Unit Operations and water and wastewater treatment lecture notes 1

1. CEE 155 – Unit Operations & Processes in
Water and Wastewater Treatment
Lecture 1
Basic Chemical Concepts
Dr. Eric M.V. Hoek
UCLA Civil & Environmental Engineering

2. Homework
! Reading Assignment #1 (due Monday, October 1)
! Required: Droste Chapter 1, 2, 3, 9, 10;
! Recommended: R&R Chapters 1, 4 to 6
! Homework Assignment #1 (due Monday, October 8)
! Droste Chapter 1: 1, 3, 5, 24, 27
! Chapter 9: 1 to 10
! Chapter 10: 1, 2, 4, 5, 6
! Project Assignment #1 (due Wednesday, October 17)
! Choose a specific water pollutant problem (e.g., Cryptosporidium
parvum, viruses, arsenic, chlorinated organic solvents, nitrogen and
phosphorous, salinity, etc.), which will be the motivating factor of
your review paper.

3. Today’s Lecture
! Basic Chemical Concepts
! Properties of water and expressions of concentration
! Conductivity, ionic strength and activity
! Example: mass-molar-normal-ionic strength, NH3-N, CaCO3 hardness
! Chemical Kinetics
! Reaction rate, order, and chemical kinetics
! Example: nuclear chemistry
! Integral method of analyzing kinetic data
! Equilibrium Chemistry
! Chemical equilibrium and balancing chemical reactions
! Acid-base, solubility product, gas laws, complexation, redox
! Example: the “carbonate system” " hardness and alkalinity, saturation
index, corrosion and stabilization, scaling and softening

4. !
Unique Properties of Water
!
!

5. Guide for Concentration Conversions
! Example:
! Express 1 mg/l of ammonia (NH3) to units of nitrogen (N)
! 1 mg/l NH3 ! 14 g-N/mol ÷ 17 g-NH3/mol = 0.82 mg/l NH3-N

6. Guide for Concentration Conversions
Example:
Express 46 ppm of Na+ to normality (milliequivalents)
(46 mg/L Na+ ! 1g/1000mg)
÷ (23 g-Na/mol ! 1mol/1000mmol) = 2 mmol/L * 1 = 2 meq/L
Example:
What are the mass concentrations of Ca2+ or Al 3+ solutions that have
equivalent charge concentrations 46 mg/L (ppm) of Na+
Equivalent concentration of Na+: (46 mg/l Na+ ! 1g/1000mg)
÷ (23 g-Na/mol ! 1mol/1000mmol) = 2 mmol/L * 1 = 2 meq/L
Ca2+: 2 meq/L ÷2 (Charge of Ca2+ ) =
(1 mmol/L*1 mol/1000mmol)*(40g-Ca/mol*1000mg/g) = 40 mg/L
Al3+: 2 meq/L÷3 (Charge of Al3+ ) =
(0.67mmol/L*1mol/1000mmol)*(27g-Al/mol*1000mg/g)=18mg/L

7. Electroneutrality = Conservation of Charge
! C = mass concentration of dissolved ions, mg/l (given)
! Mw = ion molecular weight of ions, mg/mol
! M = molarity of ions, mol/l (= C/Mw)
! z = ion valence (known)
! Ew = equivalent weight of ions, mg/meq (=Mw/z)
! N = normality of ions, meq/l (= C/Ew)
! I = ionic strength of ions, mol/l (= Mizi
2; total solution ionic strength = sum [Mizi
2])
C Mw M z Ew N I
Cations mg/l mg/mol mol/l - mg/meq meq/l mol/l
Na+ 75.5 22,990 0.0033 1 23.0 3.28 0.0033
Ca2+ 14.0 40,080 0.0003 2 20.0 0.70 0.0014
Mg2+ 35.1 24,312 0.0014 2 12.2 2.89 0.0058
Sum 124.6 0.0051 6.87 0.0105
Total Total
Dissolved Total Total Ionic
Solids Molarity Normality Strength
496.7 0.011 13.74 0.0097
C Mw M z Ew N I
Anions mg/l mg/mol mol/l - mg/meq meq/l mol/l
HCO3- 243.8 61,017 0.0040 1 61.0 4.00 0.0040
Cl- 27.5 35,453 0.0008 1 35.5 0.78 0.0008
SO42- 100.8 96,062 0.0010 2 48.0 2.10 0.0042
Sum 372.1 0.0058 6.87 0.0090
! !
= anions
cations

