Water Science• Electroneutrality, pH, Alkalinity, Acidity• Reversible Equations• Carbonate Equilibrium System• Examples

• Rain• Ocean pH• Acid Rain• Acid Mine Drainage

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Water Electroneutrality• Balanced: ∑ Cations = ∑ Anions

• ∑ CC x eC = ∑ CA x eA

• CC = moles / liter of cation c (one mole = 6.02x1023)

• eC = number of charges per molecule of cation C

• A subscript is for anions

• Pure water: [H+] = [OH-]

• Natural water: [H+] = [OH-] + [HCO3

-] + 2[CO3-2]

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pH - reporting H+ concentration• pH = - log {H+}

• {} = activity, the effective concentration

• pH = - log [H+] for dilute solutions• [] = Molar

concentration (moles/Liter)

• [H+] = 10-pH

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Why do we care about pH?• Biological systems

• Extremes are disruptive

• Corrosivity

• Equilibrium relationships involving H+

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Good pH ranges• Freshwater...

• Marine ...

• Drinking...

• Soda?

Alkalinity• Capacity of water sample to neutralize an...

• Capacity of a water sample to take H+ without significant change in...

• Common ions that give water alkalinity• HCO3

-, CO32- & OH-

Acidity• Capacity of water to take OH- without significant pH change

• Opposite of Alkalinity

• Capacity of water sample to neutralize a base

• Common ion:H+

• For Acid Mine Drainage• Acidity =~f(Fe2+, Fe3+, Al, Mn, and H+)

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pH, Alkalinity & Acidity• Waters with same pH can have different amounts of

Alkalinity or Acidity

• Chemicals may be present that can react with or release H+ or OH-

• The lower the alkalinity (or acidity), the easier it is to change pH

Reversible Reactions• aA + bB ↔ cC + dD

• A & B can react to form C and D • C & D can react to form A and B

• After sufficient time has passed, equilibrium is reached

• Equilibrium can be perturbed by adding more reactant or product

Reversible Reactions: Gas - Solution• At equilibrium

• Gaseous chemical dissolves • Dissolved chemical volatilizes• At equal rate

• Henry’s Law

• Example…

Gas

Dissolved

Reversible Reactions In Solution• At equilibrium

• Reactants become products • Products become reactants• At equal rate

• Example…

Reactants

Products

Reversible Reactions: Solution - Precipitate• At equilibrium

• Precipitate is formed • Precipitate is dissolved• At equal rates

• Example…

Reactants

Precipitate

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Equilibrium Equation

aA + bB ↔ cC + dD

[C]c [D]d

[A]a [B]b = k

K is constant at given temperature & relatively low concentration

Example - Pure Water• What is water? ...• Reversible equation?...• Equilibrium equation?...

• At 25 C, Kw = ...• Even if other sources of H+

(acids) or OH- (bases) are present

• Which substance predominates?...

pH of Pure Water @ 25 C?• Follow these steps

• Write down species...• Write electroneutrality eq...• Write equilibrium equation..

• Solve equations...

Now, add…• OH- ? (add a strong base)

• Systems finds new equilbrium, with less H+ and more OH-

• pH goes up

• H+ ? (add a strong acid, precipitate iron,…)• Systems finds new equilbrium, with more H+ and less OH-

• pH goes down.

• Either way, [H+] [OH-] = Kw still holds

Precipitation of Limestone• CaCO3

-2 ↔ Ca+2 + CO3-2

• [Ca+2] [CO3-2] = Ksp

• Ksp = Solubility product

• Do not include precipitate in equilibrium equation

• [Ca+2] [CO3-2] < Ksp?...

• [Ca+2] [CO3-2] > Ksp?...

Carbonate Equilibrium System (CES)

• Keeps natural waters in good pH range

• Common Chemicals• Carbon Dioxide, CO2

• Carbonic Acid, H2CO3

• Bicarbonate, HCO3-

• Carbonate, CO3-2

• Solids containing Bicarbonate, Carbonate, Hydroxide, and (though rarely) certain Oxides (CaO),…

Main Sources• CO2 from atmosphere

• Byproduct of • biological or chemical reactions• combustion

• Solids containing carbonate• e.g., limestone

• Byproduct of sea life

CO2 g

CO2 aq

H2CO3

HCO3

CO3

Solid CO3,…

Atmosphere

Solution

Precipitate

CES Reactions

Reversible

• CO2 g ↔ CO2 aq

• CO2 aq + H2O ↔ H2CO3

• H2CO3 ↔ H+ + HCO3-

• HCO3- ↔ H+ + CO3

-2

• Ca+2 + CO3-2 ↔ CaCO3

Equilibrium (at 25C)

• CO2 aq = CO2 g / 1637 atm

• [H2CO3] / [CO2 aq] = 1.58 x 10-3

• [H+] [HCO3-] / [H2CO3*] = 4.47x10-7 M

• [H+] [CO3-2] / [HCO3

-] = 4.68x10-11 M

• [Ca+2] [CO3-2] = 3.80 x 10-9 M2

Where CO2 g is in atm & CO2 aq is in mole fraction

Carbonate System & pH• Typical Natural Water with 100 mg/L alkalinity as CaCO3

pH

100

mg

/L a

s C

aC

O3

6.5 118.5

50

CO2

CO3

HCO3

OH

Carbonate System Scenarios• Open / Closed

• Open - in equilibrium with atmosphere• open container, streams & shallow lakes, upper ocean

• Closed - not in equilibrium• Closed tank, quick reactions, deep regions of water bodies, soil gases

• Homogeneous / Heterogeneous• Homogeneous – in equilibrium with CO3 solids

• Heterogeneous– not in equilibrium with CO3 solids

• Closed & heterogeneous • bottom of stratified lake with floor of limestone• water treatment unit with soda ash / acid or base / CO2 & some

CaCO3 precipitates

Example - Natural pH of Rain• CO2 in atmosphere naturally “shifts” pH of rain from 7 to ?

