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4 Acid Base Relationships.doc

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University of Toronto St. George
Earth Sciences
John Ferris

4 Acid-Base Relationships Most reactions in the gas-water-rock system involve or are controlled by the pH of the system These include 1. acid-base equilibria, including hydrolysis and polymerization by condensation 2. adsorption, because protons compete with cations and hydroxyl ions compete with anions for adsorption sites 3. the formation of metal-ligand complexes, again because of competition 4. Oxidation-reduction reactions, because oxidation usually produce protons, whereas reduction consumes them 5. the solubility and rate of dissolution of many minerals is strongly pH dependent 4.1 Protons and pH The availability of protons in aqueous solutions is assessed +enerally in terms of pH. In principle, pH provides a measure of proton activity {H } according to the established relationship + pH = -log{H } (1) + The value of {H } is considered within the infinite dilution concept to be equivalent to proton concentration [H ] in dilute solutions (ionic strength, I < 0.1, therefore activity coefficient approaches 1, see chapter 2) Protons, like other ions in aqueous solution, are subject to hydration by water to form hydronium (H O ) 3ons H + H O 2 H O 3 + (2) By their very nature, hydronium ions themselves tend to become hydrated further through hydrogen bonds with additional water molecules; however, use of the formula H is taken + almost universally to denote all forms of hydrated protons in aqueous solutions. In all aqueous solutions, the autoprotolysis of water must always be considered. + - 2H 2 = H O 3 OH (3) The mass action relationship for the autoprotolysis reaction with the activity of water + equal to unity, and with the formula H taken normally to denote all forms of hydrated protons in aqueous solutions, can be expressed using the equilibrium constant K . w 1 Autoprotolysis is a proton transfer reaction involving two identical molecules, usually a solvent. 1 K ={H O }{OH }={H }{OH } + - (4) w 3 o -14 At 25 C and atmospheric pressure, the equilibrium constant K = 1.0 x 10 w which gives a pH = 7.0 in pure water corresponding to [H ] = [OH]. - 4.2 Acid-Base Reactions An acid refers to a substance that behaves as a proton donor, whereas a base is a 2 substance that accepts protons . In a complete acid-base reaction, an exchange of protons occurs. This process not only satisfies the condition that protons are extensively hydrated in solution, but also accounts for the familiar changes in pH that are associated commonly with the introduction of acids and bases to aqueous solutions. Consider a general reaction for the addition of an acid or base to pure water, respectively HA + H O 2 H O + 3 + - (5) B + H O3= BH + H O+ 2 (6) Each of these reactions consists of two combined parts. For the acid HA + - HA = H + A (7) + + H 2 + H = H O 3 (8) and for the base B + + H 3 = H O +2H (9) + + B + H = BH (10) In the case of the dissociation of the acid (Eqn. 7), the donated protons are accepted by water (Eqn. 8) resulting in the production of hydronium ions; this tends to decrease pH (Eqn. 1 and Eqn. 2), as anticipated for an acid. Conversely, the deprotonation of hydronium ions (Eqn. 9) yield protons that can be accepted by the base (Eqn. 10); this tends to increase pH (Eqn. 1 and Eqn. 2), as anticipated for a base. 4.3 Mass Action Relationships 2This definition extends from the Brønsted-Lowry concept of acids and bases. 