Further Physical Chemistry: Electrochemistry session 4

00:20:54
https://www.youtube.com/watch?v=pbRVBckaG70

Zusammenfassung

TLDRThis session focuses on the transport of ions in solutions, emphasizing how electric fields are crucial for ion migration. The electric field's role is dissected, showing it exerts a Coulombic force aiding ion movement but intersecting with resistance from ionic atmospheres and solvation shells. It's demonstrated how the electric field can be uniform or variable based on electrode shape. The tutorial further explores ionic drag forces influenced by solvent viscosity, hydrodynamic radius, and ion speed. Ionic mobility is introduced as a response measure to electric fields, linking bulk conductive properties to microscopic attributes. Interesting phenomena, like the disproportionately high proton transport number due to the Grotthuss mechanism, are explained. The concept of transport numbers helping determine the current share carried by specific ions is discussed, underlining their impact on overall conductivity. The importance of diffusion, especially post-electrode chemical changes, is underlined. Fick's First Law of Diffusion is elaborated, correlating flux to concentration gradients, while the session ties electrochemical processes and dual forces of diffusion and migration, depicting their equilibrium and impact on charge transport.

Mitbringsel

  • ⚡ Electric fields are crucial for ion movement.
  • 🧲 Ionic drag affects how ions move.
  • 📏 Electrode shape influences electric field uniformity.
  • 💧 Solvent viscosity and hydrodynamic radius impact ionic drag.
  • 🔋 Ionic mobility links micro-level response to bulk conductivity.
  • 🔍 Transport numbers define ion-specific current share.
  • 🔄 Diffusion complements migration in charge transport.
  • 🔬 Fick's First Law ties flux to concentration gradients.
  • 🏃‍♂️ Protons move swiftly through solutions due to the Grotthuss mechanism.
  • 🔗 Ionic mobility and conductivity are interconnected.

Zeitleiste

  • 00:00:00 - 00:05:00

    Ion transport in solutions is influenced by factors like electric fields and resistance. Electric fields, measured in volts per meter, drive ion migration, while resistance from other ions and solvent drag slows it down. The distribution of electric fields is also affected by electrode shape, and drag forces can be modeled using Stokes Law, considering factors like solvent viscosity and hydrodynamic radius. Ionic drift is reached when forces balance, defined by electric field and ionic mobility, which describes ion response to electric fields.

  • 00:05:00 - 00:10:00

    Ionic mobility, a microscopic property, influences bulk conductivity of solutions. Smaller ions like lithium have larger hydration shells affecting mobility. Bulk conductivity relates to ionic mobility, linking macro and microscopic behaviors. Transport numbers indicate the share of current by ions, with mobility affecting ion's ability to carry charge. Visualization of ionic current in solutions involves breaking them into sections and considering charge balance, showing that cations contribute more when they are more mobile than anions.

  • 00:10:00 - 00:15:00

    During electrochemical processes, cations and anions interact with electrodes, moving under concentration gradients and electric fields. Drag and diffusion forces affect their movement. The Grothuss mechanism explains why protons in water are highly mobile, as they form and reform bonds, facilitating fast charge transport. Understanding diffusion, especially in neutral and charged species, helps in predicting electrochemical behavior. Ficks' Law and the Einstein relation are key in linking diffusion coefficients with mobility and conductivity.

  • 00:15:00 - 00:20:54

    Ionic mobility and diffusion are interconnected. Mobility reflects how ions move under an electric field, while diffusion relates to concentration gradients. Together, they define ionic conductivity. The Einstein relation expresses this interrelationship, allowing conversion between mobility and diffusion coefficients. Summary emphasizes that understanding ion mobility and diffusion is crucial in electrochemistry, affecting how ions contribute to overall current and conductivity, illustrating their complementary roles in electrochemical processes.

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Mind Map

Video-Fragen und Antworten

  • What is the role of an electric field in ion transport?

    The electric field is vital for electrochemistry, providing the force necessary for ions to migrate through the solution.

  • How does the shape of electrodes affect the electric field?

    The electrode shape defines the electric field. Uniform fields occur between plate electrodes, while variable fields occur with rod electrodes.

