electrochemistry

fundamental equation of chemical thermodynamics

dG = Vdp - SdT + sumj(partial molar gibbs energy of j x change in the anount of j)

• last term is added for each component

chemical potential of A in an ideal solution

chemical potential(A) = standard chemical potential(A) + RTln([A]/[A]^o)

• ([A]/[A]^o) is the normalised concentration

chemical potential of A in a non-ideal solution

chemical potential(A) = standard chemical potential(A) + RTln(effective concentration)

ionic strength

I = ½ * sum(mz²) for each component

relationship between activity and concentration

activity(A) = gamma(A) * [A]/[A]o

• gamma is the activity coefficient

Debeye-Huckel theory

• predicts gamma (activity coefficient) by considering the balance between inter-ion interactions and thermal motion

• log10(gamma_j) = -Az_j² * sqrt(I)

mean ionic activity coefficient

mean ionic activity coefficient = (gamma a * gamma b) ^1/(a+b)

assumptions made in the debeye-huckel limiting law

1. non-ideality is caused only by ion-ion interactions not ion-solvent interactions

2. ionic interactions are described quantitatively by coulomb’s law for point charges

3. the electrolyte is fully dissociated (no ion pairs)

works well for dilute solutions - predicts that the deviation from ideality increases with the ionic strength

extended debeye-huckel limiting law

can improve the theory by representing the charges as spheres rather than points

• log10gammaj = (-Az_j² sqrt(I))/(1 + Basqrt(I))

• introduces a correction factor

• A and B depend on solvent and temp

• a is the radius of ion j

• works for slightly higher concentrations but still doesn’t fit the real experimental results

debeye length

• the distance over which potential falls to 1/e of its original values

• can be viewed as the distance between an ion and an average location of the charge in its ionic atmosphere

• for a high conc of electrolyte we have a short debeye length

• r_D is proportional to 1/sqrt(I)

• as the ionic strength increases the distance between the ion and the average charge in the atmosphere shrinks - the effect of the ionic atmosphere on free energy increases with ionic strength and the solution is more non-ideal

transport properties

• describe the response of a system to a gradient

• for electrolytes and processes on electrodes we need to think about the following processes

• temperature - thermal convection currents

• concentration - diffusion

• mechanical - stirring/flow

• potential - response to electrical potential gradient

potential difference

• the difference in electrical potential between two points in spaces - measure in volts

• electrical potential at a point in space is the work per nit charge to bring a charged particle from infinity to that point

electric field (potential gradient)

• electric field (E) is the potential difference between two points divided by the difference between them

• E = V/I

current and current density

current is the rate of flow of charge I = dQ/dt

proportional to the number of particles flowing past in that time

current density, j = current per unit area = I/A

ohm’s law

V=IR

• R = the resistance on the electrolyte

resistance and resistivity

R = rho * l /A

• l = length

• A = area

• rho = resistivity

• resistivity is a property of a material/electrolyte

• resistance is measured in ohms

conductance and conductivity

• conductivity k is the reciprocal of resistivity

• conductance G is the reciprocal of resistance

• therfore G = kA/l

• conductance is measured in siemen

• one sieman is equal to ohm-1

Ohms law in terms of conductivity ^{*need to know this derivation}

V = IR = I*rho*length/A = I*length/kA

• V/length = I/kA

• kV/length = I/A

• volts/distance = electric field E

• I/A = current density j

• therefore Ek=j

molar conductivity

• it has been found that conductivity of a solution depends linearly on concentration

• molar conductivity = k/C (units of ohms-1 m2 mol-1)

• kjhkjhj other equation for a salt

• conductivity of the salt is the sum of the conductivities of individual ions - assumes cations and anions move independently of each other

how do we measure molar conductivity

• use an alternating voltage supply - voltage alternates faster than the reactions can happen at the electrode so the ion concentration stays constant

transport numbers

• transport number tells us how much of the current is carried by a particular ion

• the fraction of the charge being carried by the ion

• t+ = molar conductivity +/ (molar conductivity + + molar conductivity -

effect of charge on deviation from EDHL

• higher charge density = interacts more strongly with water ie. more stongely solvated

• the hydration of ions takes up a lot of water both in the primary and outer hydration shells

• at higher concentrations we run out of water molecules to solvate the ions fully

• the solvation becomes imperfect and destabilisation occurs - free energy becomes less negative causing changed in gamma j and mean ionic activity

• therefore the deviation from DH laws at higher concentrations is because of the ion solvent interactions that the law ignores in its assumptions

• the robinson and stokes equation accounts for these interactions

what forces might be acting upon an ion in the solution is we apply a potential difference?

• the ion is attracted to the electron of opposite charge- electrical attraction

• but its speed is reduced by viscous drag

• electrical force on cation = zeV/l

• volts over l meters

• e charge on an electron

stokes law:

• viscous force = 6 pi a v * viscosity

• drift velocity is when electrical force = viscous force

• mobility u = drift velocity / electric field

trends in ions and conductivities

based on equation for flux of charge

• solvents on low viscosity allow higher conductivity

• highly charged ions have higher conductivity

• small ions have higher conductivity

experimentally

• divalent molecules have higher conductivities than monovalent ions

• smaller ions have a higher charge density and attract more water molecules - more solvated so hydrated ions follow the opposite trend in size radius K+ aq < Na+ < Li+

• lithium ion smallest but most solvated so less mobile hence lowest conductivity

• if the ions are travelling with their solvation shells then stokes law holds

• conductivities oh H+ and OH- are anomalously large - Grotthuss mechanism

Grotthuss mechanism

• conductivities of H+ and OH- are anomalously large

• these ions are thought to migrate by a different specific mechanism called the grotthuss mechanism

• form H-bonds between molecules - the charge moves along these networks faster than the actual ion physically moves leading to greater conductivity - ions aren’t actually moving

strong and weak electrolytes

molar conductivity varies with concentration

• molar conductivity for a strong electrolyte obey Kohlrausch’s law (molar conductivity = limiting molar conductivity - Kc^1/2)

weak electrolytes are more complicated because the conc of the electrolyte is not equal to the conc of ions bc it doesn’t fully dissociate

• fraction present as ions alpha = molar conductivity/limting molar conductivity

• Ka = aof cation * a of anion / a acid = x2/conc - x

• if x is small then Ka = x2/conc

• conductivity will give fraction present as ions a

• a = x/conc = (Ka/conc)^1/2

• sub all in to get Ka the disscoiation constant

origin of electrode potentials

• an equilibrium is established

• the metal acts as a source of or sink for electrons

• the electrons are transferred between the metal and solution phases

• a charge separation is established

• if the equilibrium lies to the left then electrons will be added to the electrode and it will become more negative than the solution

• we can change the potential by changing the concentrations in solution