THE CO2H2O SYSTEM

1
THE CO2-H2O SYSTEM

• Carbonic acid is a weak acid of great importance
  in natural waters. The first step in its
  formation is the dissolution of CO2(g) in water
  according to
• CO2(g) ? CO2(aq)
• At equilibrium we have
• Once in solution, CO2(aq) reacts with water to
  form carbonic acid
• CO2(aq) H2O(l) ? H2CO30

2
THE CO2-H2O SYSTEM

• In practice, CO2(aq) and H2CO30 are combined and
  this combination is denoted as H2CO3. Its
  formation is dictated by the reaction
• CO2(g) H2O(l) ? H2CO3
• For which the equilibrium constant at 25C is
• Most of the dissolved CO2 is actually present as
  CO2(aq) only a small amount is actually present
  as true carbonic acid H2CO30.

3
THE CO2-H2O SYSTEM

• Carbonic acid (H2CO3) is a weak acid that
  dissociates according to
• H2CO3 ? HCO3- H
• For which the dissociation constant at 25C and 1
  bar is
• Bicarbonate then dissociates according to
• HCO3- ? CO32- H

4
THE RELATIONSHIP BETWEEN H2CO3 AND HCO3-

• We can rearrange the expression for K1 to obtain
• This equation shows that, when pH pK1 (when pH
  6.35), the activities of carbonic acid and
  bicarbonate are equal.
• We can also rearrange the expression for K2 to
  obtain
• This equation shows that, when pH pK2 (when pH
  10.33), the activities of bicarbonate and
  carbonate ion are equal.

5
BJERRUM PLOTS

• These are used for closed systems with a
  specified total carbonate concentration. They
  plot the log of the concentrations of various
  species in the system as a function of pH.
• The species in the CO2-H2O system H2CO3, HCO3-,
  CO32-, H, and OH-.
• At each pK value, conjugate acid-base pairs have
  equal concentrations.
• At pH lt pK1, H2CO3 is predominant, and accounts
  for nearly 100 of total carbonate.
• pH lt 6.35
• At pK1 lt pH lt pK2, HCO3- is predominant, and
  accounts for nearly 100 of total carbonate.
• 6.35 lt pH lt 10.33
• At pH gt pK2, CO32- is predominant.
• pH lt 10.33

6
Bjerrum plot showing the activities of inorganic
carbon species as a function of pH for a value of
total inorganic carbon of 10-3 mol L-1.
In most natural waters, bicarbonate is the
dominant carbonate species!
7
SPECIATION IN OPEN CO2-H2O SYSTEMS

• In an open system, the system is in contact with
  its surroundings and components such as CO2 can
  migrate in and out of the system. Therefore, the
  total carbonate concentration will not be
  constant.
• In an open system, the solubility of CO2
  increases dramatically with pH, once pH has
  increased beyond pK1
• At low pH, the solubility of CO2 is independent
  of pH.
• Let us consider two natural waters
• open to the atmosphere, for which pCO2 10-3.5
  atm.
• open to local exchange, for which pCO2 10-2.0
  atm.

8
Plot of log concentrations of inorganic carbon
species H and OH-, for open-system conditions
with a fixed pCO2 10-3.5 atm.
9
Plot of log concentrations of inorganic carbon
species H and OH-, for open-system conditions
with a fixed pCO2 10-2.0 atm.
10
SOURCES OF CO2 IN NATURAL WATERS

• When we determine pCO2 in natural waters,
  particularly ground waters and soil solutions,
  values greater than atmospheric are commonly
  obtained.
• A system closed to atmospheric CO2 is implied.
• Respiration by plant roots and microbes consumes
  organic matter and produces CO2
• CH2O O2 ? CO2 H2O
• Amount of CO2 production depends on temperature,
  soil moisture content, and the amount of organic
  matter.

