pH, pOH, Kw, Ka, Kb, pKa, pKb
• Water
Kw = [H+][OH-] 10-14
• Strong acid (e.g., HNO3, HCl)
100% dissociated: HCl == Cl- + H+
• Strong base (e.g., NaOH, KOH)
100% dissociated: NaOH == Na+ + OH-
• Weak acid (e.g., H2CO3, CH3COOH)
Monoprotonic weak acids (e.g., CH3COOH): Ka
CH3COOH (Given Ka = 1.8x10-5)
Polyprotonic acids (e.g., H2CO3): Ka1, Ka2..
H2CO3 (Ka1 = 4,3x10-7, Ka2 = 4.7 x10-11)
H3PO4 (Ka1 = 7.5x10-3, Ka2 = 6.2x10-8, Ka3 = 4.8x10-13)
• Weak base (e.g., NaOCl)
Equilibrium constant of bases:Kb, Kb1, Kb2… 1
Acids and Bases
• Strong acids and bases:
– H2SO4, HNO3, HCl, HF
– NaOH, KOH
• Weak acids, bases and salts
– Acids: HAC, NH4+, H2CO3, HCN, H2S, phenol,
H3PO4, protein, fatty acid
– Bases: AC-, NH3, Ca(OH)2 (lime), Mg(OH)2
– Salts: NaCl, Al2(SO4)3 (alum)
Water Chemistry Acid-Base 2
Acidity & Alkalinity
• Definition:
– Acidity: The capacity of water to neutralize OH-
– Alkalinity: The capacity of water to neutralize H+
• Source of acidity:
– Natural water: CO2 (air, bacteria, etc), H2PO4-, H2S, protein, fatty
acids, Fe3+, hydrated Al3+, e.g.:
Fe(H2O)63+ <=> Fe(H2O)5OH2+ + H+
Al(H2O)63+ <=> Al(H2O)5OH2+ + H+
– Polluted water: free mineral acid (H2SO4, HCl) from metallurgical
industry (steel pickling liquor), acid mine drainage, acid rain,
organic acid waste
• Source of alkalinity:
– Major: HCO3-, CO32-, OH-
– Minor: NH3, conjugate bases of H3PO4, HBO3, and organic acids
Water Chemistry Acid-Base 3
Effects of Acidity and Alkalinity
• Acidity
– Increase corrosion
– Affect aquatic life
– Increase soil leaching and therefore water quality
– Affect dosage of chemicals used in water treatment
• Alkalinity
– Corrosive if high in alkalinity, hence a parameter used for corrosion control
– A parameter in deciding whether treated waters meet drinking water standards, and whether
industrial water can discharged into municipal wastewater treatment plant for biological
treatment
– Moderate alkalinity is needed in swimming pool, for complete coagulation in water
treatment plant, or for natural water to resist acid rain / pH change
Water Chemistry Acid-Base 4
Acidity Measurement
10
9
8 Phenolphthalein end point
(pH 8.3: Colorless Red)
7
6 Range of CO2 acidity
5
Methyl orange end point
4 (pH 4.3: Red Yellow Orange)
3
2 Range of mineral acidity
1
Water Chemistry Acid-Base 5
Alkalinity Measurement
Titration Curve for a Hydroxide-Carbonate Mixture
-
OH- Y OH When P > T/2
Titrate with H2SO4
12 2X+Y=T ……..(i)
X+Y=P …….(ii)
11 CO3=
P So, X= (T – P)
T 10 X CO3= And, Y= (2P – T)
Point of inflection
CO3=
9 (Phenolphthalein) So, CO3= =2X= 2(T – P)
8
CO3=
7 CO3 =
CO3= So, OH- = Y = (2P – T)
X HCO3-
6 HCO3-
Point of inflection
5 Hydroxide Carbonate (Methyl Orange)
4
OH- +H+ H2O CO32- + H+ HCO3- HCO3- + H+ H2CO3
3
2 mL Acid
Water Chemistry Acid-Base 6
For finding out approximate Alkalinity, there are five alkalinity conditions possible in a water sample:
(1) hydroxide alone, [pH >12] (2) carbonate and hydroxide, [pH ~ 11] (3) carbonate alone, [pH ~ 10]
(4) bicarbonate and carbonate, [pH ~ 9] and (5) bicarbonate alone. [pH < 8.3]
Alkalinity, mg/L as CaCO3
Titration
Bicarbonate Carbonate Hydroxide
Result
(5) P=0 T 0 0
(4) P < T/2 T - 2P 2P 0
(3) P = T/2 0 2P 0
(2) P > T/2 0 2T - 2P 2P - T
(1) P=T 0 0 T
where P = phenolphthalein alkalinity and
T = total alkalinity.