  • What factors affect the drag force on ions?

    Drag force is influenced by solvent viscosity, the hydrodynamic radius of ions, and their speed through the solution.

  • How is ionic mobility defined?

    Ionic mobility measures how ions respond to an electric field and is determined by factors excluding the electric field itself.

  • What is the relationship between ionic mobility and conductivity?

    Conductivity, a bulk property, can be linked to microscopic ionic mobility through derived equations.

  • Why do protons have high transport numbers?

    Protons have high transport numbers due to the Grotthuss mechanism, where they transfer quickly through water via continuous proton exchange.

  • What is the significance of transport numbers?

    Transport numbers denote the share of current each ion type carries, influencing overall conductivity.

  • How does diffusion relate to charge transport?

    Diffusion occurs across concentration gradients and involves neutral species moving away from electrodes, essential to understanding electrochemical reactions.

  • What is Fick's First Law of Diffusion?

    Fick's First Law states that the flux of a species is proportional to the concentration gradient across a distance.

  • How are diffusion and migration linked in solutions?

    Diffusion and migration complement each other, with diffusion managing concentration gradients and migration affected by electric fields.

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Untertitel
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Automatisches Blättern:
  • 00:00:00
    in this session we'll be looking at how
  • 00:00:02
    I ins move through solutions and how
  • 00:00:04
    this affects their ability to transport
  • 00:00:06
    charge through that solution so when we
  • 00:00:09
    think about ion transport there's a
  • 00:00:10
    number of factors which affect their
  • 00:00:12
    ability to move through the solution
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    ions move through an electric field and
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    any electric field has magnitude and
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    direct all of these exerted coulombic
  • 00:00:19
    force on our ion but as it's moving
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    through the solution it experiences
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    resistance it experiences movement
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    against officer ions and the experience
  • 00:00:26
    is solvent drag we covered this in terms
  • 00:00:28
    of an ionic atmosphere and salvation'
  • 00:00:30
    shells and these are the models that
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    we've explored already without the
  • 00:00:35
    electric field however ions will not
  • 00:00:37
    migrate they won't move through solution
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    and while it seems like we're stating
  • 00:00:40
    the obvious it is important to remember
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    that the electric field is absolutely
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    vital for electrochemistry so
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    understanding how it works how it
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    behaves is a necessary component of our
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    study the electric field itself is
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    measured in volts per meter so a
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    potential difference over a distance so
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    if we think about what's going on
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    between two uniform plates the electric
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    field we assume is uniform between these
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    plate electrodes by convention it
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    travels from positive to negative so our
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    field goes from the positive electrode
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    to the negative electrode that's simply
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    a convention this field exerts a force
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    on the ions in solution which we can
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    fairly easily quantify where the force
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    is the charged number of the ion
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    multiplied by the charge on an electron
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    and the electric field itself this is
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    the force which is driving our migration
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    forward it's the thing that's pushing
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    our ions through the solution now one
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    thing I'd like you to make sure you're