11
Reactions Controlling CO2 and pH

• Key
• Blue results in pH increase (more alkaline)
• Red results in pH decrease (more acidic)
• CO2(g) dissolution ?, CO2 (aq) exsolution ?
• CO2(g) H2O ? CO2 (aq) H2O ? H2CO3
• Photosynthesis ?, Respiration aerobic decay ?
• CO2(g) H2O ? 1/6C6H12O6 (aq) O2
• Methane fermentation (anaerobic decay) ?
• C6H12O6 (aq) O2 ? CH4 H2O CO2
• Nitrate uptake and reduction ?
• NO3- 2H 2CH2O ? NH4 2CO2 H2O

12
Reactions Controlling CO2 and pH

• Key
• Blue results in pH increase (more alkaline)
• Red results in pH decrease (more acidic)
• Common-ion driven calcite precipitation ?
• CaSO42H2O 2HCO3- ? CaCO3 SO42- CO2 2H2O
• Carbonate mineral Dissolution?, or precipitation
  ?
• CaCO3 (calcite ) H ? Ca2 H2O CO2
• Sulfate reduction ?
• 2CH2O SO42- H ? HS- 2H2O 2CO2
• Denitrification ?
• 5CH2O 4NO3- 4H ? 2N2 5CO2 7H2O
• Chemical weathering of Al-silicate weathering
• KAlSi3O8 2CO2 11H2O ? Al2Si2O5(OH)4 2K 2
  HCO3-

13
CO2 in Natural Settings

• General Controls on CO2
• Time of day
• Higher pCO2 values occur in surface waters at
  night because of respiration and aerobic decay
  and groundwater inflow.
• Lower pCO2 values occur in surface waters during
  the day because of photosynthesis.
• Time of year
• Soil pCO2 values are highest during the growing
  season because of plant respiration.
• Consequently, shallow groundwaters will have
  their highest pCO2 values during the growing
  season.

14
CO2 in Natural Settings

• CO2 in atmosphere related to temperature
• log PCO2 -3.3 0.08T (C)
• Seasonal control on PCO2
• highest in summer
• CO2 production in soil must depend on moisture

15
ALKALINITY

• In aqueous solutions, positive and negative
  charges must balance.
• In a pure CO2-H2O system, the charge-balance
  condition is
• This equation shows that, as H2CO3 dissociates
  to form HCO3- the concentration of H also
  increases to maintain charge balance.
• Often, because CO32- and OH- are negligible, the
  charge-balance expression can be approximated as

16
ALKALINITY

• Reactions with minerals can affect this
  relationship. For example, dissolution of calcite
  would result in
• If this solution is removed from contact with
  calcite, and strong acid is added, the
  concentration of H and all the carbonate species
  would change, but the concentration of Ca2 would
  not change.
• Thus, Ca2 is a conservative ion, and HCO3-,
  CO32-, H and OH- are non-conservative. Grouping
  these ions accordingly we get

17
ALKALINITY

• The quantity is called the total
  alkalinity.
• Another definition of total alkalinity the
  equivalent sum of bases titratable with a strong
  acid.
• Total alkalinity is the neutralizing capacity of
  a solution the greater the total alkalinity, the
  more acid the solution can neutralize.
• For a general natural water, the charge-balance
  can be written

18
ALKALINITY

• Because all the terms on the left-hand side of
  the previous charge-balance expression are
  conservative, then the alkalinity must also be
  conservative.
• The only way to change alkalinity is to either
  add strong acid or base, or for solids to
  dissolve or precipitate. This is why it is
  important to measure alkalinity in the field
  before precipitation can occur.

