처리공정 및 반응공학 (1996학년도 2학기)

II. BASIC WATER CHEMISTRY

1. Governing Concepts

- Stoichiometry (화학양론식): material balance to transformation processes - Chemical Equilibrium (

화학적 평형

steady state

- Reaction Kinetics (

반응 동역학

1.1 Stoichiometry

1 2 1 2

R + R P + P b⋅ c⋅ → m⋅ n⋅ where R1 and R2 = reactants,

P1 and P2 = products, and

b, c, m, and n = stoichiometric coefficients.

- A chemical reaction must conserve the number of atoms for each element involved in the reaction and the electrical charge associated with ions.

- Stoichiometry permits to calculate the value of some stoichiometric coefficients based on the values of other coefficients.

1.2 Chemical Equilibrium

- The underlying theory for chemical equilibrium is based on thermodynamics.

A + B ⇔ C + D

At equilibrium, the rate of “forward” reaction is identical to it of “reverse” reaction. The rate of forward reaction is expected to proportional to the rate of collisions between A and B. It means that the rate of forward reaction is directly proportional to the concentrations of A and B.

= [A] [B]

f f

R k ⋅ ⋅

where Rf = rate of the forward reaction;

kf = rate constant (vary with temperature); and [A], and [B] = concentrations of A and B.

- Equilibrium is a steady-state condition, not a static condition. Although the concentrations of impurities do not vary with time, transformation and transport processes may still be occurring. They must be only balanced so as to have no observed net effect.

= [C] [D]

r r

R k ⋅ ⋅

where Rr = rate of the reverse reaction;

kr = rate constant (vary with temperature); and [C], and [D] = concentrations of C and D.

At equilibrium,

f = r

R R

[A] [B] = [C] [D]

f r

k ⋅ ⋅ k ⋅ ⋅ [C] [D]

= = [A] [B]

f r

k K

k

⋅

⋅

where K = equilibrium constant of the reaction (constant at a fixed temperature)

A + B C + D

a⋅ b⋅ ⇔ ⋅c d⋅

c d

a b

[C] [D]

[A] [B]⋅ = K

⋅

1.3 Reaction Kinetics

- When a system is at equilibrium?

- How much time is needed for a system to reach equilibrium?

- What can we say about systems that are not at equilibrium?

A + B 1→ C

1

1 1 1

[A] [B] [C]

= - d = - d = d

R dt dt dt

     

     

     

where a, b, c, and d = stoichiometric coefficients;

A and B = reactants;

C = product; and

“1” = arbitrary symbol to identify the reaction.

A + B C + D

a⋅ b⋅ ^γ→ ⋅c d⋅

1 [A] 1 [B] 1 [C] 1 [D]

= - d = - d = d = d

R^γ a dt _γ b dt _γ c dt _γ d dt _γ

       

       

       

= [A] [B]

R_γ k_γ ⋅ ^α⋅ ^β

where kγ = rate constant (a function of temperature, or a function of pressure for gaseous reactions); and

α and β = empirical coefficients.

For an elementary reaction (On the other hand, α and β must be determined experimentally)

= [A] [B]^{a b} R_γ k_γ ⋅ ⋅

Zero-order reaction: R_γ = k_γ

First-order reaction: R_γ = k_γ ⋅[A] or R_γ = k_γ ⋅[B]

Second-order reaction: R_γ = k_γ ⋅[A]², R_γ = k_γ ⋅[B]², or R_γ = k_γ ⋅[A] [B]⋅

Characteristic time (τ) of a reaction: a magnitude estimate of the time required for the process to approach completion, independent of the actions of other processes. The characteristic time of a transformation process can be estimated as the ratio of the initial quantity of a reactant divided by the initial rate of reaction. For example, for a zeor-order reaction expressed as follows;

0

A products, = d[A] = - R_γ dt k

→

0 0

= A /k τ

(Reading Assignment, 2-3 Organic Chemistry p61-64)

2. Phase Changes and Partitioning(분배)

2.1 Vapor Pressure(증기압)

Definition: the vapor pressure of a pure liquid species is the equilibrium partial pressure of the gas molecules of that species above a flat surface of the pure liquid. If the partial pressure of a liquid is less than the vapor pressure of it, the condition is called subsaturation. Converse condition is called supersaturation.

At equilibrium condition between a species in the vapor phase and a flat surface of the pure liquid of the specimen,

0 0

i vp i vp

P = K or P (T) = K (T) where Pio

= equilibrium partial pressure of species i (dependent on temperature);

Kvp = an equilibrium constant (i.e., vapor pressure, dependent on temperature).

Relative Humidity: the amount of water vapor in air

2

2

H O O H O

RH = 100% P

P (T)

×

where RH = relative humidity;

PH2O = actual partial pressure of water vapor; and PH2O

0 (T) = saturation vapor pressure at given temperature.

When the vapor pressure exceeds the total air pressure applied to the liquid surface, the liquid will boil. As higher elevations, the air pressure is lower, ad the boiling point is correspondingly reduced.

