1

Acid-base Acid-base reactions and reactions and

carbonate systemcarbonate system

2

Topics for this chapterTopics for this chapter

Acid base reactions and their Acid base reactions and their importanceimportance

Carbonate system and their Carbonate system and their importance in biogeochemical importance in biogeochemical reactionsreactions

pH range and controlling factors in pH range and controlling factors in the natural watersthe natural waters

3

ObjectivesObjectives

Better understand acid-base Better understand acid-base equilibrium in equilibrium in natural watersnatural waters

Better understand carbonate speciesBetter understand carbonate species change and alkalinity measurementchange and alkalinity measurement

Understand the method to study Understand the method to study species distributions in natural watersspecies distributions in natural waters

4

DEFINITION: ACIDS AND DEFINITION: ACIDS AND BASESBASES

Bronsted definitionBronsted definition Acid: any substance that can donate a protonAcid: any substance that can donate a proton Base: any substance that can accept a protonBase: any substance that can accept a proton

HCl(aq) HCl(aq) H H++ + Cl + Cl--

NaOH(aq) + HNaOH(aq) + H++ Na Na++ + H + H22O(l)O(l) Lewis definition:Lewis definition:

Acid: any substance that can accept electronsAcid: any substance that can accept electrons Base: any substance that can donate electronsBase: any substance that can donate electrons

HH33BOBO33(aq) + OH(aq) + OH-- B(OH) B(OH)44--

HH22O(l) O(l) H H++ + OH + OH--

HH33BOBO33(aq) + H(aq) + H22O(l) O(l) B(OH) B(OH)44- - + H+ H++

5

Acid-Base

•Acids and bases exist as conjugate acid-base pairs.

• Every time a Brønsted acid acts as an H+-ion donor, it forms a conjugate base.

HA + H2O H3O+ + A- 

• Every time a base gains an H+ ion, the product is a Brønsted acid, HA.

A- + H2O HA + OH- 

6

Conjugate acid-base pairs

Acids Bases

H3O+   H2O H2O OH-

H2CO3 HCO3-

HCl Cl-

7

THE HYDRONIUM IONTHE HYDRONIUM ION

The proton does not actually exist in aqueous The proton does not actually exist in aqueous solution as a bare Hsolution as a bare H++ ion. ion.

The proton exists as the The proton exists as the hydroniumhydronium ion (H ion (H33OO++).). Consider the acid-base reaction:Consider the acid-base reaction:

HCOHCO33-- + H + H22O O H H33OO++ + CO + CO33

2-2-

Here water acts as a base, producing the Here water acts as a base, producing the hydronium ion as its conjugate acid. hydronium ion as its conjugate acid. For For simplicity, we often just write this reaction assimplicity, we often just write this reaction as::

HCOHCO33-- H H++ + CO + CO33

2-2-

8

Expression of acid Expression of acid strengthstrength

The strength of an acid is expressed by the value of the The strength of an acid is expressed by the value of the equilibrium constant for its dissociation reaction.equilibrium constant for its dissociation reaction.

Consider:Consider: H H22COCO33 H H++ + HCO + HCO33--

The dissociation constant for this reaction at 25°C is:The dissociation constant for this reaction at 25°C is:

This can also be expressed as pThis can also be expressed as pKK aa = 6.35. = 6.35. Bicarbonate is considered to be a relatively weak acid.Bicarbonate is considered to be a relatively weak acid.

35.6103

23

HCO

COHa a

aaK

9

Strong acidsStrong acids

Now consider:Now consider: HNO HNO33 H H++ + NO + NO33--

Nitric acid is considered to be a very strong acid; Nitric acid is considered to be a very strong acid; in fact, its pin fact, its pKK a a is not well defined because the is not well defined because the concentration of undissociated acid HNOconcentration of undissociated acid HNO33

00 is too is too small to be measured accurately.small to be measured accurately.

The conjugate bases of weak acids are strong, The conjugate bases of weak acids are strong, and the conjugate bases of strong acids are weak.and the conjugate bases of strong acids are weak.

Thus, NOThus, NO33-- is a very weak base, but CO is a very weak base, but CO33

2-2- is a is a comparatively strong base.comparatively strong base.