19
ALKALINITY

• Alkalinity is measured by titration with strong
  acid. A known volume of sample is titrated
  (usually with H2SO4) until an endpoint.
• Knowing the volume of the water sample (V), the
  volume of acid solution required to reach the
  endpoint (V0) and the normality of the acid
  (Nacid), one can calculate the alkalinity in eq
  L-1 according to
• Valk V0Nacid

20
Titration curve for a 5?10-3 m Na2CO3 solution,
together with a Bjerrum plot for the same
solution. A is the beginning of the titration, B
is the carbonate endpoint, C is the region of
strong carbonate buffering, and D is the
bicarbonate endpoint.
21
ALKALINITY

• Alkalinity is often expressed as the equivalent
  weight of calcium carbonate (mg L-1 CaCO3).
• Calculation of alkalinity from a titration is
  according to
• The equivalent weight of CaCO3 is 50 g eq-1.
• Example A 100 mL sample is titrated to the
  methyl orange end point with 2 mL of 0.5 N H2SO4.
  What is the total alkalinity in mg L-1 as CaCO3
  and what is the concentration of HCO3- in mg L-1?

22
ALKALINITY

• The total alkalinity in mg L-1 as CaCO3 is given
  by
• In most natural waters, bicarbonate is the
  dominant contributor to the total alkalinity, so
  the concentration of HCO3- is given as

23
ALKALINITY

• Where total alkalinity is presented as mg/L CaCO3
• To convert mg/L CaCO3 to mg/L HCO3-
• Divide mg/L CaCO3 by 0.8202.
• To convert mg/L HCO3- to mg/L CaCO3
• multiply mg/L HCO3- by 1.22.

24
Carbonate Reactions

• Ca2 and HCO3- most abundant species in
  groundwater
• dolomite and limestone are favorable aquifers
• Ca-Mg carbonates react easily and produce
  hardness
• Increased TDS of rivers from carbonate
  dissolution
• Ca2 and HCO3- are main contributors to TDS
• Sandy aquifers also have abundant carbonate
• Rapid reaction rates of carbonates causes them to
  dominate silicates in TDS

25
CARBONATE MINERAL EQUILIBRIA

• The solubility of calcite at 25C is governed by
• For aragonite we have
• Aragonite is more soluble (less stable) than
  calcite.
• The solubility of dolomite at 25C is governed
  by

26
SOLUBILITY OF CALCITE IN AN OPEN SYSTEM

• We have six dissolved species H, OH-, H2CO3,
  HCO3-, CO32- and Ca2 whose concentrations are
  unknown.
• We need six independent equations to solve for
  these concentrations.
• Mass Action Expressions

27
SOLUBILITY OF CALCITE IN AN OPEN SYSTEM

• The sixth constraint is the charge-balance
  equation
• This can be simplified to
• When the pCO2 is known, the logarithms of the
  concentrations of each of the species can be
  expressed as a function of pH.
• To start, we determine
• aH2CO3 KCO2 pCO2 using atmospheric pCO2

28
This value plots as a straight line on a Log-log
plot of concentrations of species in solution in
equilibrium with calcite vs. pH at constant pCO2
10-3.5 atm.
29
SOLUBILITY OF CALCITE IN AN OPEN SYSTEM

• Then, Bicarbonate can be calculated from
• And carbonate from

30
SOLUBILITY OF CALCITE IN AN OPEN SYSTEM

• Calcium ion concentration is obtained from

31
Log-log plot of concentrations of species in
solution in equilibrium with calcite vs. pH at
constant pCO2 10-3.5 atm.
32
SOLUBILITY OF CALCITE IN AN OPEN SYSTEM

• What is the pH at which our simplified
  charge-balance expression holds, that is, 2MCa2
  ? MHCO3-?
• We need to find the location on the graph where
  the concentration of bicarbonate is twice as high
  as that of calcium ion.
• On the log scale, we are looking for the pH where
  the line representing the bicarbonate ion
  concentration lies exactly 0.301 (log 2) log
  units above the line representing the
  concentration of the calcium ion.
• This occurs at the pH indicated by the vertical
  red line on this diagram, i.e., at approximately
  pH 8.3.
• Note that at this pH, the concentration of
  carbonate ion is almost two orders of magnitude
  less than that of bicarbonate, and the
  concentrations of all the other species are even
  lower. This means that our assumption that the
  charge-balance expression may be written as
  2MCa2 ? MHCO3- is valid..