* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 4-Physical Chemistry of SW-Equilibrium-ion
Membrane potential wikipedia , lookup
Spinodal decomposition wikipedia , lookup
Host–guest chemistry wikipedia , lookup
Thermodynamics wikipedia , lookup
Reaction progress kinetic analysis wikipedia , lookup
Marcus theory wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Ionic compound wikipedia , lookup
Physical organic chemistry wikipedia , lookup
Acid dissociation constant wikipedia , lookup
Debye–Hückel equation wikipedia , lookup
Acid–base reaction wikipedia , lookup
George S. Hammond wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
Electrochemistry wikipedia , lookup
Enzyme catalysis wikipedia , lookup
Rate equation wikipedia , lookup
Chemical thermodynamics wikipedia , lookup
Transition state theory wikipedia , lookup
Chemical equilibrium wikipedia , lookup
Determination of equilibrium constants wikipedia , lookup
Equilibrium chemistry of seawater Governs: o o o o o o o Mineral dissolution & precipitation reactions Metal complexation and reactivity Redox chemistry pH and buffering Adsorption/desorption Kinetics (rates of reactions) Gas exchange at sea surface and more… It all depends on thermodynamics Chemical Equilibrium in Aqueous Systems Most chemical reactions are reversible. Forward aA + bB <=> cC + dD Small letters indicate stoichiometric coefficients. Large letters represent individual chemical species Reverse At equilibrium, the rate of forward reaction (product formation) is equal to the rate of the reverse reaction (reactant formation), and the concentrations of all species is constant with time. This is not a static condition - rather it is a dynamic equilibrium - forward and reverse reaction rates balance. The relative concentrations of products [C ]c [ D]d and reactants at equilibrium is given by K eq a b [ A ] [ B ] the equilibrium constant, Keq: The value of Keq is fundamentally tied to the thermodynamic stability of the system – it predicts the most stable allocation of product and reactant concentrations in a system. For the chemical reaction aA + bB <==> cC + dD The Gibbs free energy change (G) is given by: Reaction quotient products reactants G = Go + RT ln [(C)c(D)d]/(A)a(B)b] Where Go is the standard free energy change, R is the gas constant and T is temperature in Kelvins At equilibrium, ΔG = 0 and [(C)c(D)d]/(A)a(B)b] = Keq 0= Go + RT ln Keq Go = - RT ln Keq Also Go = Gfoproducts – Gforeactants Where Gfo is the standard free energy of formation Chemical Reaction Rates and Chemical Equilibrium The rate of a chemical reaction, say conversion of A B can be written as: d [ A] k[ A] dt which is a first order differential equation. The k is the first order rate constant and [A] is the concentration of chemical A. In other words, the rate of the reaction depends directly on the concentration of A with the proportionality constant k, which is the fraction of A reacted per unit time. Equilibrium constant concept For reaction: A B at equilibrium A A A K1 = fraction of A converted per unit time B A A B B B B B A B B B B B A B A A K2 = fraction of B converted per unit time A B B B B B B B B B BB B B B B B A B B B BB B B B B B B B B B BB B B B B B B B B B Rate of formation of B = K1 [A] Rate of formation of A = K2 [B] At equilibrium the rate in both directions is the same, therefore K1 [A] = K2 [B], which can be rearranged to: K1/K2 = [B]/[A]. Thus, the relative amount of product to reactant (B/A) depends upon the ratio of the forward rate constant to the reverse rate constant. This ratio (K1/K2) is the equilibrium constant (Keq). The value of Keq predicts the concentration of the products relative to the reactants. Equilibrium chemistry depends on the “effective concentrations” of chemicals Equilibrium expression for dissolution of a mineral Calcite: CaCO3 (s) = 1Ca2+ + 1CO32Stoichiometric coefficients Keq = {Ca2+}1 {CO32-}1 {CaCO3 (s)}1 For dissolution of a mineral, the Keq has the special name of Solubility Product (Ksp) = Products = 3.35 x 10-9 Reactants The braces { } represent chemical activities – not total analytical concentrations In an almost infinitely dilute solution, say just a few molecules of Ca2+ and CaCO32- in a liter of pure