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    happy with is that the units are indeed
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    congruent here so make sure you
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    understand the units of force the units
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    of charge and the units of electric
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    field and make sure that you understand
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    that these units are indeed congruent
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    the shape of the electrode is also
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    important in defining the electric field
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    so if we think about paddle electrode so
  • 00:01:51
    there's plate electrodes we've been kind
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    of looking at if we look at them from
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    above we imagine them as two plates our
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    positive and negative but if we think
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    about rod electrodes sticking in to the
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    solution they would have a circular
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    cross-section between these two diagrams
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    we're going to have a fixed potential
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    difference and as we explore this we're
  • 00:02:08
    looking at the electric field between
  • 00:02:09
    them so quick convention a longer field
  • 00:02:12
    line represents
  • 00:02:13
    a weaker field we justified this as the
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    electric field along a field line is
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    equal to the change in voltage across
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    that line divided by the length of it or
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    if we're looking in solution we look at
  • 00:02:23
    the potential this Delta Phi divided by
  • 00:02:26
    the length over which it acts okay so
  • 00:02:29
    these are the kind of things that we're
  • 00:02:30
    looking at with our electric field if we
  • 00:02:31
    imagine the electric field in our plate
  • 00:02:34
    electrodes the electric field has
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    straight lines between the plates so
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    there's a uniform field between these
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    plates but outside we start to get
  • 00:02:43
    curving of these field lines so we get
  • 00:02:45
    this variable field longer line weaker
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    field because of this field equation
  • 00:02:50
    that we have here if we think of rod
  • 00:02:52
    electrodes however they're not uniform
  • 00:02:54
    anymore those lines curved through the
  • 00:02:57
    solution which means no matter how we
  • 00:02:59
    were act with a with a rod electrode we
  • 00:03:01
    have a variable field so this is
  • 00:03:04
    imagining the shape of the electric
  • 00:03:05
    field and understanding how these things
  • 00:03:06
    will potentially behave we now want to
  • 00:03:10
    think about the drag forces on our ions
  • 00:03:12
    now remember the drag forces impede that
  • 00:03:14
    ionic flow in this case the diagrams
  • 00:03:16
    representing the effect of solvation
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    shells as well as the ionic atmosphere
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    it's affected by a number of factors so
  • 00:03:23
    we've got the things attached the iron
  • 00:03:25
    but we also need to think about the
  • 00:03:26
    solvent viscosity this carries a simple
  • 00:03:28
    eater here we think of the radius of the
  • 00:03:31
    migrating species whether that's the
  • 00:03:32
    radius of the iron plus the solvation
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    shell this is all summed up in a term
  • 00:03:37
    called the hydrodynamic radius it
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    includes the solvation shells and
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    includes any averaging effects that goes
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    on there there's also the speed of
  • 00:03:46
    motion the faster an ion moves the more
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    drag you would expect it to experience
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    and all of these factors are summed up
  • 00:03:52
    in Stokes law which relates the force on
  • 00:03:55
    our iron to the viscosity of solvent and
  • 00:03:57
    the hydrodynamic radius we'll come back
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    to this later on it's important to
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    recognize that the drag force on our
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    iron is a combination of all of these