8. Ionic Strength
Example: What is the ionic strength of 300 mg/L (ppm) CaCO3 solution?
300 mg/L ÷100 mg/mmol = 3 mmol/L
Cation: Ca2+
I Cation = MZ2 = 3 mmol/L * 2 2 = 12 mmol/L
Anion: CO3
2-
I Anion = MZ2 = 3 mmol/L * 2 2 = 12 mmol/L
Total
I total = * (12 mmol/L + 12 mmol/L) = 12 mmol/L

9. Conductivity and Ionic Strength
! Conductivity

10. Hardness and Alkalinity
! Hardness (HAR) = [Ca2+] + [Mg2+] + [Cu2+] + …
! Total hardness is typically considered as the sum of calcium and
magnesium concentrations, but is (fundamentally) the sum of all
divalent cations.
! Hardness is often expressed as mg/L of CaCO3
! Mw = 40 + 12 + 3(16) = 100 g/mol
! Z (valence): Ca2+ = 2; CO3
2㻙 = 2
! Ew = 40/2 + [12 + 3(16)]/2= 50 g/eq = 50 mg CaCO3/meq
Ca2+
= 50
mg
L
1
40
mmol
mg
2
meq
mmol
= 2.5
meq
L
50
mgCaCO3
meq
= 125
mg
L
as CaCO3
Mg2+
= 10
mg
L
1
24
mmol
mg
2
meq
mmol
= 0.4
meq
L
50
mgCaCO3
meq
= 20
mg
L
as CaCO3
Total Hardness = 145
mg
L
as CaCO3

11. Hardness and Alkalinity
! Alkalinity
! Alkalinity is a measure of the capacity of water to neutralize
acid.
! Alkalinity was determined by three major chemical forms in
natural water system: HCO3
-, CO3
2- and OH-
! The source of carbonate may be from dissolved atmospheric
CO2(g), from microbially produced CO2(g) (especially in
groundwater), or from dissolution of carbonate minerals (e.g.,
calcite, dolomite, magnesite) by natural erosion or weathering.
! Total alkalinity may also be expressed in mg/L as CaCO3.

12. Hardness and Alkalinity
! Alkalinity
The total alkalinity of a water sample is the sum of all salts
that react with acid, i.e., basic ions, and is determined
from
[ALK] = [OH-] + [HCO3
-] + [CO3
2-] + other alkaline ions
(“proton acceptors”).
The calculation is performed as follows assuming a pH of 8.0 and the total carbonate
concentration is 0.005 M:
)
HCO
g
considerin
solely
(
CaCO
as
L
mg
250
Alkalinity
Total
CaCO
as
L
mg
35
.
252
Alkalinity
Total
CaCO
as
L
mg
3
.
2
meq
mgCaCO
50
L
meq
045
.
0
mmol
meq
2
mg
mmol
60
1
L
mg
1.36
CO
CaCO
as
L
mg
250
meq
mgCaCO
50
L
meq
5
mmol
meq
1
mg
mmol
61
1
L
mg
305
HCO
CaCO
as
L
mg
05
.
0
meq
mgCaCO
50
L
meq
001
.
0
mmol
meq
1
mg
mmol
17
1
L
mg
0.017
OH
-
3
3
3
3
3
-
2
3
3
3
-
3
3
3
-
!
=
=
=
=
=
=
=
=
=
=

13. Oxidation State
! The oxidation state of an atom can be expressed through the oxidation number, which
depends on the number of electrons associated with the atom.
! In compounds, electrons are associated with atoms according to their electronegativity.
! Electrons are assigned to the more electronegative element according to these rules.
1. The algebraic sum of the oxidation numbers of all atoms in a neutral compound is zero;
otherwise, the sum must equal the charge on the ionic species.
2. The oxidation number of all free elements is zero. When an atom is bonded to another
identical atom, the bond makes no contribution to the oxidation state of either atom.
3. Alkali metals (first column of periodic table) assume a +1 oxidation state in their
compounds; the alkaline earth metals (second column) have oxidation state of +2.
4. The oxidation state of oxygen is -2 except in peroxide, where it is -1 and when it is bonded
to itself (O2), where it is zero (as in rule 2).
5. Hydrogen has an oxidation number of +1 except when bonded to metallic hydrides such as
NaH, in which case it has oxidation state of -1.