H2O, the ions will behave in a nearly ideal manner. That is, their effective concentrations (activities) will be equal to their absolute molal concentration. However, as total solute concentrations increase, the solution deviates further from ideality, and the “effective concentration” of solutes is no longer equal to the absolute molal concentration (This is because the increasingly crowded ions affect the solvent, which in turn effects how the ions react) This is an example of a non-specific interaction Solvent – ion interactions Solvent structure The ion in solution affects the solvent (water), and this alters the “effective” concentration of the ion Electrostriction The effective concentration of a solute is called its activity (ai) and this is not necessarily equal to its molal concentration (it is usually lower). The activity of an ion (ai) is equal to its molality (mi) times an activity coefficient (i), which is the fraction of the ion that is available to react at any given time ai = i * m i Thus an equilibrium constant should be expressed in terms of its activities (the effective concentrations): Keq = {Ca2+}1 {CO32-}1 / {CaCO3}1 or Keq = (Ca2+ mCa2+)1 (CO32- mCO3-2)1 / (CaCO3 mCaCO3)1 The { } denotes activities, whereas [ ] denotes absolute concentration Activity coefficients are dependent on T & P, and thus, the conditions of the reaction. As ionic strength, I, (defined below) increases, the activity coefficient of an ion deviates from 1. It usually decreases but the decrease is not always so dramatic as pictured here - and it sometimes actually increases! It depends entirely1 on the characteristics of the solutes and solvent. 1 activity coefficient Ac 0 Ionic St rengt h --> Ionic strength 1 2 I mi zi 2 where mi is the molal concentration of an ion and zi is the charge on that ion. Ionic strength is one half the summation of each ion concentration times the square of its charge. A solution of 10-3 molal Na2SO4 dissociates as follows: Na2SO4 <=> 2Na+ + SO42- Thus, it has an ionic strength of: I = 0.5 [( .001 x 2) (1)2 + (.001 x -22)] = .003 = 3 x 10-3 Seawater has an ionic strength of ~0.7 (You should be able to work this out from major ion concentrations). At this ionic strength, simple theoretical calculations of activity coefficients (i.e. the Debye-Huckel equation) cannot be used. Seawater is very far from being an ideal solution and this needs to be taken into account in some circumstances To predict the solubilities of solids, liquids and gases in seawater requires knowledge of the activity and activity coefficients of these solutes in seawater. Activity coefficients for major species are tabulated. Ion Pairing – a specific interaction Single ions with their hydration sphere are termed free ions - also known as “aquo” ions. When hydration is relatively weak, the ions can interact - their primary solvation shells can be shared momentarily. This is called ion pairing. Many ions in seawater are significantly paired. e.g. Mg2+ + SO42- MgSO4o Ion-pairing can occur among groups to form higher order associations ternary, quaternary etc. i.e. Na+K+SO42- but the concentrations of these associations is low because of the low probability of collision of all three components. Ion – ion interactions More specific Ion pair Less specific The fraction The fraction available to that is not ionreact based on paired i.e. free. solvent effects only (nonspecific effect) The effective concentration as a fraction of the total Garrels and Thompson (1962) were the first to surmise the existence of ion pairs in seawater and they calculated the ion speciation for major ionic species in seawater. Major Cation speciation Major Anion speciation Major Cations and chloride are mostly free ions, but other major anions are highly paired in seawater Non-specific vs. specific interactions in solutions a continuum. Non-specific effects Ion-solvent interactions affect activity coefficients of chemical species Specific effects Weak Ion Pairing Strong Ligand binding Coordination complexes A stronger specific interaction is when electrons are shared, held together more strongly than in ion-pairing, (but not enough for an ionic bond). These can be termed ligand complexes. An even stronger specific