00:00:00
we're now going to consider the effect
00:00:02
of the solvent in all of our
00:00:04
electrochemical interactions so when we
00:00:06
think about solvent effects remember
00:00:08
that almost all chemistry happens in
00:00:10
solvent so the solutions account for
00:00:12
most of these chemical reactions
00:00:13
whenever you're in a lab doing synthetic
00:00:15
chemistry you have to dissolve the
00:00:17
reactants which facilitate them coming
00:00:18
into contact with each other so
00:00:21
understanding the behavior of these
00:00:22
solutions is absolutely essential to
00:00:24
understanding more about the chemical
00:00:26
reaction most electrochemistry
00:00:27
experiments are done in water but some
00:00:29
measurements in organic solvents exist
00:00:30
so it's worth bearing in mind this is
00:00:33
where we're going to be focusing our
00:00:34
studies and remember that a great deal
00:00:37
of biochemistry happens in aqueous
00:00:38
solutions so inside the body we're
00:00:40
predominantly aqueous with some lipid
00:00:42
but there's a lot of biochemistry that
00:00:43
happens there in so the first thing
00:00:45
we're gonna consider is concentration of
00:00:46
solutions so you've done a bit of this
00:00:48
in your previous course with
00:00:49
thermodynamics but remember to recall
00:00:51
the standard state so we have this
00:00:54
symbol here where we have standardized
00:00:56
pressures we have our standardized
00:00:57
molality which is moles per unit mass
00:01:00
and then we have our standardized
00:01:01
concentration which is moles per unit
00:01:03
volume in electrochemistry we use
00:01:05
molality which carries the symbol M the
00:01:08
reason for this is that the mass of the
00:01:09
solvent is independent of temperature so
00:01:11
when we start doing electrochemistry
00:01:13
solutions can expand they can contract
00:01:15
and it's important to remember that as
00:01:18
solutions are heated the concentration
00:01:20
the molarity will change but the
00:01:22
molality will not so many factors affect
00:01:26
the behavior of these solutions and
00:01:28
we're going to cover a few of them in
00:01:29
this session the solution activity which
00:01:32
is one way of thinking of the effective
00:01:34
concentration is one of the key things
00:01:37
that we're going to consider here so
00:01:39
many different things affect the
00:01:40
behavior we introduced the iní
00:01:42
interaction salvations spheres but also
00:01:44
the size the ionic atmosphere so all
00:01:46
these things affect the behavior of the
00:01:48
solution they affect the mobility of
00:01:50
ions within that solution fundamentally
00:01:52
affecting its behavior and changing the
00:01:54
way in which it behaves so we think of
00:01:56
ideal solutions where the concentration
00:01:58
is equal to the activity but very few
00:02:01
solutions are ideal and we've
00:02:03
demonstrated this by discussing the
00:02:05
presence of the ionic atmosphere so
00:02:09
fundamentally we need to use something
00:02:10
different we use the activity to
00:02:11
summarize all of these effects
00:02:13
the activity a-and the activity
00:02:16
coefficient which is simply a way of
00:02:17
scaling our concentration to give us the
00:02:21
overall activity to explore this in more
00:02:24
depth we need to go so go over some
00:02:26
basic principles firstly we ignore water
00:02:29
this seems daft we've been talking all
00:02:31
about the solutions but we just treat
00:02:33
water as an unstructured uniform
00:02:35
material providing a relative
00:02:36
permittivity of 78 that's all we
00:02:39
consider water to be for the purposes of
00:02:40
exploring solution activity we assume
00:02:43
the only thing that affects the
00:02:46
interactions is the electrostatic
00:02:48
interactions so we completely ignore any
00:02:50
dispersion forces any of these London
00:02:52
forces that might otherwise cause
00:02:53
attraction ionic attraction or
00:02:56
electrostatic attraction is far stronger
00:03:00
and would far outweigh any dispersion
00:03:02
force that might be there we also need
00:03:04