10

Ka and pKa

HA(aq) + H2O(l) H3O+(aq) + A-

(aq) 

The stronger the acids, the larger the Ka

The stronger the acids, the smaller the pKa

pKa = -log Ka

11 The larger the pKa, the weaker the acid

12

DISSOCIATION DISSOCIATION CONSTANTS OF WEAK CONSTANTS OF WEAK

ACIDS AT 25°CACIDS AT 25°CAcid pK1 pK2 pK3

Acetic (CH3COOH) 4.75 ----- -----Boric (H3BO3) 9.2 ----- -----

Carbonic (H2CO3) 6.35 10.33 -----Phosphoric (H3PO4) 2.1 7.0 12.2Hydrosulfuric (H2S) 7.0 13.0 -----

Silicic (H4SiO4) 9.9 11.7 9.9Hydrofluoric (HF) 3.2 ----- -----Arsenic (H3AsO4

0) 2.2 7.0 11.5Sulfurous (H2SO3

0) 1.7 6.9 -----

13

Range of pH values in the natural environment

Most natural waters have pH between 4-9.Most natural waters have pH between 4-9. The acids are usually weak, The acids are usually weak, mainly carbonic acid and organic mainly carbonic acid and organic

acids (e.g. fulvic and humic acids, formic and acetic acid)acids (e.g. fulvic and humic acids, formic and acetic acid) pH values > 8.5 are rare, occurring only in evaporitic lakes,

lakes clogged with photosynthetic plants, and springs discharging from serpentine or ultramafic rocks.

14

Natural Water pH

15

Control of pH on natural Control of pH on natural reactionsreactions

The solubility rate of dissolution of most minerals is The solubility rate of dissolution of most minerals is strongly pH-dependent. Weathering of carbonate, silicate, strongly pH-dependent. Weathering of carbonate, silicate, and alumino-silicate minerals consumes protons and and alumino-silicate minerals consumes protons and releases metal cations.releases metal cations.

Aqueous acid-base equilibria, including hydrolysis and Aqueous acid-base equilibria, including hydrolysis and polymerization.polymerization.

Adsorption, because protons compete with cations and Adsorption, because protons compete with cations and hydroxyl ions compete with anions for adsorption sites. hydroxyl ions compete with anions for adsorption sites. Also, the surface charge of most minerals is pH Also, the surface charge of most minerals is pH dependent.dependent.

The formation of metal ligand complexes, because protons The formation of metal ligand complexes, because protons compete with metal ions to bond with weak-acid ions, and compete with metal ions to bond with weak-acid ions, and OH- competes with other ligands that would form OH- competes with other ligands that would form complexes.complexes.

Oxidation-reduction reactions, whether abiological or Oxidation-reduction reactions, whether abiological or biologically mediated. Oxidation usually produced biologically mediated. Oxidation usually produced protons, whereas reduction consumes them.protons, whereas reduction consumes them.

16

pH effect on adsorption of metals by ferrihydrite

17

Carbonic acid system: the Carbonic acid system: the importanceimportance

Carbonic acid is the most abundant acid in natural water systems

Carbonic acid is the acid most responsible for rock weathering.

The pH of most natural waters is controlled by reactions involving the carbonate system

Bicarbonate ion is generally the dominant anion in fresh surface- and ground- waters.

Bicarbonate and carbonate ions are the chief contributors to total alkalinity in natural waters.

An example of acid-base systems in general; the species relationship developed for carbonate equilibrium can be used with little modification for equilibira involving such species as phosphate, sulfide, and silicic acid.

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Unanswered questions from Unanswered questions from previous chaptersprevious chapters

Alkalinity Alkalinity = = [HCO[HCO33––] + 2[CO] + 2[CO33

2-2-] + [OH] + [OH––] – [H] – [H++] ] ≈ [HCO≈ [HCO33

––] +2[CO] +2[CO332–2–] ]

≈ ≈ [HCO[HCO33––] ]

[H[H++] = [HCO] = [HCO33--] + 2[CO] + 2[CO33

2-2-] + [OH] + [OH--]]When pH<7, When pH<7,

[H[H++] ≈ [HCO] ≈ [HCO33--]]

Why?Why?