interaction is called a coordination complex which has fixed geometry. Most coordination complexes involve metal cations (Me+) and multiple ligands (L). Ligands need not be anions. Dipoles can function as ligands (H2O actually functions as a ligand, albeit a weak one). Specific interactions form a continuum from weak ion pairing to strong coordination complexes. When complexation occurs on a solid surface or colloid surface the term adsorption or ionexchange is used. Many trace metals are complexed by surface ligands. Non-specific vs. specific interactions in solutions a continuum. Non-specific effects Ion-solvent interactions affect activity coefficients of chemical species Specific effects Weak Ion Pairing Strong Ligand binding Coordination complexes Metals and complexation We can write an equilibrium constant for the following equation describing the association of a metal (Me) with a ligand (L): aMe+ + bL- <=> MeaLb {Mea Lb } K stab a b {Me } {L } This form of Keq is termed a stability constant - Kstab A large Stability constant indicates that the complex is favored over the dissolved ions. 10x molar X= Much higher in seawater Metals are extensively complexed by ligands in seawater - this affects their bioavailability! Major anionic ligand species include Cl-, SO42-, HCO3-, CO32- and OH-. These ligands form weak complexes, but are present at high concentrations. H2O also can be considered a ligand as hydration of ions attests. See Comans and van Dijk (1988) for info on Cd2+ complexation Chemical species of metals in seawater using iron (Fe) as an example Operationally filterable Dissolved Colloidal Particulate The speciation of iron is extremely important in the biological context – some forms of Fe are available to algae and some are not! Growth of Raphidophyceae (red tide microalgae) as measured by change in fluorescence. These bioassays were conducted under conditions of iron limitation and emendation with four insoluble iron species [FeO(OH), Fe2O3, FeS, and FePO4.4H2O], soluble inorganic iron (FeCl3.6H2O), and an artificial organic ion species (Fe-EDTA). Source: From Naito et al. 2005. Harmful Algae 4, 1021–1032. In seawater, Ligands affect the chemistry of trace metals much more than the trace metals affect the chemistry of the ligands. In most cases [Ligands] >>>>> [metals]. Exceptions may be the highly specific Zn, Fe and Cu binding ligands present in ocean water. Since metals are the limiting reactant, the effects of metal-metal competition for the ligands is minor and can be neglected. Thus, speciation calculations can be done independently as a function of ligand competition for the metal ion. Simple case – free metal plus one ligand in solution The metal can exist in only two forms, free and complexed with the ligand. The mass balance for the metal is therefore: [Mtotal] = [Mfree] + [ML] Kstab = [ML]/[Mfree][L] Use the equation for Kstab to express [ML] in terms of Mfree [Mtotal] = [Mfree] + Kstab[Mfree][L] [Mtotal] = [Mfree] (1+ Kstab[L] Factor out Mfree on the right side [Mfree] = [Mtotal]/(1+Kstab[L]) Rearrange to solve for Mfree Use values for ΣFe (1 nM) in seawater and a major ironspecific ligand (L1 @ 4 nM) Calculations [Mtotal] = 1.00E-09 Molar [L] = 4.00E-09 Molar log Kstab = [Mfree] 25 2.5E-26 0.0000000000000025% Molar free The “strength” of a ligand for a metal is gauged by its stability constant. A large stability constant means that the complex is very stable and thermodynamically favorable. But, All things are relative Ligands compete with each other for metals The ligand-metal complex with the greater Kstab tends to win the competition: If the Kstab of CdL1 is 1 x 102 and the Kstab of CdL2 is 1 x 106 Then L2 forms more stable complexes with Cd2+ than L1. Thus, Cd is most likely to be found in association with L2. In fact, if the L1 and L2 are present at equal concentrations, the concentration ratio of the complexes (CdL2/CdL1) will be 106/102 = 104. But! What if L1 is present at a higher concentration than L2? How could the solution be modified to achieve roughly equal distribution of Cd between the two ligands (i.e. 50% of Cd as CdL1 and 50% as CdL2)? Increasing the concentration of L1 by a factor of 104 greater than L2 will result in