to assume a spherically symmetric ionic
00:03:06
atmosphere so whenever we look at this
00:03:08
I'll that's fear we have to assume it's
00:03:09
spherically symmetric otherwise our
00:03:11
exploration of solution activity breaks
00:03:13
down using these assumptions we can
00:03:15
determine activities using the Debye
00:03:17
Huckel theory we'll cover more on this
00:03:19
later on but it's important to flag it
00:03:21
here so that we know to come back to it
00:03:23
later on we need to know consider the
00:03:25
ionic strength of solutions the ionic
00:03:27
strength affects the activity so the
00:03:29
stronger the iron solution is the more
00:03:31
it affects that activity the ionic
00:03:33
strength can be found simply by summing
00:03:36
up the square of all the charges
00:03:38
multiplied by the concentration this is
00:03:39
simply a formula that we use to
00:03:41
calculate ionic strength it depends on
00:03:44
the concentration of each ion moles per
00:03:47
kilogram again remember but it also
00:03:49
depends on the charge on the ions
00:03:50
themselves and this can have a great
00:03:52
effect depending on what ions and what
00:03:54
concentration we're using so if we
00:03:56
consider 1 molar NaCl if we simply
00:03:59
substitute the values in so we think
00:04:01
okay well let's deal the sodium first
00:04:03
I've got a plus 1 charge we square that
00:04:05
multiply it by the concentration divided
00:04:08
by the standard concentration and then
00:04:10
we add on to this the charge of the
00:04:12
chloride and square that we end up with
00:04:14
an ionic strength of 1 for 1 molar
00:04:17
sodium chloride ok that's fine for
00:04:20
magnesium chloride we're going to look
00:04:23
at half the concentrations we're going
00:04:24
to look at 1/2 moles concentration
00:04:26
but if we examine this equation we find
00:04:29
that if we take the charge on the
00:04:31
magnesium the charge in the chloride and
00:04:33
I remember there's twice as much
00:04:34
chloride in concentration as there is
00:04:36
magnesium so we've doubled up here we
00:04:39
find that we end up with an overall
00:04:41
ionic strength which is higher than the
00:04:44
sodium chloride despite having a
00:04:45
concentration which is half so this is
00:04:48
an important consideration this ionic
00:04:50
strength because it effects other
00:04:52
measurements we're going to do further
00:04:53
down the line whenever we think of an
00:04:56
activity we think of the mean activity
00:04:58
of a solution
00:04:58
remember it's impossible to measure
00:05:00
these things in isolation because these
00:05:02
are anions and cations coexist so that
00:05:04
means any time we determine an activity
00:05:07
what we're really looking at is the
00:05:09
combined activity of a cation and the
00:05:10
anion so we cannot separate their
00:05:14
effects so fundamentally we're looking
00:05:16
at solution activity as a net effect of
00:05:18
these two things combining and the mean
00:05:20
activity coefficient covers the entire
00:05:22
solution so if we have a different salt
00:05:25
with different components we would
00:05:26
expect the mean activity to combine in
00:05:29
this manner where we simply have an
00:05:31
algebraic relationship between the mean
00:05:33
activity of each of the components
00:05:34
combining to give us that mean activity
00:05:37
of solution but how does the activity
00:05:38
coefficient vary with concentration we
00:05:41
need to understand a little bit about
00:05:42
how this works so this introduces the
00:05:45
law known as the Debye Huckel limiting
00:05:47
law its expression is fairly
00:05:48
straightforward where we simply combine
00:05:51
the product of the charges and the ionic
00:05:53
strength and we get an expression for
00:05:56
the mean activity of solution so it's a
00:05:58
fairly straightforward thing to match we
00:05:59
simply determine the ionic strength we
00:06:01
look at the charges and that gives us a
00:06:03
way to predict the mean activity of the
00:06:04
solution looking at this we should see
00:06:07
that well we have a fairly
00:06:09