  • 00:04:06
    factors together okay so let's think
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    about the drift speed of our ions what
  • 00:04:11
    is the maximum speed that our ions
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    travel so this is the constant speed
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    reached when all the forces balanced so
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    when the electrical force pushing the
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    iron through solution balances the drag
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    force well we've got our definitions
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    we've defined the drag force we've
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    defined the electrical force and all we
  • 00:04:26
    need to do is just
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    simply equate them this allows us to
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    find the ionic drift speed s as a
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    function of our electric field solvent
  • 00:04:33
    factor and the hydrodynamic radius
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    another way of looking at this is to
  • 00:04:37
    consider ionic mobility so if we define
  • 00:04:40
    another term ionic mobility of U this is
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    simply a measure of how the iron
  • 00:04:44
    responds to the electric field this u
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    term is simply everything in this
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    equation except for the electric field
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    so it simply says how the speed varies
  • 00:04:53
    as we vary the electric field mobility
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    is a microscopic property so remember we
  • 00:05:00
    talked about conductivity before
  • 00:05:01
    conductivity looks at the entire solvent
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    it's a bulk property of the solvent but
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    the ionic mobility just looks at the
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    individual ions and we have many
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    different factors which affect the
  • 00:05:11
    mobility of our solvent so we looked at
  • 00:05:13
    a Onix size so we'd think that would
  • 00:05:16
    affect our ionic radii if we look at our
  • 00:05:18
    Group one ions lithium is absolutely the
  • 00:05:22
    smallest iron but the ionic size isn't
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    the main important main factor we need
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    to look at the hydration shells so we
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    spoke before about how lithium even
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    though it's the smallest ion has the
  • 00:05:33
    largest primary hydration shell so we
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    have these two factors we have
  • 00:05:38
    conductivity which is a bulk property we
  • 00:05:40
    have mobility which is a microscopic
  • 00:05:42
    property so can we link the two together
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    it would seem logical that we should do
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    this because ultimately the bulk
  • 00:05:48
    property that we observe the
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    conductivity must be a factor of the
  • 00:05:52
    mobility and it turns out that yes we
  • 00:05:54
    absolutely can relate these the
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    derivation of this is outside the scope
  • 00:05:59
    of this course however when we work it
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    through we find that there is a
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    connection between our limiting molar
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    conductivity that we spoke about the
  • 00:06:06
    last few videos and the mobility that
  • 00:06:09
    you factor of our ion and there's a very
  • 00:06:13
    simple relationship between them if we
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    simply sum up the contribution from the
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    positive ions and the negative ions we
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    can derive the limiting molar
  • 00:06:22
    conductivity
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    the next factor we wish to look at is
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    transport numbers as said before we have
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    looked extensively at bulk properties in
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    terms of conductivity but we need to
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    think about what's going on we need to
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    think about how the charge moves around
  • 00:06:36