equal partitioning of Cd2+ between L1 and L2 i.e. [ML1] = [ML2] These calculations assume that only the two complexes of Cd2+ are possible. In most aquatic systems many ligand combinations are possible. Some possible ligands for Cd2+ include Cl-, OH-, CO32- and some organics like phytochelatins. Solid phase adsorption Ligand associations on particle surfaces Solid particle -O Cd2+(aq) (e.g. clay) Cd2+ -O -O (charged surface groups serve as ligands for complexation of metals) Dominated by free Cd+ ion Dominated by CdCl+ complexes Co-dominated by CdCl+ & CdCl2 complexes From Commans & van Dijk, 1988 Cd adsorption onto suspended particles in freshwater (0 salinity) Cd desorption at different salinities 35.5 ppt 5.9 ppt 2 ppt 0 ppt Solid lines represent Cd concentration of 1 µg L-1 and dashed lines represent 20 µg L-1 From Commans and van Dijk, 1988 Commans and van Dijk, 1988 0%0 2%0 5.9%0 35.5%0 Corrections for activity of Cd2+ is critical for calculation of adsorbed amount. In addition to major ions, dissolved organic matter (DOM) is an important ligand complexing agent for metals in seawater. Most of the ligand binding sites on DOM are occupied by major ions such as Ca2+ and Mg2+ rather than trace metals (e.g. Fe3+, Zn2+, Cd2+). This complexation has little effect on the major ion’s activities but affects the trace metals ability to compete for a site. The trace metals may have a higher affinity for a site (i.e. the trace metal complex is more stable), but the major ions may be so much more abundant that they out compete the trace metal. Binding of metals in a 3-D coordination complex is called chelation. Examples of chelators include: ETDA - Ethylenediamine tetra acetic acid - hexadentate ligand - strong complexes with di- and trivalent metal ions. NTA - Nitrilotriacetic acid - tridentate ligand for metals cations Siderophores - Natural Fe3+ binding ligands - and example is desferroximine (Desferal; DFOB) Chlorophyll a - Mg2+ coordination complex Enzymes and co-factors - many have coordinated metals. Chelators Ligand functional groups Desferoximine (DFOB) – a Siderophore (Fe binding chelator) Fe(III):DFOB Log Kstab = 30.5 EDTA (ethylene diamine tetraacetic acid) Fe(III):EDTA Log Kstab = 25.1 Log K values for 0.1 M ionic strength and 25 oC Phytochelatin (Cd2+, Cu2+ and Zn2+ binding chelator) Siderophores of biological origin. Fascinating Fe-binding ligands! Some of the aquachelins and marinobactins have conditional stability constants for Fe3+ of 1024 to 1050! The complex is greatly favored over ionic forms. See work of Alison Butler for more on natural marine siderophores Mineral dissolution and precipitation The solubility of a particular mineral is predicted by its solubility product (Ksp), a type of equilibrium constant. Consider: CaCO3 (s) <=> Ca2+(aq) + CO32-(aq) Ksp = {Ca2+} {CO32-} {CaCO3} Note that since CaCO3 is a solid, and the activity of solids (or water) is taken as 1 then the Ksp simplifies to Ksp = {Ca2+} {CO32-} For calcite, a form of CaCO3, Ksp = 10-8.35 @ 25oC and Ionic strength of 0 (a std condition). From the value of this Ksp (about 10-8) it is obvious that the concentrations of Ca2+ and CO32in equilibrium with the solid mineral will be relatively low since when multiplied they have to equal 10-8.35 M. The Ksp for NaCl is much larger (10+1.5 ), indicating it is a more soluble mineral. For: Ksp = {Ca2+} {CO32-} = 10-8.35 In a complex solution like seawater there are an infinite number of combinations of the activities (effective concentrations) for the two ions that can satisfy the equation. The right side of the equation is called the Ion Activity product (IAP). Consider again, CaCO3 <=> Ca2+ + CO32For a system not necessarily at equilibrium we can measure the activities of the ions in solution, say Ca2+ and CO32- in the example above, and calculate the ion product (IAP): IAP = {Ca2+} {CO32-} If the IAP is greater than Ksp, then solution is super saturated and thermodynamics predicts that precipitation should occur (the rate of the precipitation reaction will be faster than dissolution reaction). If the IAP is lower than Ksp, the solution is undersaturated and more mineral salt should dissolve (dissolution faster than ppt), until equilibrium is