straightforward relationship for a given
00:06:10
solution we would have a fixed ionic
00:06:12
strength we'd have a fixed relationship
00:06:15
between the charges which means that we
00:06:18
should have a straight line plot and we
00:06:20
see that this is indeed the case by
00:06:22
plotting the log gamma we see we have a
00:06:24
straight line relationship for different
00:06:26
electrolytes and that's fine that's very
00:06:29
straightforward
00:06:30
remember that the concentration effect
00:06:31
comes into the ionic strength so
00:06:33
whenever we think about changing
00:06:34
concentration that's what we're varying
00:06:38
this a term whenever we're considering
00:06:40
solvent this will be a particular
00:06:42
scaling factor for a given solvent for
00:06:44
water it's point 509 at 25 Celsius
00:06:48
however this law only works at low
00:06:50
concentrations and when we say low we
00:06:52
mean as low as a thousandth mol/l so a
00:06:55
very small concentration indeed but what
00:06:58
we see is that as I approaches zeros as
00:07:00
this ionic strength approaches zero so
00:07:02
the as a concentrations approaching zero
00:07:04
log gamma so this term here approaches
00:07:08
zero which must mean that gamma
00:07:10
approaches one remember this is a power
00:07:12
of 10 so if log base 10 is zero that
00:07:15
means that the number we're looking at
00:07:16
tends to 1 and that certainly aligns
00:07:20
with this graph so as we reduce the
00:07:22
concentration reduce the ratio there we
00:07:24
get close to a log gamma of zero which
00:07:27
means gamma must be approaching 1 that
00:07:28
means the activity is approaching the
00:07:31
measured concentration as we increase
00:07:34
the concentration the activity decreases
00:07:35
the reason for this is that at higher
00:07:37
concentrations ion-ion interactions
00:07:39
become much more significant the
00:07:41
long-range effects of ionic interactions
00:07:43
affect the way in which the solution
00:07:45
behaves exploring the Debye Huckel
00:07:47
limiting law further we need to think
00:07:49
about what the limits are in this so
00:07:51
what what can we look at well let's
00:07:53
think about what happens with higher
00:07:54
ionic charges the higher the charge the
00:07:58
greater the faster the ionic strength
00:07:59
grows but also the faster this component
00:08:01
grows as well we get a faster and faster
00:08:03
deviation from theory so if we look at
00:08:05
this particular one we're looking at
00:08:06
sodium chloride magnesium sulfate and
00:08:09
magnesium chloride the green one here
00:08:10
represents low ionic charge while the
00:08:12
red one represents very high ionic
00:08:14
charge we see this deviation becoming
00:08:16
more and more prevalent for highly
00:08:18
charged ions the theory predicts a
00:08:20
negative logarithm we see these cropping
00:08:22
up everywhere in chemistry which must
00:08:24
mean that our activity coefficient must
00:08:26
be less than 1 so because the activity
00:08:28
is less than 1 that means that these
00:08:29
ions which are surrounded by this ionic
00:08:31
atmosphere have a lower chemical
00:08:33
potential when the gamma is less than 1
00:08:35
however as we said this atmosphere model
00:08:37
only applies at very low concentrations
00:08:39
when we get to high concentrations this
00:08:41
Debye Huckel limiting law starts to
00:08:43
break down so as we increase the ionic
00:08:45
strength I log gamma becomes more and
00:08:47
more negative but then it turns around
00:08:49
and what we find is that that high
00:08:52
when we measure it at high ionic
00:08:54
strengths log gamma actually increases
00:08:57
it becomes greater than one so what does
00:08:59
that mean for our activity coefficient
00:09:02
so this means the effective
00:09:03
concentration of the activity has become
00:09:06
greater than the actual concentration in
00:09:08
solution but how can this possibly be
00:09:11
the case now how can we suddenly be in a
00:09:14
place where we have a greater effective
00:09:16
concentration well in order to
00:09:18
understand what's going on we need to