• Open system• No solid source of CO3

CO2 g

CO2 aq

H2CO3

HCO3-

CO3- H+

H+ Lowers pH

Atmosphere• Nitrogen - 0.781 atm• Oxygen - 0.209 atm• Argon - 0.0093 atm• CO2 - 0.00033 atm

• When this example was created. It’s now 0.00040 atm (398.78 ppm)

• Misc. - 0.0004 atm• TOTAL - 1.0 atm

Solution: pH of Rain (1)• Atmosphere to raindrop - Henry’s Law:

CO2 aq = CO2 g / 1637 atm

•

• Convert to M: [CO2 aq] = CO2 aq x Mw

• Mw = molar density of water = 55.56 mol/l

•

Solution: pH of Rain (2)• Reaction with water forms carbonic acid - Equilibrium

Equation: [H2CO3 aq] = 1.58x10-3 M • [CO2 aq]

•

• [H2CO3* aq] = [CO2 aq] + [H2CO2 aq]

•

Solution: pH of Rain (3)• Dissociation of carbonic acid - Equilibrium Equation:

[H+] [HCO3-] = 4.47 x 10-7 M • [H2CO3*]

• Two unknowns? Use electroneutrality: [H+] = [OH-] + [HCO3

-] + 2[CO3-2]

• Rain water is acidic, so [OH-] & [CO3-2] will be small giving

[H+] ≈ [HCO3-], leading to…

•

•

Solution: pH of Rain (4)• pH = - log [H+] = -log (2.13x10-6) =…

• Check assumptions? Use equilibrium equations:

• [OH-] = 10-14 M2 / [H+] = 10-14 M2 / 2.13x10-6 M = 4.68x10-9 M(small, OK))

• [CO3-2] = 4.68x10-11 M • [H+] / [HCO3

-] = 4.68x10-11 M • 2.13x10-6 M / 2.13x10-6 M = 4.68x10-11 M (small, OK)

pH of Rain

• CO2 in atmosphere goes up?...•

• Use this method for different conditions?• Need to check assumptions about relative concentration of [OH-] &

[CO3-2]

Atmospheric CO2 & Ocean pH

• Oceans can be CO2 sink or source• Currently: sink, taking ~ 30% of anthropocentric CO2

• Primary mechanisms• Carbonate equilibrium system (Henry’s Law,…)• Biological Pump

• Living creatures take up carbon, some are trapped in sea bed

• Too much CO2?• pH drop of oceans could effect sea organisms• From 1751 to 1994 surface ocean pH estimated to have

dropped from ~ 8.18 to 8.10

Ocean pH Change

• ~half Anthropogenic CO2 has been absorbed by ocean so far• Currently absorbing ~1/3• 22 M tons / day

• Could drop to 7.6• Drastic effect on shell-forming organisms

National Geographic (2014) “Ocean Acidification”, ocean.nationalgeographic.com.

Acid Rain• Rain with pH below 5.7

• Most prevalent cause: • SOx produced from burning coal

• SOx reacts with water to form sulfuric acid

• Sulfuric acid dissolves into atmospheric water and dissociates into H- and SO4

-2

Precipitation pH downwind of Ohio Valleypower plants

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Sulfur Cap & Trade

Program

CES, Alkalinity, Acid Rain’s Effect• Carbonate solids

• Common source of alkalinity in natural waters (as they dissolve)

• Lakes and streams with alkalinity can accept acid rain without big pH changes • Alkalinity buffers acid rain

• Acid rain can damage water bodies that don’t have alkalinity

Acid Mine Drainage

http://www.ei.lehigh.edu/

Red Oak Mine Site

Mine Side ViewWater Infiltration

AnaerobicConditions

Low pHHigh AcidityHigh metals

FeS2 + O2 + H2O → Fe2+ + SO4

2- + H+ Fe2+ + O2 + H+ → Fe3+ + H2O

Fe3+ + H2O → Fe(OH)3 ↓ + H+

Presence of limestone will buffer the mine water, resisting pH change

Even lower pH

Oxidation of organic matter can lead to high concentrations of CO2 in mine headspace

pH – 4.4 (low) [drops to ~2 after seep]Acidity 434 ppm CaCO3 (high)

Partial Pressure CO2 in mine headspace - ~6% [200x higher than atmosphere]

Red Oak Seep

seep discharge

Plan View

Not to scale

Red Oak Remediation

Post injection, seep characteristics were pH - 6.3, Alkalinity - 150 mg/L as CaCO3, Fe- 120 mg/l; however, this level of treatment lasted only 15 months.