reached when both reaction rates are equal. It helps to keep in mind the dynamic nature of chemical reactions. There is no static condition – any steady state is a dynamic one. From Libes – Web appendices (this is just a small section from Table 14A) Acids and bases Acid: proton donor Base: proton acceptor protons exit in the hydrated form, H3O+ or hydronium ion, but are often abbreviated to H+ Water is a weak acid which can dissociate to a proton and hydroxyl ion: H2O <=> H+ + OH- K a {H } {O H } { H O} 2 Since the activity of liquid water is considered to be 1, it drops out and the equilibrium equation becomes Kw = {H+} {OH-} which has a value of 1 x 10-14 @25 oC This equilibrium must be satisfied in all cases. In pure water at 1 atm, 25 oC, the equilibrium activity of H+ is therefore: {H+} = 1 x 10-7 and {OH-} is also 1 x 10-7. That is: {H+} {OH-} = (1 x 10-7) x (1 x 10-7) = 1 x 10-14 Define pH = -log {H+} In pure water at 25 oC, the pH = -Log (10-7) = 7. Anything that adds H+ to the solution will increase the concentration of H+, but the equilibrium for water will be maintained and thus OH- will decrease (and vice versa). Thus, at pH = 4 the {H+} = 1 x 10-4 M and {OH-} = 1 x 10-10 M such that the water equilibrium is still satisfied (10-4 x 10-10 = 10-14) Acidic vs. Alkaline pH 7 = neutral pH > 7 alkaline pH < 7 acidic Remember that pH is a log scale, and a single pH unit represents a 10-fold range of {H+} or {OH-}! The “p” notation is also used with equilibrium constants in the same fashion. pK = -log K pH of natural waters Ocean Surface 8.0 - 8.2 Deep Sea 7.6 - 8.0 Pore waters 7.0 -8.0 Estuaries 6.5-8.0 Rivers & Lakes Black water (organic rich) 3.0 - 6.0 Clear water 6.0 -7.0 Natural 5.0 -5.5 Polluted 2.0 - 4.0 Rain Strong acids “Completely” dissociated in water i.e. large Ka Will not accept proton back even at very low pH Example: HCl H+ + Cl- Ka = 108 Weak acids “Incompletely” dissociated in water i.e., Smaller Ka May accept proton back at low pH Example: H2CO3 H+ + HCO3- Ka = 10-3.6 Mono protic acids: HCl, HNO3, HF etc. (yield only 1 H+ per mole) Poly protic acids H2SO4, H3PO4, H2CO3 (yield more than one H+) pH dependence of weak acid dissociation FIG 5.19 in Libes Equivalence points – where pH = pK Consider dissociation of the weak acid: H2CO3 H+ + HCO3Ka = {H+} {HCO3-}/{H2CO3} Rearrange to isolate {H+} Ka {H2CO3} / {HCO3-} = {H+} Take “p” or negative Log of both sides pKa {H2CO3} / {HCO3-} = pH or {H2CO3} / {HCO3-} = pH/ pKa At pH = pKa, then {H2CO3} / {HCO3-} = 1 Thus, at pH =pKa, the {H2CO3} and {HCO3-} must be equal, hence the equivalence point Less buffering O-H+ O- More buffering OH Silica (SiO2) in the tests of diatoms functions as a pH buffer -Si—Si—SiBuffering is critical for function of carbonic anhydrase Milligan & Morel 2002 Time-series of mean carbonic acid system measurements within selected depth layers at Station ALOHA, 1988–2007 Surface pH In thermocline Below thermocline Dore J E et al. PNAS 2009;106:12235-12240 ©2009 by National Academy of Sciences Stop! Apparent equilibrium constants Keq': Often used for seawater systems Uses total analytical concentration measured at equilibrium, rather than activities. Empirical determination of activity - good only for conditions specified. * K app ( CaCO3 ) K sp (CaCO ) 3 Ca CO 2 2 [Ca 2 ][CO3 ] 2 3 The Kapp depend on solution conditions. Fortunately, in oceanic seawater, the major ion composition (which makes the solution non-ideal) is relatively constant, so once determined, the apparent activity values can be used reliably. Weak acids have small Ka values and therefore are not completely dissociated. They also have the ability to accept H+, whereas strong acids will not accept protons in aqueous solution. For this reason, weak acids (their conjugate bases actually), can act as buffers, absorbing H+ and minimizing effects on pH. Any reaction that involves H+ as a reactant or product, will be affected by pH. Complexing of ions in solution affects the total solubility of a mineral compound. The influence of ion pairing can be seen in the following example involving dissolution of calcium carbonate (CaCO3). The amount of ions in solution at equilibrium is given by the solubility product: Ksp = {Ca2+}{CO32-} where { } denotes ion activities the activity of carbonate ion is given by aCO32- = CO32- * mCO32For carbonate ion in seawater the is very small due to nonspecific effects at ionic strength of ~=0.7. Therefore, the total concentration of carbonate (m) needed to satisfy the equilibrium expression for Ksp is higher than it would be in pure water, where the the activity coefficient () is close to 1. Thus, much more CaCO3 will dissolve in seawater than in pure water. Now for an equilibrium reaction in which A<=> B (something like H2O(l) <=> H2O(g)) d [ A] k a [ A] The rate of the forward reaction is dt whereas the rate of the reverse reaction is d [ B ] dt Note that the two rate constants are different. kb [ B ] At equilibrium the forward and reverse reactions rates are equal: ka[A] = kb[B]. Rearranging we can get: k a [ B] kb [ A] Since both k’s in this case are constants, they can be lumped together to form a new constant, we’ll call Keq: [ B] K eq [ A] The equilibrium constant, then, is really a ratio of the forward reaction rate constant to the reverse reaction rate constant and its value predicts the concentration of the products relative to the reactants. Rate constants are inverse functions of the Activation energy (Ea). In other words, a reaction with a large Ea will have a small k (slow reaction rate constant). The relation between k and Ea is : k Ae Ea / RT Arrhenius equation Where A is and Ea are characteristic reaction constants, R is the gas constant, and T is temperature in Kelvins. Therefore, ln k = ln A - EA/RT (rearrange slightly to isolate T as 1/T) ln k = ln A - EA/R (1/T) A plot of ln k vs. 1/T yields a straight line with slope -EA/R and intercept of ln A. Since R is constant, EA can be calculated Activation energy (Ea) – The energy required to overcome electrostatic inertial forces that either keep molecules together (as in the case of complex) or apart (as in the case of two molecules trying to collide and combine). The Gibbs free energy per mole of reaction is the difference between free energy of the products and reactants: G = Gproducts - Greactants If products have more free energy than reactants, then G will be positive (and have a small Keq). Since all reactions proceed to minimize free energy, this would be an unfavorable reaction. Products must contain less free energy for a reaction to proceed spontaneously. The reaction would proceed in the reverse direction. What governs whether the reactants will be favored over products or whether the reaction will proceed as written? It depends on thermodynamics. (G= H + TS) Where G is the Gibbs free energy, H is the enthalpy, T is absolute temperature, and S is the Entropy reactants products For a given chemical reaction: bB + cC <=> dD + eE The change in free energy is: G = Gproducts - Greactants Absent inputs of external energy, all reactions proceed in the direction that minimizes free energy - in other words, to the most stable state. Thus, to proceed, the reaction must lose free energy and G must be negative. Every chemical has a standard free energy of formation Gfo These are measured under standard conditions (1 atm pressure, 25 oC, 1 Molar activities for each species Go = Gfoproducts – Gforeactants For our example reaction Go = (dGfoD + eGfoE) – (bGfoB + cGfoC) Standard free energies of formation for each chemical species times the # moles of that species in the reaction Consider the reaction: CaCO3 (s) <=> Ca2+ + CO32- How much CaCO3 will dissolve in an aqueous solution? The relative concentrations {activities} of products and reactants in a chemical system at equilibrium is predicted by: 2 K sp (CALCITE ) {Ca 2 }{CO3 } 3.35 *10 9 {CaCO3} Many organisms deposit minerals. Furthermore, dissolution/precipitation reactions are extremely important with respect to the chemistry of many elements. Knowledge of the equilibrium constant for a given reaction and the concentrations of some of the reactants and products we can predict whether the precipitation is thermodynamically favored. Organisms cannot work against thermodynamics !- only external energy can drive seemingly unfavorable reactions - an example would be photosynthesis which is the reduction of CO2 to organic carbon driven by light energy.