14:01
regardless of whether it comes from HCl
00:14:03
sulfuric acid whether it comes from
00:14:05
ethanoic acid or whether it even comes
00:14:07
from water itself this allows us to
00:14:09
determine the limiting molar
00:14:10
conductivity for any weak electrolyte we
00:14:12
can't measure it directly because we
00:14:14
can't measure a limiting contact if we
00:14:16
have to predict it based on the
00:14:17
observations we make but because this
00:14:19
isn't fully dissociated because the
00:14:22
ethanoic acid isn't fully dissociated we
00:14:24
can't measure it directly so we need to
00:14:26
work around a little bit but we use this
00:14:28
idea that the molar limiting molar
00:14:30
conductivity for any ion is the same
00:14:32
regardless of where it comes from all we
00:14:35
need to do to calculate the limiting
00:14:37
molar conductivity for acetic acid is
00:14:39
just to find strong electrolytes that
00:14:41
provide the data we need as it happens
00:14:43
there's a complete set we can use we can
00:14:45
use the limiting molar conductivity of
00:14:46
hydrochloric acid this will give us our
00:14:48
limiting molar conductivity of a proton
00:14:50
which is what we need and we can use the
00:14:52
limiting molar conductivity of sodium
00:14:54
acetate this is a strong electrolyte
00:14:57
remember it's 100% associated this will
00:15:00
give us the limiting molar conductivity
00:15:01
of the ethanoate ion and then we can
00:15:05
simply just substitute use these into
00:15:07
the original equation to get our final
00:15:09
expression you've used a method very
00:15:11
similar to this whenever you were doing
00:15:13
hess cycles for solving simultaneous
00:15:15
equations in maths and so on simply
00:15:17
we're looking for the terms that we can
00:15:19
substitute into our equation remember we
00:15:21
can treat chemical equations just like a
00:15:23
mathematical one so let's do this it's
00:15:26
fairly straightforward to get the proton
00:15:28
so if we look at this is the equation
00:15:30
we're interested in we want to find the
00:15:31
limiting molar conductivity of ethanoic
00:15:33
acid so
00:15:35
let's look at our proton first very
00:15:37
straightforward if we consider
00:15:38
hydrochloric acid is the limiting molar
00:15:41
conductivity of hydrochloric acid is
00:15:42
simply the sum of the proton and the
00:15:44
chloride let's rearrange that subtract
00:15:46
the chloride from both sides and we get
00:15:48
an expression here which is simply the
00:15:50
molar conductivity of the proton we can
00:15:52
just take this and replace the proton
00:15:55
conductivity in the original equation
00:15:57
which gives us this expression here so
00:15:59
we've got the limiting molar
00:16:01
conductivity of ethanoic acid expressed
00:16:02
in terms of a strong electrolyte which
00:16:05
we can determine fairly easily and then
00:16:07
we've got two ions which we need to
00:16:08
consider now so let's go back to our
00:16:10
next electrolyte it's harder to spot the
00:16:13
earth animate and ion conductivity but
00:16:15
remember that the sodium if analyte is a
00:16:18
strong electrolyte as well so it is 100%
00:16:20
dissociated therefore we do the same
00:16:22
thing we set up the equation where we
00:16:25
have the limiting molar conductivity of
00:16:26
sodium ion and the athan away time
00:16:29
rearranged and we've got a value that we
00:16:31
can simply take this and plug it in for
00:16:33
our a fan away tine here and this gives
00:16:36
us yet another strong electrolytes that
00:16:39
we can use to work backwards to
00:16:41
calculate the limiting molar
00:16:42
conductivity of ethanoic acid the last
00:16:45
one we need to unify is the chloride and
00:16:47
the sodium well this seems fairly
00:16:49
straightforward again sodium chloride
00:16:51
provides the data we need however it's
00:16:54
worth noting that these are negative
00:16:55
signs that we need to consider but we
00:16:58
already know how to handle this in terms
00:16:59
of mathematics we simply subtract the
00:17:02
expression for the limiting molar
00:17:03
conductivity of sodium chloride put it
00:17:05
into our equation and remember that
00:17:07
we've got a reversed sign fundamentally
00:17:09
what was shown here is that we can
00:17:11
express any limiting molar conductivity
00:17:12
as a sum of other limiting molar
00:17:15
conductivity we cannot measure directly
00:17:18
the limiting molar conductivity of a
00:17:21
weak electrolyte but we can always find
00:17:23
it in terms of strong electrolytes we
00:17:25
can always find a strong electrolyte
00:17:27
containing the ions that we need and do
00:17:29
the appropriate measurements so we can
00:17:31
look at any limiting molar conductivity
00:17:33
however it is much easier to determine
00:17:36
the limiting conductivity for a strong
00:17:37
electrolyte we can take measure the data
00:17:39
directly and abstract to find
00:17:41
values in summary for this session ions
00:17:45
move by the diffusion migration and
00:17:47
convection through solution the only two
00:17:50
were interested in is diffusion and
00:17:51
migration convection we leave relate the
00:17:54
solution conductivity is affected by
00:17:55
concentration and the strength of the
00:17:57
electrolyte but not in the way we
00:17:58
predict at higher concentrations we see
00:18:00
a reduction in the conductivity due to
00:18:03
the effect of the solvation and the
00:18:05
ionic atmosphere and we remember that
00:18:06
while we can determine limiting molar
00:18:08
conductivity for strong electrolytes we
00:18:10
can't directly measure the conductivity
00:18:12
of weak electrolytes so we need to use
00:18:14
this idea of independent migration of
00:18:16
ions
