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1 THE GEOCHEMISTRY OF NATURAL WATERS THE CARBONATE SYSTEM CHAPTER 3 - Kehew (2001) Alkalinity

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2 LEARNING OBJECTIVES zUnderstand sources of CO 2 in natural waters. zDefine and understand alkalinity. zLearn to calculate the solubility of carbonate minerals such as calcite. zUnderstand the common-ion effect. zBecome familiar with the concept of incongruent dissolution. zApply these concepts to some case studies.

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3 BRIEF REVIEW zWe saw in Lecture 3 that pH, p CO 2 and bicarbonate ion concentrations are all interrelated. zRearrangement of the equations we have worked with previously yields: zThus, if we measure pH and bicarbonate ion concentration, we can calculate p CO 2.

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4 SOURCES OF CO 2 IN NATURAL WATERS zWhen the equation in the previous slide is applied to natural waters, particularly ground waters and soil solutions, p CO 2 values greater than atmospheric are commonly obtained. Why? zA system closed to atmospheric CO 2 is implied. zRespiration by plant roots and microbes consumes organic matter and produces CO 2 : CH 2 O + O 2 CO 2 + H 2 O zAmount of CO 2 production depends on temperature, soil moisture content, and the amount of organic matter.

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5 ALKALINITY - I zIn aqueous solutions, positive and negative charges must balance. zIn a pure CO 2 -H 2 O system, the charge-balance condition is: zThis equation shows that, as H 2 CO 3 * dissociates to form HCO 3 -, the concentration of H + also increases to maintain charge balance. zOften, because CO 3 2- and OH - are negligible, the charge- balance expression can be approximated as:

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6 ALKALINITY - II zReactions with minerals can affect this relationship. For example, dissolution of calcite would result in: zIf 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 Ca 2+ would not change. zThus, Ca 2+ is a conservative ion, and HCO 3 -, CO 3 2-, H + and OH - are non-conservative. Grouping these ions accordingly we get:

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7 ALKALINITY - III zThe quantity:is called the total alkalinity. zAnother definition of total alkalinity: the equivalent sum of bases titratable with a strong acid. zTotal alkalinity is the neutralizing capacity of a solution; the greater the total alkalinity, the more acid the solution can neutralize. zFor a general natural water, the charge-balance can be written:

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8 ALKALINITY - IV zBecause all the terms on the left-hand side of the previous charge-balance expression are conservative, then the alkalinity must also be conservative. zThe 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. zAlkalinity is measured by titration with strong acid. A known volume of sample is titrated (usually with H 2 SO 4 ) until an endpoint.

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9 Titration curve for a 5 m Na 2 CO 3 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.

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10 ALKALINITY - V zAlkalinity is often expressed as the equivalent weight of calcium carbonate (mg L -1 CaCO 3 ). zCalculation of alkalinity from a titration is according to: zThe equivalent weight of CaCO 3 is 50 g eq -1. zExample: A 100 mL sample is titrated to the methyl orange end point with 2 mL of 0.5 N H 2 SO 4. What is the total alkalinity in mg L -1 as CaCO 3 and what is the concentration of HCO 3 - in mg L -1 ?

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11 ALKALINITY - VI zThe total alkalinity in mg L -1 as CaCO 3 is given by: zIn most natural waters, bicarbonate is the dominant contributor to the total alkalinity, so the concentration of HCO 3 - is given as:

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12 LEARNING OBJECTIVES zUnderstand sources of CO 2 in natural waters. zDefine and understand alkalinity. zLearn to calculate the solubility of carbonate minerals such as calcite. zUnderstand the common-ion effect. zBecome familiar with the concept of incongruent dissolution. zApply these concepts to some case studies.

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13 CARBONATE MINERAL EQUILIBRIA zThe solubility of calcite at 25°C is governed by: zFor aragonite we have: zAragonite is more soluble (less stable) than calcite. zThe solubility of dolomite at 25°C is governed by:

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14 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - I We have six dissolved species: H +, OH -, H 2 CO 3 *, HCO 3 -, CO 3 2- and Ca 2+ whose concentrations are unknown. We need six independent equations to solve for these concentrations. Mass Action Expressions:

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15 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - II The sixth constraint is the charge-balance equation: This can be simplified to: At a constant value of p CO 2, the logarithms of the concentrations of each of the species can be expressed as a straight-line function of pH. For example:

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16 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - III Bicarbonate can be calculated from: And carbonate from:

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17 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - IV Calcium ion concentration is obtained from:

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18 Log-log plot of concentrations of species in solution in equilibrium with calcite vs. pH at constant p CO 2 = atm.