14. Oxidation State
Most elements have more than one possible oxidation state —
with carbon having nine, as follows below:
–4:!CH4
–3:!C2H6
–2:!CH3Cl
–1:!C2H2
0:!CH2Cl2
+1:!C2H2Cl4
+2:!CHCl3
+3:!C2Cl6
+4:!CCl4
Acetic acid Oxidation:
CO2 + H2O
+4
Benzene Oxidation:
CO2 + H2O
C6H6
+4
-1

15. Basic Chemical Principles
! Irreversible Reaction
! Proceeds only in one direction and continues until the
reactants are exhausted*
! Aggregation, Deposition, Oxidation, Adsorption
A + B C + D
! Reversible Reaction
! Proceed in either direction, depending on the
concentrations of reactants and products relative to the
equilibrium concentrations
! Acid-base, Precipitation-Dissolution, Complexation
! A + B # C + D
* Strictly speaking, no chemical reaction is completely irreversible, but for many reactions the
equilibrium point lies so far to the right that they are treated as irreversible reactions. The noted
“irreversible reactions” can be reverse, but it requires significant energy input to achieve.

16. Basic Chemical Principles
! Homogeneous Reactions
! Reaction occurs in bulk of the flowing water (aggregation,
disinfection, precipitation, neutralization)
! Mixing increases the rate of molecular or particle collisions in
the bulk, and thus, the overall rate of reaction
! Heterogeneous Reactions
! Reaction occurs at the interface between two phases (absorption/
stripping) or at a surface (adsorption, ion-exchange, or catalytic
reactions)
! Diffusion of reactants to the reactive interface is often the rate
limiting step, but the rate of mass transfer can be improved by
increasing fluid flow velocity; and hence, these processes are
typically “mass transfer limited” … and appear 1st order.
! Therefore, kA is also a function of mixing and fluid flow

17. Common Chemical Reactions
! Acid-base reactions
! HA = H! + A!
! Acid-base chemistry forms the foundation for understanding carbonate chemistry,
corrosion, scaling, and stabilization of water, in addition to many water quality
analyses (e.g., hardness/alkalinity titrations).
! pH control is common for process optimization (coagulant dosing, softening, etc.) as
well as environment and infrastructure protection
! Precipitation-dissolution reactions
! AaBb(s) = aAm! + bBn!
! Ksp = {Am!}a{Bn!}b
= {X} = activity = ![X], where [X] = molarity; !!= activity coefficient
! Often used in combination with pH control for water softening, metal precipitation, or
stabilization (providing buffer capacity to a corrosive water)
! Also, precipitation is used to generate ‘sweep flocs’ in coagulation
! Complexation reactions
! M(L)m
x! + nLy! = M(L)m!n
x!ny
! Selective binding of metal ions by inorganic anions (Cl!, OH!, etc.) and organic
chelating agents is common in industrial wastewater treatment and recycling, as well
as in many water quality analytical methods

18. Precipitation/Dissolution Reactions
! concentration of solids in EQBM with solution
! AaBb(s) = aAb+ + bBa-
! Ksp = {Ab+}a{Ba-}b = “solubility product”
= {X} = activity = ![X], where [X] = molarity; != activity coefficient
! Often used in combination with pH control for water softening, metal
precipitation, or stabilization (providing buffer capacity to a corrosive
water)
! Also, precipitation is used to generate ‘sweep flocs’ in coagulation

19. Precipitation/Dissolution Reactions
! concentration of solids in EQBM with solution
! AaBb(s) = aAb+ + bBa-
! Ksp = {Ab+}a{Ba-}b = “solubility product”
= {X} = activity = ![X], where [X] = molarity; != activity coefficient
! Often used in combination with pH control for water softening, metal precipitation, or
stabilization (providing buffer capacity to a corrosive water)
! Also, precipitation is used to generate ‘sweep flocs’ in coagulation

20. Carbonate Chemistry
• Carbonate system is important acid-base system in water, which
controls the pH of most natural waters.
• Carbonate system include
gaseous carbon dioxides (CO2)g,
aqueous carbon dioxide (CO2)aq,
carbonic acid (H2CO3),
bicarbonate (HCO3-),
carbonate (CO3
2-)
and solids containing carbonate.

