1. CE 541
Electrochemistry

2. It is needed in Environmental Engineering to understand:
Electrochemistry is the relationship between Chemical Phenomena and Electrical Phenomena
It is needed in Environmental Engineering to understand:
Corrosion
Electrochemical oxidation of wastes
Analytical procedures
Automatic monitoring of waste streams
Oxidation-reduction reactions

3. Current Flow in Solution
Current can flow through:
Solution of electrolyte
Metallic conductors
Characteristics of current flow through a metal:
Chemical properties of metal are not changed
Current is carried by electrons
Increase in temperature increases resistance

4. Characteristics of current flow through a solution:
Chemical change occurs in solution
Current is carried by ions
Increase in temperature decreases resistance
Resistance is normally greater than that with metals

5. E = IR Conductivity of Solution
"Is its ability to carry an electrical current"
Conductivity can be measured by a conductivity meter and it is affected by:
Number of ions
Type of ions
E = IR
Where:
E = electromotive force (volts)
I = current (amperes)
R = resistance (ohms)

6. And
Where
l = length of conductor
A = cross-sectional area of conductor
 = specific resistance of conductor (ohm-cm)
k = specific conductance (1 / ohm-cm) or siemens (S)
Specific conductance is conductance afforded by 1 cm3 of an electrolyte solution

7. Specific Conductance of a Solution = C / R
Conductivity cells are calibrated by determining the resistance of a standard solution (Rs) and the cell constant (C) can be found.
C = ksRs
In such cases N KCl is used in calibrating conductivity cells. For N KCl:
ks = S =  C
So,
Specific Conductance of a Solution = C / R
R needs to be determined

8. Equivalent Conductance ()
Where
N = normality of the solution
k = specific conductance
or,
and are equivalent ionic conductance of cations and anions, respectively

9. Table 3-3 shows equivalent ionic conductance @ 25 C in S-cm3/equivalent.
Only ions can carry current. Un-ionized species of weak acids or bases will not carry current. Also uncharged soluble organics (ethanol and glucose) can not carry current.
Study Example page 80

10. What is the approximate specific conductance at 25 C of a solution containing 100 mg/l of CaCl2 and 75 mg/l of Na2SO4

11. Current and Chemical Change
Chemical change depends on:
Nature of solution (composition)
Nature of electrodes
Magnitude of electromotive force imposed

12. Applying a voltage of 1.3 v H2 evolves at Cathode Cl2 evolves at Anode
HCl H+ e-
Cathode (-)
Cl-
Anode (+)
Platinum
Electrodes
Applying a voltage of 1.3 v H2 evolves at Cathode Cl2 evolves at Anode

14. To bring about 1 equivalent of chemical change at an electrode:
An Avogadro No of electrons must flow through the external circuit
This quantity of electrons is called the faraday (F)
The rate of flow of electrons gives the current (I) in amperes
1 F is equivalent to an ampere of current flowing for seconds
An ampere is defined as a Coulomb per second
1 F = Coulomb
Study Example page 78

15. What weight of silver will pass into solution from a silver anode by the passage of 0.02 A of current through the solution for 24 hours?

16. Electrochemical Cell
two electrodes will be connected by metallic conductor
electrons will flow
chemical change begins
electromotive force (emf) will be generated by the cell
this emf is a measure of the driving force of the chemical reaction occurring in the solution
the driving force represents the chemical potential or free energy of the reaction

17. Electrical Energy = EIt
Based on that, a relationship between electrical potential and chemical free energy can be found:
Electrical Energy = EIt
E = emf in volts
I = current in amperes
t = time in seconds
Electrical energy is expressed in Volt-Coulomb or Joule
Electrical energy required to produce one mole of chemical change = zEF
Where
z = number of electron-equivalent per mole
F = faraday or coulombs per equivalent

18. If reaction proceeds (E is +ve), then:
where
G is the free energy
-zEF is the electrical energy

19. aA + bB  cC + dD Consider the following reaction: Substituting in:
we get:

20. The value of R in electrical units is:
R = J / K-mol
At 25 C and converting ln to log

21. If an electrochemical cell reaches the state of equilibrium, then:
The emf can be found in Tables (Table 3-4) just like free-energy and enthalpy. The values in the table are for a reaction written for 1 mole of e- change, such as:
If an electrochemical cell reaches the state of equilibrium, then:
no current can flow
emf is zero

22. In this case:
since or
log K = 16.9zE
Study Examples page 85

23. Estimate the solubility-product constant for Mg(OH)2(s) at 25  C from standard electrode potential?

24. Chemical Kinetics then, the rate of reaction could be:
Chemical kinetics deal with speed of reactions. If
then, the rate of reaction could be:
first – order reaction (exponent 1)
kCa
second – order reaction (exponent 2)
kCa2
kCaCb
third – order reaction (exponent 3)
kCa3
kCa2Cb
kCaCbCc
Ca, Cb, and Cc = concentrations of A, B, and C, respectively
k = rate constant

25. The reaction rates are required in:
These are simple reaction rates, but in reality there are more complex equations. The unit of k depends on the reaction order and units of concentration of A, B, and C.
The reaction rates are required in:
Microbial growth
Aeration
Disinfection
Radioactive decay

26. Zero-Order Reactions They are independent of concentration
Most of biological growth occur in linear relationship over a range of concentrations of substance (C).