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19 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - V In addition to the graphical solution, we have the numerical solution based on:

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20 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - VI Substituting the appropriate values for the K ’ s we get: pH = 8.28 Now based on the equation: we obtain

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21 SOLUBILITY OF CALCITE IN AN OPEN SYSTEM - VII If we take into account activity coefficients, then the following expressions can be derived (see pp in Kehew, 2001 for details): These equations may be used to derive the plots on the next two slides (assuming activity coefficients are unity).

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22 The pH of pure water in equilibrium with calcite at 25°C as a function of the partial pressure of CO 2. Note that pH decreases linearly with increasing CO 2 partial pressure.

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23 Plot of calcium concentration vs. partial pressure of CO 2 for a water in equilibrium with calcite at 25°C. Mixing of two saturated waters A and B can lead to undersaturation and calcite dissolution.

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24 LEARNING OBJECTIVES zUnderstand sources of CO 2 in natural waters. zDefine and understand alkalinity. zLearn to calculate the solubility of carbonate minerals such as calcite. zUnderstand the common-ion effect. zBecome familiar with the concept of incongruent dissolution. zApply these concepts to some case studies.

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25 THE COMMON-ION EFFECT - I Calcite solubility is governed by the reaction: CaCO 3 (s) Ca 2+ + CO 3 2- (1) Suppose we added a second compound containing carbonate, and this compound is more soluble than calcite, e.g., Na 2 CO 3. This compound will dissolve according to: Na 2 CO 3 (s) 2Na + + CO 3 2- (2) To the extent that reaction (2) proceeds to the right, by Le Chatlier ’ s principle, this will force reaction (1) to the left, precipitating calcite.

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26 THE COMMON-ION EFFECT - II The effect of adding sodium carbonate to the solution can be demonstrated by adjusting the charge-balance expression to be: By repeating the derivation of the equations on a previous slide using this charge-balance expression we obtain: Increasing Na + concentration leads to decreased Ca 2+ concentration.

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27 Figure 3-14 from Kehew (2001). Curves showing Ca concentration in equilibrium with calcite as increasing amounts of NaHCO 3 are added to solution. Addition of the common ion (HCO 3 - ) in the form of sodium bicarbonate causes precipitation of calcite and a consequent decrease in the concentration of dissolved Ca.

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28 ANOTHER EXAMPLE OF THE COMMON-ION EFFECT Consider a groundwater just saturated with respect to calcite. This water encounters a rock formation containing gypsum. Gypsum is more soluble than calcite; it dissolves according to: CaSO 4 ·2H 2 O Ca 2+ + SO H 2 O(l) To the extent that this reaction goes to the right, it pushes the following reaction to the left: CaCO 3 (s) Ca 2+ + CO 3 2- causing calcite to precipitate.

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29 INCONGRUENT DISSOLUTION OF CALCITE AND DOLOMITE - I zIncongruent dissolution - when one mineral dissolves simultaneously with the precipitation of another. zExample: when calcite and dolomite are both encountered along a ground water flow path. zHow do we determine what will happen when both dolomite and calcite are present? zStart by rearranging the K SP for dolomite:

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30 INCONGRUENT DISSOLUTION OF CALCITE AND DOLOMITE - II zIf a solution were in equilibrium with dolomite alone, then the activities of Ca 2+ and Mg 2+ would be equal so that: zAt 10°C we have K dol ½ = , which is exactly equal to K cal = for this temperature. If dolomite had first reached equilibrium, then calcite would not be able to dissolve because IAP = K cal !

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31 INCONGRUENT DISSOLUTION OF CALCITE AND DOLOMITE - III zHowever, at other temperatures, in general IAP would not be equal to K cal. zFor example, at 30°C we have: K dol ½ = , and K cal = zIn this case calcite would dissolve, because the ion activity product would be less than the solubility product for calcite. zDissolution of calcite would then cause dolomite to precipitate via the common-ion effect.