21. Carbonate Chemistry
Air
Water
CO
2(g)
CO2(aq)
( ) ( )
CO CO
g aq
2 2
!
Where
= mole fraction of CO2 at equilibrium in liquid phase
= Henry’s Law Constant, atm-1
= partial pressure of CO2
What is the pH of
water exposed to
atmosphere at
equilibrium?

22. Carbonate Chemistry
• Aqueous Phase Reactions
2 2 2 3
( )aq
CO H O H CO
+ ! 3
2 3
2
[ ]
( 25 , 1.58 10 )
[ ]
m m
aq
H CO
K at C K is
CO
!
=
Reaction Equilibrium Constant
2 3 3
*
H CO H HCO
+ !
= + 7
3
1
2 3
[ ][ ]
(4.47 10 / 25 C )
[ *]
o
H HCO
K mol L at
H CO
+ !
!
=
2
3 3
HCO H CO
! + !
= +
2
11
3
2
3
[ ][ ]
(4.68 10 / 25 C )
[ ]
o
H CO
K mol L at
HCO
+ !
!
!
=

23. Oxidation Reduction
! Oxidation-reduction reactions involve the transfer of electrons
! Reductant: the substance giving up electrons is oxidized (oxidation
number becomes more positive); the reductant is oxidized
! Oxidant: the substance receiving electrons is reduced (oxidation
number becomes more negative) ; the oxidant is reduced
! General rules for redox reactions:
1. Write out the core reactants and products and balance the equation
w.r.t the atom that is changing it’s oxidation state
2. Balance the reaction w.r.t oxygen by adding H2O where needed
3. Balance H by adding H+ ions.
4. Balance the charge by adjusting the number of electrons
5. Add any extraneous ions that do not participate in the redox
reaction

24. Oxidation Reduction
OxA + RedB # RedA + OxB
! Redox half reactions – the oxidant is reduced
OxA + ne㻙 $ RedA
! OxA = oxidized form of species A (“oxidant”/electron acceptor)
! n = number of electrons transferred
! e = electron
! RedA = reduced form of species A
! Redox half reactions – the reductant is oxidized
RedB $ OxB + ne㻙
! RedB = reduced form of species B (“reductant”/electron donor)
! OxB = oxidized form of species B

25. Fundamentals of Oxidation Reduction
! Consider the oxidation of Fe(II) to Fe(III) by oxygen
! Half reaction for iron – the reductant is oxidized
! Write down half reaction for target contaminant
! Fe2+ $ Fe3+
! Balance all atoms except hydrogen and oxygen
! already balanced
! Balance oxygen atoms with oxygen in water
! n/a
! Balance remaining hydrogen atoms with H+
! n/a
! Balance total charge with electrons
Fe2+ $ Fe3+ + e㻙

26. Fundamentals of Oxidation Reduction
! Half reaction for oxygen – the oxidant is reduced
! Write down half reaction for oxidizing compound
! O2 $ ?
! Balance all atoms except hydrogen and oxygen
! n/a
! Balance oxygen atoms with oxygen in water
! O2 $ 2H2O
! Balance remaining hydrogen atoms with H+
! O2 + 4H+ $ 2H2O
! Balance total charge with electrons
! O2 + 4H+ + 4e㻙 $ 2H2O … 4!( Fe2+ $ Fe3+ + e㻙 )
! Multiply Fe reaction by 4, sum the two reactions, and
eliminate electrons to obtain:
4Fe2+ + O2 + 4H+ 4Fe3+ + 2H2O