    in our solution so how do we look at the
  • 00:06:39
    movement of the individual ions when all
  • 00:06:41
    we can measure is the external current I
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    so what we need to do is need to
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    consider both sides of this particular
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    cell we need to factor in the external
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    circuit going through the ammeter and we
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    need to consider the internal circuit
  • 00:06:55
    going through the solvent because the
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    total current will be the overall sum of
  • 00:06:59
    all components so inside the solution we
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    have an ions carrying our negative
  • 00:07:05
    charge across we have our cations
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    carrying and positive charge to the
  • 00:07:10
    other electrode and this results in a
  • 00:07:13
    flow of electrons around the external
  • 00:07:15
    circuit the transport number simply
  • 00:07:18
    represents the share of the total
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    measured current carried by any
  • 00:07:22
    individual ion so it's a fraction so the
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    transport number simply indicates how
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    much of the current is carried by the
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    cation and how much is carried by the
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    anion ions rarely carry an equal share
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    of the current it's tempting to believe
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    that since we have an equal number of
  • 00:07:36
    positive charges as negative charges
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    that each would carry an equal share but
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    it depends on the mobility if something
  • 00:07:42
    is more able to move through the
  • 00:07:44
    solution if it's able to move more
  • 00:07:46
    freely through the solution it can carry
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    its charge faster through the solution
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    and can deposit it quicker at the
  • 00:07:52
    electrode so we need to consider this
  • 00:07:54
    factor as well it's a tricky thing to
  • 00:07:57
    visualize but let's start building up
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    how charge is transported through a
  • 00:08:01
    solution if we look at our standard
  • 00:08:04
    solution we have our two electrodes here
  • 00:08:05
    we're going to do a few things to this
  • 00:08:07
    system what firstly we're going to
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    divide it into sections so we have an
  • 00:08:11
    area close to the anode we call the
  • 00:08:13
    anode area so this is the area space
  • 00:08:16
    which is mainly affected by the anode
  • 00:08:17
    likewise we have an area of space which
  • 00:08:20
    is affected by the cathode and in the
  • 00:08:22
    middle we have a bulk area which is not
  • 00:08:24
    affected by either the anode or the
  • 00:08:26
    cathode the next thing we need to say is
  • 00:08:28
    that the overall charge in each section
  • 00:08:30
    must be zero so whenever we have a
  • 00:08:33
    solution in equilibrium the charge is
  • 00:08:35
    moving around we must have
  • 00:08:37
    an equal charge distribution so in the
  • 00:08:39
    anode area we have an equal number of
  • 00:08:41
    positive and negative charges in the
  • 00:08:43
    bulk area we also have an equal quantity
  • 00:08:45
    of each and likewise in the cathode area
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    we have an equal quantity of each so
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    this sets up our model to start
  • 00:08:50
    consideration so let's move into what
  • 00:08:54
    happens when we allow a current to flow
  • 00:08:56
    when we connect those we're going to say
  • 00:08:58
    that the cation is twice as mobile as
  • 00:09:01
    the anion okay that's the first thing
  • 00:09:04
    we're going to say if we have a very
  • 00:09:05
    small nimble cation but a very big bulky
  • 00:09:08
    anion then we would expect it to move
  • 00:09:11
    quicker and it would resolve charge
  • 00:09:12
    imbalance quicker so let's think about
  • 00:09:15
    what happens the cations they pick up
  • 00:09:18
    let's start with these cations pick up
  • 00:09:20
    three electrons from the cathode and are
  • 00:09:22
    removed from solution so these three
  • 00:09:24
    pick up another electron and are removed
  • 00:09:26
    from solution likewise to keep the
  • 00:09:29
    external current equal the electrons
  • 00:09:32
    flow through the circuit and
  • 00:09:33
    redistribute themselves which means the
  • 00:09:35
    anions have to deposit three electrons
  • 00:09:38