For a mixture of single volatile liquid and nonvolatile impurities, the dilution of a liquid with nonvolatile impurities reduces the vapor pressure of the liquid because nonvolatile molecules occupy a portion of the surface, reducing the area from which evaporation takes place. Thus, higher temperature is needed than the pure liquid boils (Raoult’s law).

0 0

i,mix i i

P (T) = X P (T)⋅

where Xi = the mole fraction of the volatile component in the mixture.

The vapor pressure of the components in a mixed of volatile substances usually cannot be estimated reliably from simple relationship such as Raoult’s law (e.g., cosolvent effect). Instead, empirical data must be used.

2.2 Dissolution of Species in Water

Partitioning between the gas phase and water: Henry’s law

w H,g g g g w

C = K ⋅P or P = H ⋅C

where Cw = equilibrium concentration in the aqueous phase;

KH,g and Hg = Henry’s law constant; and

Pg = equilibrium partial pressure in the gas phase.

The dimension of Henry’s law constant is dependent on the dimensions of Cw and Pg. For example, it can be expressed by [mole/L,atm], dimensionless, et al.

Solubility of Nonaqueous-Phase Liquids

NAPL (nonaqueous-phase liquid): Liquids under environmental conditions and do not mix with water

Under equilibrium conditions, the quantity of the NAPL that dissolves in water depends on the species and the temperature, but not on the volume of the NAPL.

Ci (T) = Kws(T)

where Ci = equilibrium concentration of NAPL compound i dissolved in water; and Kws = water solubility for the compound.

Dissolution and Precipitation of Solids

x y

A B ↔ xA +yB (→: dissolution, and ←: precipitation)

x y

[A] [B] = K (T)⋅ sp

where Ksp = solubility product (

용해도적

The quantity of solid material does not influence the amount of dissolved ions in solution because dissolution and precipitation occur only at the interface between the solid and the liquid.

2.3 Sorption (

수착

- Adsorption(

흡착

- Absorption(흡수): a bulk phenomenon in which a chemical species becomes distributed throughout a solid or liquid absorbent.

Sometimes it is not possible to distinguish between adsorption and absorption. Then, the term sorption is used.

Sorption Isotherms

Linear: q = K_{e ads}⋅C_e Freundlich: q = K_{e f} ⋅C^1/n_e

Langmuir: _{e max} ^e

e

q = q b C

1 + b C

⋅ ⋅

⋅

where qe = equilibrium concentration of sorbed molecules in a sorbent; and Ce = equilibrium concentration of sorbed molecules in a fluid.

“Isotherm” means “uniform temperature”. Partitioning varies with temperature.

3. Acid-Base Reactions

- Since acid-base reactions are generally very fast, pH predictions are almost always based on the assumption of equilibrium.

3.1 Acid-Base Reactions and the Hydrogen Ion

- Hydrogen ions do not exit as free H⁺ species in aqueous solution. H3O⁺ is highly favored. The resulting ion may have one or more additional water molecules loosely bound to it.

- Acid and Base (donate or lose hydrogen ion or electron)

3.2 pH of Pure Water H₂O ↔ H⁺ + OH^-

+ '

2

[H ] [OH ] K =

[H O]

⋅ −

K’[H2O] = [H+][OH^-] = Kw = 10^-14

where Kw = equilibrium or dissolution constant for water (dependent on temperature)

3.3 Strong and Weak Acids HA ↔ H⁺ + A^-

+ A

[H ] [A ] K =

[HA]

⋅ −

where KA = acid dissociation constant pKA are less than 1, “strong acid”

3.4 Carbonate-Bicarbonate System

CO2(g) carbon dioxide gas CO2(aq) dissolved carbon dioxide

H2CO3(aq) carbonic acid (a diprotic, weak acid) HCO3-

(aq) bicarbonate ion CO32-

(aq) carbonate ion

CaCO3(s) calcium carbonate (limestone) CO2(g) vs. CO2(aq) [CO2(aq)] = KH∙PCO2

CO2(aq) vs. H2CO3(aq) CO2(aq) + H2O ↔ H2CO3(aq)

2 3 -2.8

A 2

[H CO ]

= K = 10 [CO (aq)]

For engineering purposes we combine CO2(aq) and H2CO3(aq) into one variable, H2CO3*

because it is difficult to experimentally differentiate between CO2(aq) and H2CO3.