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32 INCONGRUENT DISSOLUTION OF CALCITE AND DOLOMITE - IV zThe latter process would be termed incongruent dissolution of calcite. zAt 0°C we have: K dol ½ = , K cal = zIn this case, calcite would precipitate and dolomite would dissolve incongruently. zWe might also get incongruent dissolution because calcite dissolves more rapidly than dolomite. In this case, Ca 2+ and CO 3 2- concentrations increase more rapidly than Mg 2+, so calcite may reach supersaturation while dolomite is still undersaturated.

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33 SOLUBILITY PRODUCTS FOR CALCITE AND DOLOMITE IN PURE WATER AT 1 BAR Source: Freeze and Cherry (1979)

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34 LEARNING OBJECTIVES zUnderstand sources of CO 2 in natural waters. zDefine and understand alkalinity. zLearn to calculate the solubility of carbonate minerals such as calcite. zUnderstand the common-ion effect. zBecome familiar with the concept of incongruent dissolution. zApply these concepts to some case studies.

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35 THE MADISON AQUIFER - I zThe Madison aquifer is located east of the Rocky Mountains. zIn this aquifer, we can see the effects of both the common-ion effect, and incongruent dissolution. zThe aquifer comprises Mississippian carbonates in which the primary minerals are calcite, dolomite and anhydrite.

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36 Predevelopment potentiometric surface of the Madison aquifer. Contours in meters above sea level (from Plummer et al., 1990, Water Resources Research, v. 26, pp ).

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37 THE MADISON AQUIFER - II zAlong the flow path to the northeast, dissolution of anhydrite induces calcite precipitation via the common-ion effect. zPrecipitation of calcite results in decreased pH and Ca 2+ concentration and increased p CO 2 according to: Ca HCO 3 - CaCO 3 (s) + CO 2 (s) + H 2 O zThis results in dolomite becoming undersaturated, so it dissolves.

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38 THE MADISON AQUIFER - III zThe dissolution of dolomite is a type of incongruent dissolution called dedolomitization. zSulfate concentration increases along the flow path until saturation with respect to anhydrite, thus sulfate serves as a measure of distance from the recharge area. zCalcite is close to saturation throughout the aquifer, so very little anhydrite dissolution is required to precipitate calcite.

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39 Saturation indices of gypsum as a function of SO 4 2- concentration for the Madison aquifer. The relationship between these variables shows that dissolution of gypsum /anhydrite is the source of sulfate in these waters. (Data from Plummer et al., 1990, Water Resources Research, v. 26, pp )

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40 Saturation indices of calcite as a function of SO 4 2- concentration for the Madison aquifer. The majority of the waters are saturated to slightly oversaturated. (Data from Plummer et al., 1990, Water Resources Research, v. 26, pp )

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41 Saturation indices of dolomite as a function of SO 4 2- concentration for the Madison aquifer. The SI for dolomite is more variable, with undersaturation present across the aquifer. (Data from Plummer et al., 1990, Water Resources Research, v. 26, pp )

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42 Precipitation of calcite by the common-ion effect as a function of anhydrite dissolution in the Madison aquifer. The dashed line shows the trend due to dedolomitization alone, and the solid arrow shows dedolomitization plus cation exchange reactions.

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43 Dissolution of dolomite by the common-ion effect as a function of anhydrite dissolution in the Madison aquifer. The dashed line shows the trend due to dedolomitization alone, and the solid arrow shows dedolomitization plus cation exchange reactions.

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44 Plot of calcite precipitated vs. dolomite dissolved in the Madison aquifer. The remarkably linear relationship demonstrates the nature of the incongruent dissolution.

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45 IONIC STRENGTH EFFECT ON SOLUBILITY - I zIf NaCl is added to a solution saturated with calcite, what will happen? zNaCl contains no ions in common with calcite, so we would not expect solubility to decrease from a direct common-ion effect. zOn the other hand, NaCl will increase the ionic strength of the solution. What will this do? zConsider the equation:

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46 IONIC STRENGTH EFFECT ON SOLUBILITY - II zAddition of NaCl will increase ionic strength, which in general decreases the activity coefficients. zTo keep the solubility product constant, if the activity coefficients decrease, the concentration terms must increase. Thus, addition of NaCl will generally increase calcite solubility. zMinerals tend to be more soluble in concentrated solutions than in dilute ones (providing there is no common-ion effect).

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