Water Chemistry Acid-Base 7
Calculation of Acidity
• Two different types of acidity
– Methyl orange acidity = free mineral acids
– Total acidity = Phenolphthalein acidity
• Acidity by measurement of titration
– Titration with NaOH and is reported as “methyl orange
acidity” and “total acidity” in CaCO3 in mg/L
– Acidity = V x N x 5 x 104/Vs
• V = volume of base used in titration (mL)
– V1 = mL of NaOH needed to pH 4.3
– V2 = ml of NaOH needed to pH 8.3
• N = normality of base used in titration (N)
• Vs = volume of water sample (ml)
Water Chemistry Acid-Base 8
Calculation of alkalinity
• Two different types of alkalinity
– Phenolphthalein alkalinity
– Total alkalinity = methyl orange alkalinity
• Alkalinity by measurement of titration
– Titration with H2SO4, and is reported as
“Phenolphthalein alkalinity” and “Total alkalinity” in
mg/L as CaCO3
– Alkalinity = V x N x 5 x 104/Vs
• V = volume of acid used in titration (mL)
– V1 = mL of H2SO4 needed to pH 8.3
– V2 = ml of H2SO4 needed to pH 4.3
• N = normality of acid used in titration (N)
• Vs = volume of water sample (ml)
Water Chemistry Acid-Base 9
Example Alkalinity Calculation
A water contains 100 mg/l CO3= and 75 mg/l HCO3- at a pH of 10. Calculate the alkalinity
exactly and also approximate alkalinity by ignoring [OH-] and [H+].
Exact alkalinity = [OH-] + [CO3=] + [HCO3-] – [H+]
First convert the concentration of ion to mg/l as CaCO3 [EW of CaCO3 = [100]/2 = 50]
Equivalent weight:
CO3= MW = [12+48] ; Valence z = 2; So, EW of CO3= = [12+48] /2 = 30
EW of HCO3- = [1+12+48]/1 = 61; EW of OH- = [16+1]/1 = 17; EW of H+ = [1]/1 = 1
CO3= = 100 (mg/l) (50/30) = 167 mg/l as CaCO3
HCO3- = 75 (mg/l) (50/61) = 61 mg/l as CaCO3
10
Example Alkalinity Calculation
As pH = 10, So, concentration of H+ = 10-10 M/l = 10-10 N/l (as z = 1)
= 10-10 N/l × 50 × 103 = 50 × 10-6 mg/l as CaCO3
As pH = 10, So, concentration of OH- = 10-4 M/l = 10-4 N/l (as z = 1)
= 10-4 N/l × 50 × 103 = 5 mg/l as CaCO3
Exact alkalinity = [OH-] + [CO3=] + [HCO3-] – [H+] = 5 + 167 + 61 - 50 × 10-6
= 233 mg/l as CaCO3
Approximate alkalinity by ignoring [OH-] and [H+]= [CO3=] + [HCO3-]
= 167 + 61 = 228 mg/l as CaCO3
11
Example Alkalinity Calculation
A sample of water from the overflow of the recarbonation basin that follows a
precipitation/softening process has a pH of 9.0; 200 mL of the water require 1.1 mL of
0.02 N H2SO4 to titrate it to the phenolphthalein endpoint and additional 22.9 mL of 0.02
N H2SO4 to titrate it further to the orange endpoint. Assuming the sample contains no
calcite particles, what are phenolphthalein alkalinity and the total alkalinity in mg/L as
CaCO3?
Volume of water sample Vs = 200 mL ; Ss = alkalinity of water sample
Using the relation V1 S1 = V2 S2
So, phenolphthalein alkalinity = Ssp 200 × Ssp = 1.1× 0.002 (N);
So, Ssp= 1.1× 0.002 (N)/200 = [1.1× 0.002 /200] (N) × 50 × 1000 mg/L as CaCO3
= 5.5 mg/L as CaCO3 (Phenolphthalein alkalinity [P])
12
Example Alkalinity Calculation
So, Total alkalinity SST = (1.1+22.9) × 0.002 (N)/200
= [(1.1+22.9) × 0.002 /200] (N) × 50 × 1000 mg/L as CaCO3
= 120 mg/L as CaCO3 (Total alkalinity [T])
It is case (4), i.e. P < T/2
Ions for approximate alkalinity are [CO3=] and [HCO3-]
Phenolphthalein alkalinity [P] = 5.5 mg/L as CaCO3
CO3=
P CO3= = 2P = 11 mg/L as CaCO3
CO3=
HCO3- = T – 2P = 120 – 11 = 109 mg/L as CaCO3
HCO3-
T
13
Carbon Dioxide (CO2):
The Most Important Weak Acid
• Abundant in air (CO2 (g) = 0.037% v/v in dry air)
• Dissolved CO2 is present in virtually all natural waters and
wastewater; Even rainfall in unpolluted air is slightly acidic due
to CO2
– CO2 (g) CO2 (aq)
– CO2 (aq) + H2O H+ + HCO3-
• Algae need CO2 for photosynthesis
– 2HCO3- + hv (CH2O) + O2 + CO3- (pH )
• Bacteria produce CO2 during decay of organic compounds
– (CH2O) + O2 CO2 + H2O (pH )
Water Chemistry Acid-Base 14
Carbon Dioxide (CO2):
The Most Important Weak Acid
Water Chemistry Acid-Base 15
Species Distribution Diagram
CO2 HCO3- CO32-
Fraction as designated species
1
0.8
0.6
0.4
0.2
0
4 5 6 7 8 9 10 11 12
pH
Water Chemistry Acid-Base 16