[H2CO3

*] = [CO2(aq)] + [H2CO3(aq)] = [CO2(aq)] ∙(1 + KA) ≈ [CO2(aq)]

H2CO3*

vs. HCO3-

(aq) H2CO3*↔ H⁺ + HCO3-

(aq)

+

3 -6.3 1

2 3

[H ] [HCO ]

= K = 10 [H CO *]

⋅ −

HCO3-

(aq) vs. CO32-

(aq) HCO3-

(aq) ↔ H⁺ + CO32-

(aq)

+ 2-

-10.3 3

- 2 3

[H ] [CO ]

= K = 10 [HCO ]

⋅ CO3

2-(aq) vs. CaCO3(s) CaCO3(s) ↔ Ca²⁺ + CO3 2-(aq) Ksp = [Ca²⁺]∙[ CO3

2-(aq)]

Ccarbonate = [H2CO3*

] + [HCO3-

(aq)] + [CO32-

(aq)]

Distribution of aqueous carbonate species as a function of pH - Figure 2-10 (p. 69), and 2-11 (p.70)

Closed system

Open system

3.5 Inorganic Impurities 3.5.1 Ions in water

Table Most prevalent ions in natural waters, along with typical molar concentrations

Ion Seawater (M) River water (M)

Na⁺ 0.47 0.23 x 10^-3

Mg²⁺ 0.053 0.15 x 10^-3

Ca²⁺ 0.010 0.33 x 10^-3

K⁺ 0.010 0.03 x 10^-3

Cl^- 0.55 0.16 x 10^-3

SO4

2- 0.028 0.07 x 10^-3

HCO3

- 0.0024 0.86 x 10^-3

- Ion concentrations are typically 100-1000 times higher in seawater than in freshwater. Bicarbonate is an exception. Why?

3.5.2 Electroneutrality

i i

z C = 0⋅

∑

where zi = charge per molecule on the i^th ion; and

Ci = the molar concentration of the i^th ionic species [M].

3.5.3 Ionic strength (

이온강도

2

i i

i

I = 1 (C z ) 2

∑

- Ionic strength of water significantly affect the activities of ionic species in water.

3.5.4 Hardness (

경도

- the sum of normalities of all multivalent cations (i.e., charge of +2 or greater) - Hardness is often expressed in terms of the equivalent mass concentration of

calcium carbonate (CaCO3). For example, a hardness of 1 meq/L is the same as a hardness of 50 mg/L as CaCO3.

- Soft (< 75 mg/L as CaCO3), Hard (150 - 300 mg/L as CaCO3), very Hard (> 300 mg/L as CaCO3).

3.5.5 Alkalinity(

알칼리도

- the capacity of water to neutralize acids

- 2

- +

3 3

A = [OH ] + [HCO ] + 2[CO ⁻] - [H ] where A = alkalinity

- Alkalinity is measured by titration. A strong acid is slowly added to the water of interest until the pH diminished to 4.5.

4. Oxidation-Reduction Reactions

- Acid-base reactions: transfer of protons

- Oxidation-reduction reactions (Redox reactions): transfer of electrons

- The oxidation of one species is accomplished by a reduction of equal magnitude in another species.

- Redox reaction is much slower than acid-base reactions, making the subject of kinetics more important and that of chemical equilibrium less important relative to acid-base reactions.

4.1 Corrosion

A galvanic cell may occur in a water supply system when two dissimilar metals, such as iron and copper pipe, are connected. In this case, the iron will corrode.

Microbial Fuel Cell(미생물연료전지)

4.2 Combustion

Complete combustion of pure hydrocarbon fuel using O2 would produce only CO2

and H2O vapor as products. Air pollution problems associate with combustion can be traced to (1) chemical elements other than H, C, and O may be present in the fuel; (2) the exhaust gases under incomplete combustion; and (3) the high temperature of combustion can lead to partial oxidation of N2 from air.

4.3 Atmospheric oxidation processes Thermal reactions vs. Photolytic reactions

Chemical equilibrium does not adequately describe gas-phase atmospheric chemistry because of kinetic limitations. On the other hand, equilibrium

relationship can be used (1) to estimate the partitioning of a species between the gas phase and liquid water droplets and (2) to describe the acid-base chemistry in fog, cloud, and rain drops because these do not involve redox reactions.

4. 4 Microbial Reactions

Photosynthetic production of biomass

+4 -2 0 0

hv

2 2 2 2

C O + H O → {C H O} + O Aerobic Respiration

0 0 +4 -2

2 2 2 2

{C H O} + O → C O + H O Nitrogen Fixation

0 0 +4 -3

+

2 2 2 2 4

3{C H O} + 2 N + 3H O + 4H → 3C O + 4 N H ⁺

“Fixed nitrogen” such as ammonia and nitrate, is a necessary nutrient for plant growth.

Nitrification (질산화

반응)

3 0 +5 -2 -2

+ - +

2 3

4 2

N H + 2 O N O + 2H + H O

− →

Plants absorb nitrate more efficiently than ammonium as a nutrient.

Nitrate Reduction (or Denitrification,

탈질반응)

0 +5 +4 0

- +

2 3 2 2 2

5{C H O} + 4 N O + 4H → 5 C O + 7H O + 2 N Sulfate Reduction

0 +6 +4 -2

+ 2-

2 4 2 2 2

2{C H O} + 2H + S O → 2 C O + 2H O + 2H S Methane Formation

0 +4 -4

2 2 4

2{C H O} → C O + C H

5. Organic Chemistry

Reading Assignment (2.3 Organic chemistry)