    at the anode these are also removed from
  • 00:09:41
    solution so what we've ended up with is
  • 00:09:43
    a charge imbalance so we need to rectify
  • 00:09:47
    this charge imbalance in each area the
  • 00:09:48
    bulk area is still charged balanced but
  • 00:09:51
    the anode area is not and neither is the
  • 00:09:53
    cathode area so it would seem sensible
  • 00:09:54
    that the rectification of charge comes
  • 00:09:56
    from the bulk so how does this happen
  • 00:09:59
    well we've said that the cations are
  • 00:10:03
    considerably more mobile than the anions
  • 00:10:05
    so let's say they flow twice as fast so
  • 00:10:07
    we would expect two cations to flow in
  • 00:10:10
    here to make a three plus and we would
  • 00:10:13
    get one anion flowing out of this area
  • 00:10:15
    into the bulk giving us an overall zero
  • 00:10:18
    charge in the cathode area we would
  • 00:10:20
    expect the same thing to happen in the
  • 00:10:22
    anode area and this gives us an equal
  • 00:10:26
    distribution of charge in each area
  • 00:10:28
    there are several ways of accomplishing
  • 00:10:30
    this we can have we can have all three
  • 00:10:32
    charges being balanced by one type of
  • 00:10:34
    ion or we can have it going the other
  • 00:10:36
    way as well in this example we have
  • 00:10:39
    simply said that our anion is less
  • 00:10:40
    mobile so only one anion moves for a
  • 00:10:44
    pair of cations so what we can say here
  • 00:10:47
    then is that the
  • 00:10:49
    cation is carrying twice as much current
  • 00:10:51
    as the anion but notice what's happening
  • 00:10:54
    we get a depletion of charge happening
  • 00:10:58
    in the anode area and an accretion of
  • 00:11:00
    charge eventually in the cathode area
  • 00:11:02
    this will become more significant as we
  • 00:11:05
    go through the course experiments such
  • 00:11:07
    as this allows to determine ionic
  • 00:11:09
    transport numbers if we look at a table
  • 00:11:11
    of data it's immediately quite dry to
  • 00:11:13
    look at but let's just quickly sort out
  • 00:11:16
    a few things
  • 00:11:16
    this solution normality is simply a way
  • 00:11:19
    of reflecting the basicity of the ions
  • 00:11:21
    and the only thing we need to worry
  • 00:11:22
    about is it's related to the
  • 00:11:23
    concentration that's related to
  • 00:11:25
    concentration it's related to activity
  • 00:11:27
    so let's look at what happens as we go
  • 00:11:29
    down a particular group so let's look at
  • 00:11:31
    the barium chloride what we see here is
  • 00:11:34
    we have a gradual decreasing in
  • 00:11:37
    transport number so that means the
  • 00:11:39
    barium is carrying less and less of the
  • 00:11:42
    charge as its concentration increases
  • 00:11:44
    that goes along what we were saying
  • 00:11:46
    about ionic atmospheres and the
  • 00:11:48
    solvation shells so as we increase the
  • 00:11:51
    number of solvation shells the more
  • 00:11:52
    resistance there is to that flow so
  • 00:11:53
    barium is less able to carry the charge
  • 00:11:56
    so we see that decrease if we now look
  • 00:11:59
    across the next three columns looking at
  • 00:12:01
    the group one cations they follow the
  • 00:12:04
    mobility we mentioned earlier lithium
  • 00:12:06
    chloride has a bigger solvation shell so
  • 00:12:09
    is able to move through less experience
  • 00:12:11
    more drag so its mobility is decreased
  • 00:12:13
    which means it's less able to carry that
  • 00:12:15
    charge if we look at sodium it's
  • 00:12:18
    slightly better able and potassium it's
  • 00:12:20
    about 50/50 okay so we can see all of
  • 00:12:23
    these values here are with the exception
  • 00:12:26
    of lithium around about 1/2 for a lot of
  • 00:12:29
    them so there's if we've got transport
  • 00:12:31
    number about 1/2 that means there's an
  • 00:12:33
    equal share of current being carried by
  • 00:12:35
    each of the anions and cations however
  • 00:12:37
    let's turn our attention now to hydrogen
  • 00:12:39
    chloride or HCl in this case we're
  • 00:12:43
    seeing a proton transport number which
  • 00:12:45
    is exceptionally high so everything else
  • 00:12:47
    is about 1/2 plus or minus a little bit
  • 00:12:50
    but the proton transport number is huge
  • 00:12:52
    it's carrying over 80 percent of the
  • 00:12:54
    current why is it the protons are able
  • 00:12:57
    to carry this and it comes down to the
  • 00:13:00
    phenomenon known as the growth house
  • 00:13:01
    mechanism
  • 00:13:02
    we covered this very briefly in first
  • 00:13:04
    year but let's look at it again remember
  • 00:13:07
    protons appear to be unusually mobile
  • 00:13:09
    they are moving much quicker through the
  • 00:13:11
    solution than we would otherwise predict
  • 00:13:13
    and carrying a massive share of the
  • 00:13:14
    current so let's think about what is
  • 00:13:18
    happening we're doing these measurements
  • 00:13:19
    in water so what is water well h2o if we
  • 00:13:23
    populate our system with more and more
  • 00:13:24
    water molecules and then think about
  • 00:13:26
    what happens as we introduce hydrogen