2 The strength of an acid is conceived in a generic way by its capacity to donate a proton. In this context, a weak acid has a poor proton-donating capacity, whereas a strong base is one that has a strong capacity to accept protons. Herein rests a point of departure for the establishment of another reasonable reference point, specifically against which to measure the strength of acids and bases. A common approach is to adopt a general reaction for an acid-base reaction, such as that described by Eqn. 5, which is represented formally by two steps as indicated by Eqn. 7 and Eqn. 8. The respective mass action relationships are + − K = {H Os}{A } 1 {HA} (11) {H+}{A−} K 2 (12) {HA} + {H O3} K 3 + (13) {H } Because the actual equilibrium activity of the hydronium ion and protons are not known precisely, chemical thermodynamic conventions set ΔG for Eqn. 13 to zero, or in terms of Eqn 11, chapter 2, K = 1. As such, the combined mass action expressions yield 3 {H }{A } − K 1 K K 2 K3= a (14) {HA} where K can be recognized as the more familiar acid dissociation constant. From this formulation it is evident that the strength of acids as measured by acid dissociation constants are actually referenced in thermodynamic terms against the equilibrium concentrations of hydronium ions and protons (Eqn. 13). Rearrangement of the final form of Eqn. 14 with pK = alog K givea {A }  pH = pKa + log   (15) {HA}  A compelling result from Eqn. 15 that resonates deeply across the broad fields of - - chemistry and biology is that when {HA} = {A}, pH = pK . a For strong acids that give up protons readily, the dissociation constant K a anticipated from mass action relationship illustrated by Eqn. 14 will be largeand the pK a value will be small. Conversely, the K vaaue of a weak acid will be small and the pK a value will be large. These basic relationships between K and aK permitaevaluations of the relative strengths of different acids that occur in aqueous systems. 3 Table 4.1: Some important acids in natural waters Acid Base Ka pK a Hydrochloric HCl Cl ~1000 -3 2- Sulfuric H 2O 4 SO 4 ~1000 -3 - Nitric HNO 3 NO 3 ~1 0 Phosphoric H 3O 4 H 2O 4 10-2.15 2.15 3+ 2+ -2.19 Ferric iron* Fe (6H O2 Fe(OH) (5H O)2 10 2.19 Carbonic* H CO HCO - 10-6.35 6.35 2 3 3 Bicarbonate* HCO 3- CO 32- 10-10.33 10.33 - -4.76 Acetic CH 3OOH CH 3OO 10 4.76 The pH of most natural waters extends from 4.0 to 8.5, which is taken to be representative of the pKarange of weak acids (Table 3.1). This means that strong monoprotic acids with pK values less than 4.0 will occur under normal conditions as fully deprotonated species. The situation is quite different for diprotic and triprotic acids that can exist as partly deprotonated species over a wide range of pH. These partly deprotonated species are called ampholytes because they can behave as acids or bases, depending on the proton condition. The ability of a chemical species to participate in reactions as an acid or base is referred to as amphoteric behavior. Example 4.1 Determine the pH of a solution containing 0.005 M acetic acid that is 75 percent dissociated. From Table 3.1, the pKa of acetic acid is 4.76. The concentration of acetate (i.e., the conjugate base) = 0.005 x 0.75 = 0.00375 M, and the concentration of acetic acid = 0.005 x 0.25 = .00125 M. Applying Eqn. 15 0.00375  pH = pKa+log  = 4.76+log 3 = 5.24 0.00125  4 4.4 Dissolved Carbon Dioxide The pH of most aqueous systems is controlled by reactions involving dissolved carbon dioxide species. When carbon dioxide in brought into contact with water it will dissolved until equilibrium is reached. At equilibrium in a dilute solution, the concentration of dissolved carbon dioxide will be proportional to the partial pressure of carbon dioxide in the gas phase. The reaction is represented by the equation CO +2H O =2H CO 2 3 (16) with a corresponding mass action relationship [H 2O ]3 −1.47 K H =10 (17) pCO 2 Most of the carbon dioxide that dissolved in water exists as a hydrated form rather than carbonic acid, H CO ; however, by convention it is assumed that dissolved carbon 2 3 dioxide is all carbonic acid, and to use equilibrium constants consistent with this convention. The first dissociation step of carbonic acid is written as H CO = HCO + H − + (18) 2 3 3 and − + [HCO ][3 ] −6.35 K 1 =10 (19) [H C2 ] 3 The second dissociation step involving bicarbonate is − 2− + HCO = 3O 3 + H (20) and [CO ]3H ] + −10.33 K 2 − =10 (21) [HCO ]3 The mass action relationships permit evaluation of the distribution of dissolved carbon dioxide species as a function of pH. In the first instance it is useful to consider a closed system with a fixed total dissolved inorganic carbon (DIC) concentration C . In T this case, the mass balance is defined by
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