Chapter 6 Activity Scales and Activity Corrections(10/10/01) James W. MurrayUniv. Washington6.1 Total Activity Coefficient: Electrostatic Interactions and Ion Complexing6.1.A ActivityIons in solution interact with each other as well as with water. At lowconcentrations (Ci) and background salt concentrations these interactions can possibly beignored, but at higher concentrations the ions behave like they are less concentrated thanthey really are. Equilibrium constants calculated from the standard free energy of reaction(e.g. ∆Gr°) are expressed in terms of this effective concentration, which is formally calledthe activity, which is the concentration available for reaction. Thus we define activity as:Activity (ai) = Effective concentrationIn infinitely dilute solutions where ionic interactions can be ignored: ai = Ci. These arecalled ideal solutions.In concentrated solutions like seawater: ai < Ci. These are non-ideal solutions.There are two main reasons for these differences:6.1.B Electrostatic InteractionsThe background ions in solution shield the charge and interactions between ions.Example: Say we have a solution of calcium and sulfate in water. The ions are Ca2+ andSO42-.The tendency of Ca2+ and SO42- ions to hydrate induces shielding which affects the abilityof Ca2+ and SO42- to meet and react (and precipitate as a solid in this case). If we addother ions like Na+ and Cl- to solution, they are attracted to the ions of opposite chargeand we effectively increase the amount of electrostatic shielding. The other ions decreasethe ability of Ca2+ and SO42- to interact. Therefore, gypsum or CaSO4.2H2O, will appearmore soluble in seawater than in freshwater. These interactions result in non-idealsolutions. Ions with higher charge are more effective than ions with lower charge at thisshielding effect.6.1.C Ion Complexing or specific interactionIn some cases there are specific interactions between ions - solutes come close enoughthat they make direct contact and are considered a new species! These new species arecalled ion pairs (when ions are separated by H2O molecules but share their first hydrationshell) or complexes (when ions are in contact and share electrons)(see Libes, P. 62).Example: Ca2+ + SO42- == CaSO4°Let's say we have a solution containing some of the major ions:Ca2+ , K+, F- and SO42-The negatively charged species like F- and SO42- are known as ligands. Because of theinteraction between ions, not only do we have the free ions present (e.g. Ca2+, F-) but alsocomplexes such as:CaF+, CaSO4° , KF° , and KSO4-Like shielded or hydrated ions these complexes are less able to react so their formationlowers the effective concentration. In some cases complexes are so dominant that the freeion population is only a small fraction of the total. We will see this later for some tracemetals. For example, the speciation of iron and copper in seawater is dominated bycomplexes with organic compounds and the free, uncomplexed Fe3+ and Cu2+ ions havevery low concentrations..We can ignore higher order complexes involving more than one cation and one anionsuch as:CaF2° , Ca(SO4)22-, etcThese may form but their concentrations are very small and they can be ignored.6.2 The Activity CoefficientWe generally only know the total concentration of an element (mT). This isusually what can be most easily measured analytically. First we need to convert the totalconcentration (mT) to the concentration of the ion or species (mi) that we are interestedin. In order to calculate mi from mT we need to do an equilibrium calculation of thepercent free which we express as fi. Thus:mi = mT ×××× fiFor the case where we have CaT but we want Ca2+ we need to calculate the ratio:fCa2+ = [Ca2+]/ CaT = [Ca2+] / ([Ca2+]+ [CaSO4°]+ [CaCO3°])Once we have the concentration of the free ion (mi) we need to convert it to the activityof the free ion (ai). To do that we use the free ion activity coefficient (γγγγi) that corrects forelectrostatic shielding by other ions. This correction is written as:ai = γγγγi ×××× mi molal concentration of a free ionfree ion activity coefficient for that speciesThe total expression with both correction factors is then written as:ai = γγγγi × fi ×××× mT mT is the total ion concentration % of the total concentration, mT, that is freeSometimes γγγγi and fi are combined together and called the total activity coefficient, γγγγT.Then,ai = γγγγT mTWhere, the total activity coefficient = γγγγT = γγγγi fiexample: a solution with Ca2+, SO42- and CO32- forms the complexes CaSO4° and CaCO3°γγγγT,Ca = fi × . γγγγCa2+= ([Ca2+]/ CaT) ×. γγγγCa2+= ([Ca2+]/ ([Ca2+]+ [CaSO4°] + [CaCO3°])) × γγγγCa2+How do we obtain values for γγγγi and fi .1. γγγγi --- Free Ion Activity CoefficientThe free ion activity coefficient describes the relation between the activity andconcentration of a free ion species. We use either some form of the Debye-Huckel typeequations or the mean salt method2. fi --- % free ==== We obtain this from a chemical speciation calculation done byhand or using a computer program like MINTEQA2 or HYDRAQL.6.3 Ionic StrengthFirst you need to know the ionic strength ( I ) of the solution because the electrostaticinteractions depend on the concentration of charge. The value of I is calculated asfollows:I = 1/2 Σ mi . Zi2charge of i th ion concentration of i th ionNote that the ionic strength places greater emphasis on ions with higher charge. A 2+charged ion contributes 4 times more to the ionic strength than a 1+ ion For amonovalent ion, its contribution to the ionic strength is the same as its concentration. Theionic strength has concentration units.Example: Compare the ionic strength of freshwater and seawater. MolalitySeawater (SW) Lake Water (LW)Na+0.49 0.2 x 10-3Mg2+0.053 0.14 x 10-3Ca2+0.010 0.22 x 10-3K+0.010 0.03 x 10-3Cl-0.57 0.09 x 10-3SO42-0.028 0.102 x 10-3HCO3-0.002 0.816 x 10-3ISW = 1/2 (mNa x 12 + mMg x 22 + mCa x 22 + mK x 12 + mCl x 12 + mSO4 x 22 + mHCO3 x 12) = 0.72 mol kg-1ILW = 0.0015 = 1.5 x 10-3 mol kg-1So the ionic strength of seawater is about 500 times larger than that of fresh water.6.4 Activity ScalesThe free energy change for an infinitely small change in concentration is called the partialmolal free energy or chemical potential. The chemical potential (µ) for