19

THE COTHE CO22-H-H22O SYSTEMO SYSTEM

Carbonic acid is a weak acid of great importance Carbonic acid is a weak acid of great importance in natural waters. The first step in its formation in natural waters. The first step in its formation is the dissolution of COis the dissolution of CO22(g) in water according to:(g) in water according to:

COCO22(g) (g) CO CO22(aq)(aq)

At equilibrium we have:At equilibrium we have:

Once in solution, COOnce in solution, CO22(aq) reacts with water to (aq) reacts with water to form carbonic acid:form carbonic acid:

COCO22(aq) + H(aq) + H22O(l) O(l) H H22COCO3300

2

2

2

CO

COCO p

aK

20

THE COTHE CO22-H-H22O SYSTEMO SYSTEM

In practice, COIn practice, CO22(aq) and H(aq) and H22COCO3300 are combined and are combined and

this combination is denoted as Hthis combination is denoted as H22COCO33*. It’s *. It’s formation is dictated by the reaction:formation is dictated by the reaction:

COCO22(g) + H(g) + H22O(l) O(l) H H22COCO33**

For which the equilibrium constant at 25°C is:For which the equilibrium constant at 25°C is:

Most of the dissolved COMost of the dissolved CO22 is actually present as is actually present as COCO22(aq); only a small amount is actually present (aq); only a small amount is actually present as true carbonic acid Has true carbonic acid H22COCO33

00. .

46.1* 102

32

2

CO

COHCO p

aK

21

THE COTHE CO22-H-H22O SYSTEMO SYSTEM

Carbonic acid (HCarbonic acid (H22COCO33*) is a weak acid that *) is a weak acid that dissociates according to:dissociates according to:

HH22COCO33* * HCO HCO33-- + H + H++

For which the dissociation constant at 25°C For which the dissociation constant at 25°C and 1 bar is:and 1 bar is:

Bicarbonate then dissociates according to:Bicarbonate then dissociates according to:

HCOHCO33-- CO CO33

2-2- + H + H++

35.6

*1 10

32

3

COH

HHCO

a

aaK

33.102 10

3

23

HCO

HCO

a

aaK

22

THE RELATIONSHIP THE RELATIONSHIP BETWEEN HBETWEEN H22COCO33* AND * AND

HCOHCO33--

We can rearrange the expression for We can rearrange the expression for KK11 to obtain: to obtain:

This equation shows that, This equation shows that, when pH = pwhen pH = pKK1 1 (when pH = 6.35), (when pH = 6.35), the activities of carbonic acid and bicarbonate are equal.the activities of carbonic acid and bicarbonate are equal.

We can also rearrange the expression for We can also rearrange the expression for KK22 to obtain: to obtain:

This equation shows that, This equation shows that, when pH = pwhen pH = pKK22 (when pH = (when pH = 10.33), the activities of bicarbonate and carbonate ion 10.33), the activities of bicarbonate and carbonate ion are equal.are equal.

*

1

32

3

COH

HCO

Ha

a

a

K

3

232

HCO

CO

Ha

a

a

K

23

BJERRUM PLOTSBJERRUM PLOTS PPlot of the log of the concentrations of various species lot of the log of the concentrations of various species

in a closed COin a closed CO22-H-H22O system as a function of pH.O system as a function of pH.

The species in the COThe species in the CO22-H-H22O system: HO system: H22COCO33*, HCO*, HCO33--, ,

COCO332-2-, H, H++, and OH, and OH--..

At each pAt each pKK value, conjugate acid-base pairs have equal value, conjugate acid-base pairs have equal concentrations, andconcentrations, and At pH < pAt pH < pKK11, H, H22COCO33* is predominant, and accounts for nearly * is predominant, and accounts for nearly

100% of total carbonate.100% of total carbonate. pH < 6.35pH < 6.35

At pAt pKK11 < pH < p < pH < pKK22, HCO, HCO33- - is predominant, and accounts for is predominant, and accounts for

nearly 100% of total carbonate.nearly 100% of total carbonate. 6.35 < pH < 10.336.35 < pH < 10.33

At pH > pAt pH > pKK22, CO, CO332-2- is predominant. is predominant.

pH < 10.33pH < 10.33

24

pH0 2 4 6 8 10 12 14

log a i

-8

-7

-6

-5

-4

-3

-2

6.35 10.33H2CO3* HCO3- CO3

2-

H+

OH-

Common pHrange in nature

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!