00:09:20
think about what's happened to the
00:09:21
solvent it's useful to think where is
00:09:24
the water so if we look at one molar
00:09:27
lithium chloride so we've got lithium
00:09:28
chloride which the green curve it's the
00:09:30
most rapidly deviating model here
00:09:33
lithium chloride has when we've solve it
00:09:37
it we find that we have five water
00:09:39
molecules to each lithium ion in a
00:09:42
primary hydration cell while the
00:09:43
chloride has one water molecule in each
00:09:45
hydration shell so if we look at one
00:09:49
molar lithium chloride around about ten
00:09:51
percent of the water is tied up it's
00:09:53
locked into these primary hydration
00:09:55
channels so what that means is that
00:09:56
we've affected significantly the
00:09:59
activity of the water the effective
00:10:00
concentration of water is reduced
00:10:02
because we effectively reduced the
00:10:04
concentration of water that means we
00:10:06
must effectively increase the
00:10:08
concentration of ions and this seems
00:10:11
like a very weird thing we but we have
00:10:13
to consider the effect of concentration
00:10:15
of water and the effect of concentration
00:10:17
of our ions and we need to ask the
00:10:20
question is free water in considerable
00:10:22
access to the amount of water free in
00:10:24
solution not tied up in salvation shells
00:10:27
we have to make sure it is in
00:10:29
considerable access otherwise we will
00:10:31
start to see this deviation which allows
00:10:33
for an activity which is greater than
00:10:35
the actual concentration the effect is
00:10:38
greatest for lithium so lithium the
00:10:41
lithium cation is the smallest of the
00:10:43
group one ions because it's small it's
00:10:45
got the highest field around it and that
00:10:47
allows it to hold much more water in a
00:10:49
primary primary solvation shell than
00:10:51
either of sodium or potassium and this
00:10:53
allows it to hold much more water in a
00:10:54
primary solvation shell than either of
00:10:56
sodium or potassium because of that
00:10:58
extremely high field but remember for
00:11:02
any of this to work we need to make sure
00:11:04
there's sufficient for
00:11:05
water remember water not tied up in
00:11:07
salvation shells because that's required
00:11:09
to stabilize our ions because it forms
00:11:11
an intrinsic part of ionic atmospheres
00:11:13
letting those ions freely move around if
00:11:16
there's a significant difference in the
00:11:18
amount of free water available that
00:11:19
causes this great deviation from ideal
00:11:22
behavior and we see as I say we see this
00:11:24
most Philippian fluoride and less for
00:11:27
others but we still see the presence of
00:11:29
this deviation caused by that change in
00:11:31
activity of the water so in summary we
00:11:34
cannot ignore the effect of solvents in
00:11:36
our solutions they're an intrinsic part
00:11:38
of the system so without the solvent we
00:11:40
wouldn't have a solution but the solvent
00:11:44
the presence of the solvent effects the
00:11:45
effective concentration of the analyte
00:11:47
so as we tie up some solvent molecules
00:11:50
with the salvation shells we see that we
00:11:52
get a change in the activity of our
00:11:55
analyte as we increase the ionic
00:11:57
strength of the solution remember that's
00:11:59
related to the charge on the ions as
00:12:01
well as their concentration the ionic
00:12:03
strength of solution is intrinsically
00:12:05
linked to the concentrations via the
00:12:07
formula we saw before and it doesn't
00:12:08
always scale linearly because we have to
00:12:10
factor in the charges on the ions as
00:12:12
well finally through the formation of
00:12:14
solvent shells we find that there is an
00:12:16
absence of free solvent as we increase
00:12:19
the concentration of our analyte we have
00:12:21
more and more solvent molecules tied up
00:12:23
in these salvation shells and that
00:12:25
reduces the amount of free solvent
00:12:26
available which decreases the activity
00:12:29
of the solvent increasing the activity
00:12:32
of our analyte