27. Redox Reaction Equilibrium
! A redox reaction will proceed if the free energy change
for the overall reaction is negative – like all reactions...
! #G0 is the free energy change at standard conditions
! At equilibrium, the free energy change is zero…
! Values for #G0 are known for many common reactions
eq
rxn
a
b
a
d
a
c
rxn
rxn K
RT
G
B
A
D
C
RT
G
G
D
a
d
C
a
c
B
a
b
A
ln
}
}{
{
}
{
}
{
ln 0
/
/
/
0
+
!
=
#
$
%
%
'
+
!
=
!
+
(
+
!
!
#
$
$
%
'
(
=
+
'
=
!
!
#
$
$
%
+
+
'
=
RT
G
K
K
RT
G
B
A
D
C
RT
G
rxn
eq
eq
rxn
a
b
a
d
a
c
rxn
0
0
/
/
/
0
exp
ln
}
{
}
{
}
{
}
{
ln
0

28. Common Redox Half-Reactions

29. Basic Chemical Kinetics
The Reaction Order and Rate Law
! The dependence of the reaction rate (–rA) is almost
without exception determined experimentally.
! The order of a reaction refers to the powers to which the
concentrations are raised in the kinetic rate law.
! The reaction is 㼍 order w.r.t. A and 㼎 order w.r.t. B , but
the overall order of the reaction is n (= 㼍 + 㼎).
aA + bB ! cC + dD; rA = kACA
#
CB
$
CC
%
CD

30. Basic Chemical Kinetics
! Elementary Rate Laws and Molecularity
! A reaction has an elementary rate law if the reaction of each
species is identical with the stoichiometric coefficient of that
species for the reaction as written.
! The molecularity of a reaction refers to the number atoms, ions,
or molecules involved (colliding) in the rate-limiting step of the
reaction – unimolecular, bimolecular, termolecular, etc.
! Reversible Reactions
! At equilibrium, rate laws reduce to the thermodynamic
relationship governing species concentrations at equilibrium
n
n
n
n B
A
A
A
n
n C
C
k
r
nC
B
A =
!
+ ;
aA + bB cC + dD; Keq =
kfor
krev
=
CC,eq
c
CD,eq
d
CA,eq
a
CB,eq
b =
mol
L
#
$
%
'
(
d +c)b)a

31. Basic Chemical Kinetics
! Reversible Reactions (cont’d)
! 2B # C + D2 ; define forward and reverse rate constants w.r.t. B
! B is consumed according to 2B C + D2 with rate
#rB,for = kBCB
2
! Multiplying through by (-1) gives the “rate of production” of B via the
forward reaction 2B C + D2 with rate
rB,for = #kBCB
2
! B is produced according to C + D2 2B with rate
rB,rev = k #BCCCH2
! The NET rate of formation of B is the sum of the forward (for) and
reverse (rev) rates of formation from the forward and the reverse reaction
rB = rB,net = rB,for + rB,rev = #kBCB
2 + k #BCCCD2
! Multiplying through by (-1) yields the net rate of disappearance of B
!
!
#
$
$
%
'
=
!
!
#
$
$
%
'
=
'
=
' '
'
eq
D
C
B
B
D
C
B
B
B
B
D
C
B
B
B
B
K
C
C
C
k
C
C
k
k
C
k
C
C
k
C
k
r 2
2
2
2
2
2

32. Basic Chemical Kinetics
! The Reaction Rate “Constant”
! The rate of disappearance of A, –rA, depends on temperature and
composition; thus, the rate can be written as the product of a
reaction rate constant, k, and a function of the concentrations
(activities) of the various species involved in the reaction.
–rA = {kA(T)}!{fn(CA, CB, …)}
! The algebraic equation that relates to the species concentrations
is called the kinetic expression, or rate law
! The rate constant, k, is a strong function of temperature
kA(T) = A·exp(– EA/RT)…“Arrhenius equation”
A = pre-exponential factor
E = activation energy, J/mol or cal/mol
R = gas constant = 8.314 J/mol·K = 1.987 cal/mol·K
T = absolute temperature, K

33. y = -6087.6x + 16.121
R2
= 0.9998
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
0.0030 0.0031 0.0031 0.0032 0.0032
1/T (K-1
)
log
k
(s
-1
)
Basic Chemical Kinetics
! The Reaction Rate “Constant”
! The activation energy is equated with the minimum energy that
must be possessed by reacting molecules before the reaction will
occur. It is determined experimentally by carrying out the
reaction at several different temperatures.
ln kA = ln A – EA/(RT)
log kA = log A – EA/(2.3RT)
! Taking the log of the Arrhenius eq’n linearizes kinetic data.
T (K) 1/T (K-1
) k (s-1
) log k (s-1
)
313 0.0032 0.00043 -3.37
318 0.0031 0.00103 -2.99
323 0.0031 0.00180 -2.74
328 0.0031 0.00355 -2.45
333 0.0030 0.00717 -2.14

34. Basic Chemical Kinetics

35. Basic Chemical Kinetics
! Zero Order Reaction
- Reaction rate is independent of the concentration of the
reactant or product.