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log

(B

jerr

um p

lot)

a i

p H

H CO 3

-

H C O2 3

D

C

B

A

H CO 3

-

H CO 3

-

H C O2 3

H +

O H -

C O 3

2-

C O 3

2-

V (

mL

of a

cid)

p-alkalin itya lkalin ity

Alkalinity end points

Alkalinity = [HCOAlkalinity = [HCO33––] + 2[CO] + 2[CO33

2-2-] + [OH] + [OH––] – ] – [H[H++]]

26

pH0 2 4 6 8 10 12 14

log a i

-12

-10

-8

-6

-4

-2H2S

0HS-

S2-

H+OH-

7.0 13.0

Bjerrum plot showing the activities of reduced sulfur species as a function of pH for a value of total reduced sulfur of 10-3 mol L-1.

27

Bjerrum plot: full Bjerrum plot: full solutionsolution

Closed system, with total carbonate concentration (KClosed system, with total carbonate concentration (K11, K, K22 known)known)

CCTT= [H= [H22COCO33]+[HCO]+[HCO33--] + [CO] + [CO33

2-2-]] (1)(1)

KK11=[H=[H++][HCO][HCO33--]/[H]/[H22COCO33]] (2)(2)

KK22 =[H =[H++][CO][CO332-2-]/[HCO]/[HCO33

2-2-]] (3)(3)

Solution:Solution:

[CO[CO332-2-] = C] = CTT//HH

[HCO[HCO33--]=C]=CTT[H[H++]/K]/K22HH

[H[H22COCO33]=C]=CTT[H[H++]]22/K/K11KK22HH

where: where: HH = (1 + [H = (1 + [H++]/K]/K22 +[H +[H++]]22/K/K11KK22))

28

SPECIATION IN OPEN SPECIATION IN OPEN COCO22-H-H22O SYSTEMSO SYSTEMS

In an open system, the system is in contact with its In an open system, the system is in contact with its surroundings and components such as COsurroundings and components such as CO22 can can migrate in and out of the system. migrate in and out of the system. Therefore, the total Therefore, the total carbonate concentration (Ccarbonate concentration (CTT) is not constant.) is not constant.

In an open system, In an open system, the solubility of COthe solubility of CO22 increases increases dramatically with pH, once pH has increased beyond dramatically with pH, once pH has increased beyond ppKK11

At low pH, the solubility of COAt low pH, the solubility of CO22 is independent of pH. is independent of pH.

Let us consider two natural waters Let us consider two natural waters open to the atmosphere, for which popen to the atmosphere, for which pCOCO22

= 10 = 10-3.5-3.5 atm. atm.

open to local exchange, for which popen to local exchange, for which pCOCO22 = 10 = 10-2.0-2.0 atm. atm.

29

pH2 3 4 5 6 7 8 9 10 11 12

log

co

nce

ntr

atio

n (

mo

lar)

-8

-6

-4

-2

0

CTH+

OH-

H2CO3*

HCO3-

CO32-

pK1 pK2

Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2

= 10-3.5 atm.

30

pH2 3 4 5 6 7 8 9 10 11 12

log

con

cen

tra

tion

(m

ola

r)

-8

-6

-4

-2

0

CT

H+

OH-

H2CO3*

HCO3-

CO32-

pK1 pK2

Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2

= 10-2.0 atm.

31

SOURCES OF COSOURCES OF CO22 IN IN NATURAL WATERSNATURAL WATERS

When we determine pWhen we determine pCOCO22 in natural waters, in natural waters,

particularly ground waters and soil solutions, values particularly ground waters and soil solutions, values greater than atmospheric are commonly obtained. greater than atmospheric are commonly obtained. System essentially closed to atmospheric COSystem essentially closed to atmospheric CO22 (little (little

exchange)exchange) Respiration by plant roots and microbes consumes Respiration by plant roots and microbes consumes

organic matter and produces COorganic matter and produces CO22::

CHCH22O + OO + O22 CO CO22 + H + H22OO Amount of COAmount of CO22 production depends on temperature, production depends on temperature,

soil moisture content, and the amount of organic soil moisture content, and the amount of organic matter.matter.