27. First-Order Reactions
The rate is directly proportional to the concentration
if we are dealing with a decay or decomposition reaction, then the rate can be expressed as
Unit of k is (1/time) and the –ve sign indicates the loss of material with time.

28. Integrating the above equation:
Converting to log10

29. k = - slope of line [t versus ln(C/C0)]
k = -slope [t versus log10(C/C0)]
Half-life (t1/2)
In this case,
t = t1/2 and C = (1/2)C0
Then
Applications of 1st order reactions in Environmental Engineering:
Dissolution of gases in water
Removal of gases from water
Rate of death of microorganisms
Decomposition of organic matters (BOD5 test)
Study Example page 89

30. The radioactive nuclide P32 has a half-life of 14. 3 days
The radioactive nuclide P32 has a half-life of 14.3 days. How long would a waste containing 10 mg/l of this nuclide have to be stored in order to reduce the concentration to 0.3 mg/l?

31. Second-Order Reactions
The rate of reaction is proportional to the square of the concentration of one of the reactants or to the product of concentrations of two different reactants.

32. Ca and Cb are concentrations of A and B, respectively
Ca and Cb are concentrations of A and B, respectively. Integrating (1) and (2), we obtain:

33. Consecutive Reactions
If rates of reactions are 1st order, then:

34. Integrating between t = 0 to t = t

35. Examples of consecutive reactions in Environmental Engineering

37. Total enzyme concentration in the system = E = [Ef] + [EcS]
Enzyme Reactions
Are used to describe the rate of biological waste treatment. The relationship between Substrate (S) and the rate of utilization per unit mass of enzyme or bacteria (V/E)
Michaelis – Menton Relationship
Ef = free enzyme
S = substrate
EcS = enzyme-substrate complex
Total enzyme concentration in the system = E = [Ef] + [EcS]

38. The rate of formation of enzyme-substrate complex is:
The rate of complex formation  rate of overall reaction. Therefore, d[EcS] / dt can be considered as ZERO when overall reaction rate is required to be determined. So:

39. Rate of product formation V = k[EcS]
The rate of product formation = overall rate of reaction
Rate of product formation V = k[EcS]

40. Study Example page 95 Then Where
k is the maximum rate
Ks is the substrate concentration at arte = (1/2)k
Ks is called the "half velocity" constant
V/E  k'S when S<< Ks (1st order with respect to S)
V/E  k when S >> Ks (zero order with respect to S)
Study Example page 95

42. Temperature Dependence of Reaction Rates
"rates increase with increase in temperature"
Rate doubles for each 10 C rise.
Using Arrehenius equation:
Where
T = temperature,  K
R = universal gas constant
Ea = constant

43. Integrating
k2 and k1 are rate constants at T2 and T1. In environmental engineering processes, the range of temperature is small. So T2T1 can be assumed constant.

44. Therefore

45. Adsorption
"sorption is the concentration or movement of contaminants from one place to another"
"adsorption involves partitioning of contaminants from one phase to another"
"adsorption is the process by which ions or molecules present in one phase tend to condense and concentrate on the surface of another phase"

46. Adsorption Physical Chemical Ion exchange Weak multi-layers
free moving
reversible
Chemical
Strong
mono-layer
no movement
non-reversible in most cases
Ion exchange
electrical attraction
smaller particles
have stronger attraction
trivalent have stronger attraction than monovalent ions

47. Adsorption depends on:
Activated Carbon
1 gram has surface area of 1000 m2
Pore size ranges between 10 to 1000 A
Adsorption of gas increases wit the increase I pressure
Adsorption depends on:
Nature of materials
Concentration
Temperature

50. Freundlich Isotherm Freundlich found that:
Where
q = mass of contaminant per unit weight of the adsorbent
C = concentration of solute after adsorption
K and n = constants (they should be evaluated for each soluble and temperature)
Freundlich isotherm can be expressed as:

53. Langmuir Isotherm
Langmuir isotherm is also used to describe adsorption of single layer:
qm = maximum adsorption that can take place in grams of adsorbate per gram of adsorbent
a = constant

55. BET Isotherm
A third isotherm is BET (Brunauer, Emmett, and Teller) which can be used to describe multi-layer adsorption
Assumptions
Multi-layers of adsorbent accumulate at the surface of adsorbent
Each layer can be described by Langmuir isotherm
Cs = saturation concentration for the adsorbate in solution

56. If C > Cs then the solute precipitates or condenses from solution as solid or liquid and concentrates on the surface
BET equation can be put in this form:
If we have data, then we have to find the best isotherm that can be used to describe the data (get straight line)

58. Study Examples Page 104