CHEM-E6185 – Applied electrochemistry and Corrosion (5 cr)
Assignment 1 (graded), 26.1.2016, computer class 144.
Topic: Determining physicochemical properties of electrolyte using electrochemical
measurements
Copper is produced electrolytically using either electrolytic refining (ER) or electrowinning
(EW). In electrolytic refining the impure copper anode (98-99% Cu) is dissolved and pure
copper is deposited on the cathode (99.996% Cu). In electrowinning the anode is insoluble and
the anode reaction gas evolution. The cathodes are again pure copper. The deposition rate of
copper is affected by mass transfer rate from electrolyte to cathode surface. Usually in copper
deposition the maximum current density is about one third of the diffusion-limited maximum
current density.
Homework
The diffusion coefficient for an electrodeposition system can be estimated from cathodic
polarization curves. The electrode system is called rotating disk electrode. A rotating disk has
controlled flow rate from the electrolyte towards electrode surface. When operating at high
current densities, the deposition rate is controlled by mass transfer. This diffusion-controlled rate
is known as limiting current density and it can be calculated using so-called Levich equation (1)
ilim  0.62  z  F  D 2 / 3  1 / 6  1 / 2  c
(1)
where ilim = limiting current density, mA/cm2
z = number of electrons
F = Faraday constant, 96487 C/mol
D = diffusion coefficient, cm2/s
ν = kinematic viscosity, cm2/s
ω = angular speed (2πf), rad/s
c = concentration, mol/cm3
The viscosity of the electrolyte depends on composition and temperature. According to Price &
Davenport, Metallurgical Transactions 12B, December 1981 the dynamic viscosity can be
calculated using equation (2)
1
= 0.70 − 0.1 ∙ [4.6 ∙ 𝐴𝑠 + 8.3 ∙ 𝐶𝑢 + 8.8 ∙ 𝐹𝑒 + 1.6 ∙ 𝑎𝑐𝑖𝑑 + 10.0 ∙ 𝑁𝑖 − 18 ∙ 𝑇]
𝜇
where  = dynamic viscosity in cP, composition of the electrolyte is given as g/L and
temperature T in degrees Centigrade. Note that 1 cP = 0.001 kg·m-1·s-1. The density of the
electrolyte is given by Price & Davenport as (3)
𝜌 = 1.022 + 10−3 ∙ [1.04 ∙ 𝐴𝑠 + 2.24 ∙ 𝐶𝑢 + 2.37 ∙ 𝐹𝑒 + 0.55 ∙ 𝑎𝑐𝑖𝑑 + 2.24 ∙ 𝑁𝑖 − 0.58 ∙ 𝑇]
where  = density in g/cm3, composition of the electrolyte is given as g/L and temperature T in
degrees Centigrade.
Determine the limiting current densities at different temperatures and then the activation energy
for diffusion and the pre-exponential factor using equation (4)
𝐷 = 𝐷0 ∙ 𝑒 (−𝐸𝐷 ⁄𝑅𝑇)
(4)
where D is diffusion coefficient, D0 is the pre-exponential factor and ED is the activation energy
for diffusion.
The diffusion coefficient can also be estimated using the Stokes-Einstein equation (5)
𝑘𝑇
𝐷 = 6𝜋𝜇𝑟
(5)
where k is the Boltzmann constant and r is radius of the diffusing ion.
Calculate the diffusion coefficient of Cu2+ at T = 50, 60 and 70 C using equations (4) and (5).
Are the results same and if not, what might be the explanation?
In the MyCourses section “Assignment” you will find instructions and an Excel file with
polarization curves: one electrolyte composition, four rotating speeds and three temperatures.
The first worksheet of the file has slots for the answers. Return your Excel file in the MyCourses
return box.
The graded exercise deadline is 9.2.2016 at 23.55 MyCourses time.