32

Reactions Affecting COReactions Affecting CO2 2

and pHand pH Key: Key:

Blue results in pH increase (more alkaline)Blue results in pH increase (more alkaline) Red results in pH decrease (more acidic)Red results in pH decrease (more acidic)

COCO22(g) dissolution,(g) dissolution, COCO22 (aq) exsolution (aq) exsolution COCO22(g) + H(g) + H22O O H H22COCO33°°

Photosynthesis,Photosynthesis, Respiration & aerobic decayRespiration & aerobic decay COCO22(g) + H(g) + H22O O 1/6C 1/6C66HH1212OO66 (aq) + O (aq) + O22

Methane fermentation (anaerobic decay) Methane fermentation (anaerobic decay) CC66HH1212OO66 (aq) + O (aq) + O22 CH CH44 + H + H22O + COO + CO22

Nitrate uptake and reduction Nitrate uptake and reduction NONO33

-- + 2H + 2H++ + 2CH + 2CH22O O NH NH44++ + 2CO + 2CO22 + H + H22OO

33

Reactions Controlling COReactions Controlling CO22 and pHand pH

Carbonate mineral DissolutionCarbonate mineral Dissolution or precipitation or precipitation CaCOCaCO33 (calcite ) + H (calcite ) + H++ Ca Ca2+2+ + H + H22O+ COO+ CO22

Sulfate reduction Sulfate reduction 2CH2CH22OO + SO + SO44

2-2- + H + H++ HS HS-- + 2H + 2H22O + 2COO + 2CO22

Denitrification Denitrification 5CH5CH22O + 4NOO + 4NO33

-- + 4H + 4H++ 2N 2N22 + 5CO + 5CO22 + 7H + 7H22OO

Chemical weathering of Al-silicate weatheringChemical weathering of Al-silicate weathering KAlSiKAlSi33OO88 + 2CO + 2CO22 + 11H + 11H22O O Al Al22SiSi22OO55(OH)(OH)44 + 2K + 2K++ + 2 HCO + 2 HCO33

--

34

COCO22 in Natural Settings in Natural Settings Time of day Time of day

Higher pHigher pCO2 CO2 values occur in surface waters at night values occur in surface waters at night because of respiration and aerobic decay and because of respiration and aerobic decay and groundwater inflow.groundwater inflow.

Lower pLower pCO2 CO2 values occur in surface waters during values occur in surface waters during the day because of photosynthesis.the day because of photosynthesis.

Time of yearTime of year Soil pSoil pCO2 CO2 values are highest during the growing values are highest during the growing

season because of plant respiration. season because of plant respiration. Consequently, shallow groundwaters will have their Consequently, shallow groundwaters will have their

highest phighest pCO2 CO2 values during the growing season.values during the growing season.

35

Compute the pH of an aqueous system

Step 1: List species in solution Step 2: Identify how concentrations of

the species depend on each other Step 3: Establish the mass balance Step 4: Establish the charge balance

36

Example: HAC in waterExample: HAC in water

CH3COOH CH3COO- + H+ Ka = 10-4.75

Species: Species: CH3COOH, CH3COO- , H+, OH-

Mass balance: CT = [HAc] + [Ac-] Charge balance: [H+] = [OH-] + [Ac-] Ka =[Ac-][H+]/[HAc]=10-4.75

Kw=[H+][OH-] = 10-14

With given CT (concentration of HAC you made), we have four equations, four unknowns, we can compute [H+] hence pH

37

pH of the seapH of the sea

pH of the sea can be computed pH of the sea can be computed following the above proceduresfollowing the above procedures

Basically, pH of the sea is controlled Basically, pH of the sea is controlled by the carbonate speciesby the carbonate species

The actual computation is more The actual computation is more complicated and beyond this classcomplicated and beyond this class