  • 00:13:28
    ion well remember this is inherently
  • 00:13:30
    unstable it will associate with a water
  • 00:13:32
    molecule to create the hydronium ion
  • 00:13:35
    this can then undergo a proton exchange
  • 00:13:37
    with a nearby water molecule which can
  • 00:13:40
    then go undergo another exchange and
  • 00:13:43
    another one and as you can see the
  • 00:13:45
    hydroxo Nia mine appears to be moving
  • 00:13:47
    through solution which will then deposit
  • 00:13:49
    a proton as an electrode so it's not
  • 00:13:53
    that an individual proton is
  • 00:13:55
    particularly mobile it's just we have
  • 00:13:57
    this grotus exchange we have this
  • 00:13:59
    continuous proton transfer throughout
  • 00:14:01
    the solvent and that's what's driving
  • 00:14:03
    our proton transport number makes it
  • 00:14:05
    much higher than we would otherwise
  • 00:14:06
    expect whenever we consider what happens
  • 00:14:10
    at an electrode anion comes in it drops
  • 00:14:14
    off its electrons or picks electrons up
  • 00:14:15
    in forms and neutral species it then
  • 00:14:17
    needs to move away from the electrode in
  • 00:14:20
    order to let other ions at the electrode
  • 00:14:22
    this process is diffusion and we need to
  • 00:14:26
    think about how diffusion behaves as
  • 00:14:27
    well to understand our electric
  • 00:14:28
    processes diffusion is fundamentally a
  • 00:14:31
    transport across a concentration
  • 00:14:32
    gradient so if we have a system where we
  • 00:14:36
    have a very concentrated analyte at one
  • 00:14:38
    end and free solution at the other end
  • 00:14:41
    this is going to diffuse across that
  • 00:14:43
    concentration gradient it's going to
  • 00:14:45
    distribute itself until we have an even
  • 00:14:47
    concentration diffusion applies to all
  • 00:14:50
    species but we need to particularly
  • 00:14:51
    focus on neutral species for the reason
  • 00:14:53
    that we said these things need to
  • 00:14:54
    diffuse away from the electrode surface
  • 00:14:56
    I'm going to call you back to your
  • 00:14:58
    first-year thermodynamic diffusion
  • 00:15:00
    argument go and reference that go and
  • 00:15:03
    have a look at that make sure that
  • 00:15:04
    you're happy with that content but what
  • 00:15:06
    we're going to look at here is we're
  • 00:15:08
    going to look at a concentration
  • 00:15:09
    gradient we're going to look at how the
  • 00:15:11
    concentration varies over a region of
  • 00:15:13
    space
  • 00:15:14
    so if we have a concentration gradient
  • 00:15:15
    if there's a difference in the
  • 00:15:17
    concentration we would expect to have
  • 00:15:19
    diffusion so at what rate does that
  • 00:15:22
    particular species flow so what is its
  • 00:15:25
    flux so that's what we're looking for
  • 00:15:27
    we're looking at how it flows through a
  • 00:15:29
    given space we proposed a particular
  • 00:15:31
    model such as this where we have the
  • 00:15:34
    rate of trap of flow so the flux j is
  • 00:15:37
    equal to some constant multiplied by the
  • 00:15:39
    concentration gradient so DC by DX the
  • 00:15:42
    rate of change of concentration across a
  • 00:15:44
    given area of space so if we look at
  • 00:15:47
    this we think ok well our concentration
  • 00:15:49
    is high on the left low on the right so
  • 00:15:52
    that means our concentration gradient is
  • 00:15:54
    pointing to the left but if we think
  • 00:15:57
    about the direction of motion the
  • 00:15:58
    direction of motion is going to go to
  • 00:15:59
    the right so this means we have a
  • 00:16:01
    negative value here this is exactly the
  • 00:16:03
    same as a rate law that you've looked at
  • 00:16:05
    in kinetics it's the same mathematics
  • 00:16:07
    it's the same expression so you're
  • 00:16:09
    comfortable with this so what would
  • 00:16:11
    happen over time if we suddenly let this
  • 00:16:13
    system equilibria well we're going to
  • 00:16:16
    get a flow from left to right across
  • 00:16:18
    this little region of space and the
  • 00:16:21
    boundary between it becomes more and
  • 00:16:23
    more diffuse until we get to a point
  • 00:16:28
    where there is no difference between the
  • 00:16:31
    two so the rate of change of
  • 00:16:33
    concentration with distance becomes zero
  • 00:16:35
    and we have no more flow happening this
  • 00:16:38
    relationship is known as ficks first law
  • 00:16:39
    of diffusion and it simply states that
  • 00:16:42
    the flux is proportional to the change
  • 00:16:43
    in concentration over distance the D
  • 00:16:46
    term here is the diffusion constant and
  • 00:16:49
    we can determine it fairly easily from
  • 00:16:52
    this particular relation here there's no
  • 00:16:54
    need to derive it but this is known as
  • 00:16:56
    the Stokes Einstein relation notice that
  • 00:16:59
    there's no charge present in this
  • 00:17:00
    equation at all and the diffusion is
  • 00:17:02
    purely related to viscosity so this ETA
  • 00:17:06
    term here now we've seen this already
  • 00:17:08
    today we've looked at this and we've
  • 00:17:10