36. Basic Chemical Kinetics
! Zero Order Reaction

37. Basic Chemical Kinetics
! Zero Order Reaction

38. Basic Chemical Kinetics
! First Order Reaction
- Reaction rate is proportional to the concentration of one
reactant.

39. Basic Chemical Kinetics
! First Order Reaction

40. Basic Chemical Kinetics
! Zero Order Reaction

41. Basic Chemical Kinetics
! Second Order Reaction
- Reaction rate is proportional to the second power of
single reactant being converted to a product.

42. Basic Chemical Kinetics
! Second Order Reaction

43. Basic Chemical Kinetics
! Second Order Reaction

44. Basic Chemical Kinetics
Reaction Order and Rate Law
Order Rate Law Rate Constant
Oth –rA = kA mol$L-1$s-1
1st –rA = kACA s-1
2nd –rA = kACA
2 L$mol-1$s-1
Empirical Models
nth –rA = kACA
n Ln-1$mol-(n-1)$s-1
pseudo 1st –rA = kBODCBOD mol$L-1$s-1
declining 1st –rA = kACA mol$L-1$s-1
kA = declining 1st order rate constant
Fi, ni = fitting parameters
k1st,0 = initial first order rate constant
t = time, x = position in reactor !
!
!
!
#
$
+
+
=
i
st
i
st
n
i
n
i
A
x
F
k
t
F
k
k
)
1
(
)
1
(
0
,
1
0
,
1

45. Example: Nuclear Chemistry
! Radioactivity: elements with unfavorable proton-to-
neutron ratios spontaneously decay in order to form more
stable compounds (isotopes).
! All elements with Mw 200 are unstable, i.e., radioactive.
! Nuclear instability can also be induced by bombardment with
neutrons or radiation (particle accelerators).
! Half-life, t = 0.693/k … where does this come from?
! Radioactive decay rate: dN/dt = -kN (first order kinetics)
! N = # or mass of undecomposed nuclei
! Integrate to find: N/N0 = exp(-kt); find the time at which N = N0/2
! t = -ln(2)/k
! t = 0.693/k

46. Collection and Analysis of Rate Data
! Integral Method of Rate Analysis
! The integral method is a trial and error method, in which we (1)
guess the reaction order, (2) integrate the batch reactor
differential equation, and (3) fit the model to the data.
! * requires that the overall reaction order is an integer…
! A products … 㻙(dCA/dt) = –rA = kCA
㼍!
! Zero Order Reaction
dCA/dt = –k (integrate) % CA = CA0 – kt % k
! A plot of CA versus t is linear…
! First Order Reaction
dCA/dt = –kCA (integrate) % ln(CA0/CA) = kt % k
! A plot of ln(CA0/CA) versus t is linear…
! Second Order Reaction
dCA/dt = –kCA
2 (integrate) % 1/CA – 1/CA0 = kt % k
! A plot of 1/CA versus t is linear…

47. Zero Order Fit
y = -1.034x + 21.484
R2
= 0.930
0
5
10
15
20
25
30
0 5 10 15 20
t , min
C
,
mol/L
Collection and Analysis of Rate Data
! Integral Method – Zero Order

48. First Order Fit
y = 0.100x
R2
= 1.000
0.0
0.5
1.0
1.5
2.0
2.5
0 5 10 15 20
t , min
ln(C/C0),
mol/L
Collection and Analysis of Rate Data
! Integral Method – First Order

49. Second Order Fit
y = 0.012x + 0.010
R2
= 0.930
0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0 5 10 15 20 25
t, min
1/C,
L/mol
Collection and Analysis of Rate Data
! Integral Method – Second Order