    considered it in terms of ionic drag
  • 00:17:13
    forces this k-beauty you should
  • 00:17:16
    recognize as the thermal energy in the
  • 00:17:18
    system so the thermal energy per
  • 00:17:20
    molecule in that system and remember
  • 00:17:22
    that a is our hydrodynamic radius as
  • 00:17:24
    well chemical potential also plays an
  • 00:17:27
    important role
  • 00:17:27
    in diffusion concentration is
  • 00:17:29
    fundamentally linked to chemical
  • 00:17:31
    potential which means we can use our
  • 00:17:33
    chemical potential understanding from
  • 00:17:34
    previously this allows us to determine a
  • 00:17:37
    thermodynamic force for diffusion so
  • 00:17:40
    remember that the chemical potential is
  • 00:17:42
    simply the partial Gibbs energy of a
  • 00:17:45
    particular component and we're looking
  • 00:17:47
    at a the activity in this case so
  • 00:17:50
    remember it's a potential so if we do a
  • 00:17:52
    derivative of this this will give us a
  • 00:17:54
    thermodynamic force as such so we simply
  • 00:17:57
    do a first derivative of this with
  • 00:17:59
    respect to X so that's across that
  • 00:18:02
    concentration gradient there if we're
  • 00:18:04
    using an ideal solution we can replace
  • 00:18:06
    the activity a with our concentration C
  • 00:18:08
    and we end up with this expression here
  • 00:18:12
    we get a very straightforward diffusion
  • 00:18:14
    force on our species one thing I'd like
  • 00:18:18
    you to consider is why does the standard
  • 00:18:19
    chemical potential disappear in the
  • 00:18:21
    derivative so we have a great deal going
  • 00:18:24
    on we have diffusion and migration
  • 00:18:26
    processes happening we have diffusion
  • 00:18:28
    due to concentration gradients we have
  • 00:18:31
    migration due to electric fields but we
  • 00:18:33
    need to consider both whenever we're
  • 00:18:35
    looking at our system ions migrate to
  • 00:18:38
    the electrode they give up electrons or
  • 00:18:40
    they receive electrons depending whether
  • 00:18:42
    an ions or cations and become uncharged
  • 00:18:44
    species and those uncharged species must
  • 00:18:46
    diffuse away so we have three forces
  • 00:18:48
    going on here we have the diffusion as
  • 00:18:51
    things move across their concentration
  • 00:18:53
    gradients and we have the electrical
  • 00:18:55
    force which is which is drawing our ions
  • 00:18:57
    to the electrode and fundamentally each
  • 00:18:59
    of them is experiencing a drag force but
  • 00:19:02
    only the electrical charge species are
  • 00:19:04
    subject to that electrical driving force
  • 00:19:06
    ok we've covered a lot of concepts let's
  • 00:19:08
    start putting them all together we see
  • 00:19:11
    many of the same terms appearing so in
  • 00:19:13
    our diffusion we say that we've got a
  • 00:19:16
    solvent factor and the thermal factor
  • 00:19:20
    but we also have our ionic mobility
  • 00:19:22
    which again has a solvent factor but now
  • 00:19:24
    we're looking at the charge on our ions
  • 00:19:26
    we've got a simple equality here and we
  • 00:19:28
    can rearrange these and substitute
  • 00:19:30
    values in to express our ionic mobility
  • 00:19:33
    in terms of diffusion so this allows us
  • 00:19:36
    to relate them via the Einstein relation
  • 00:19:39
    so for a
  • 00:19:41
    and molecule we can relate our diffusion
  • 00:19:44
    coefficient to the charges but if we
  • 00:19:48
    want to look at it in terms of molar
  • 00:19:49
    terms we can relate it to our molar
  • 00:19:53
    thermal energy and the faraday constant
  • 00:19:55
    okay so that gives us our ionic mobility
  • 00:19:57
    in terms of the diffusion constant this
  • 00:20:01
    can also be related to molar
  • 00:20:02
    conductivity so remember what we did
  • 00:20:04
    last time looking at molar conductivity
  • 00:20:05
    and we have a link between our mobility
  • 00:20:09
    and connectivity from the start of this
  • 00:20:10
    session and this allows just to simply
  • 00:20:13
    do a quick substitution to express our
  • 00:20:16
    molar conductivity in terms of the
  • 00:20:18
    diffusion coefficient in summary we need
  • 00:20:21
    to look at ionic mobility ionic mobility
  • 00:20:24
    is key to how ions move through solution
  • 00:20:25
    if they are less mobile they have a
  • 00:20:27
    lower contribution to the ionic current
  • 00:20:29
    and fundamentally the conductivity as
  • 00:20:31
    well
  • 00:20:32
    ions rarely carry an equal share so
  • 00:20:35
    generally they are carrying an unequal
  • 00:20:37
    share of that current with more mobile
  • 00:20:39
    ions were carrying more of the current
  • 00:20:41
    through that solution and remember as
  • 00:20:44
    well at diffusion and migration of
  • 00:20:46
    complementary processes they are
  • 00:20:47
    intrinsically linked and we have to
  • 00:20:49
    consider both in our electrochemical
  • 00:20:51
    processes
Tags
  • ion transport
  • electric field
  • ionic mobility
  • electrochemistry
  • conductivity
  • diffusion
  • solvation shells
  • transport numbers
  • proton mobility
  • ionic drag