CHM 320 Lecture 10 Chap 8Chapter 8 - Activitydilute solutionIons in concentrated solution interactCHM 320 Lecture 10 Chap 8How do ionized species interact in solution?• The charge on the ions attracts or repels other ionic species as well as polar species.• The more dense the charge, the stronger the attraction.• The more diffuse the charge, the weaker the attraction.• The ion attracts polar water molecules and becomes surrounded or hydrated; thus, ions have a hydration sphere.• If there are other ions in solution, these ions perturb the hydration sphere. For example, if Ca+2present in distilled water, it is surrounded by H2O molecules to form its hydration sphere.CHM 320 Lecture 10 Chap 8For example: If Ca+2present in distilled water, it is surrounded by H2O molecules to form its hydration sphere.Ca+2HOHHOHHOHHOHCa+2HOHCl-HOHHOHHOHCl-Cl-Cl-Cl-If Ca+2is present in water with Cl-present also, the Cl-has a stronger negative attraction than the dipolar negative aspect of H2O. The Cl-will gainer closer access to the Ca+2ion, and perturb the hydration sphere.CHM 320 Lecture 10 Chap 8So what does that mean?• An ion in which the hydration sphere has been changed now has an ionic environment in place of the hydration sphere. • A cation will build up anions around it, and an anion will build up cations around it.• The ionic environment decreases the attraction of the ion’s ability to attract any additional ions of the opposite charge.• This ionic environment, in a sense, weakens the attractive force compared to the attractive force of the same ion that only has a hydration sphere (in water only).CHM 320 Lecture 10 Chap 8CHM 320 Lecture 10 Chap 8Addition of “inert” ionic species to solution.•By adding ions that do not react with the analyte ions in solution except to get close to them and form an ionic environment (termed inert ions), these inert ions can increase the solubility of ionic compounds.For example:BaSO4= Ba+2+ SO4-2In water only, the Ba+2and SO4-2are more attracted to each other, than to the water molecules, so they form BaSO4again. If other ions are added (like KNO3), the K+decreases the SO4-2attraction for other cations (like Ba+2). Likewise, the NO3-decreases the Ba+2attraction for other anions (like SO4-2).CHM 320 Lecture 10 Chap 8Significance•Kspfor BaSO4in water: 1 x 10-10in 0.01 M KNO3: 2.9 x 10-10• Solubility is altered because K+and NO3-act to shield Ba2+and SO42+from each other in solution so they don’t recombine.• Analogy: big class vs. small classCHM 320 Lecture 10 Chap 8Account for this effect using activity coefficent: aA= γA[A]where: aAis activity of AγAis the activity coefficient [A] is molarity (moles/L)RECALL --a A + b B = c C + d DK = [C]c[D]d/ [A]a[B]bBUT REALLY….K = Acc Add/ AaaAbborK = [C]c γcc[D]d γdd/ [A]a γaa[B]b γbbCHM 320 Lecture 10 Chap 8How do we determine the activity (A)?A = [X]xγxxWe know [X] is the molar concentration (moles/L).γxis the activity coefficient for species X. It is dependent on:• the ionic strength of the solution (μ)• the charge of the ion (z)• the ionic size (α).CHM 320 Lecture 10 Chap 8μ = 0.5 Σ cizi2where:ciis molarity of ith ionziis charge on ith ionNote: effect of square is to remove sign of charge so + and -don’t cancel out!Example: Calculate the ionic strength of 0.010 M Na2SO4-.μ = 0.5 Σ cizi2= 0.5 ([Na+](+1)2+ [SO4-2](-2)2)= 0.5 ((0.02)(1) + (0.01)(4))= 0.030 MIonic StrengthCHM 320 Lecture 10 Chap 8Ionic SizeIonic sizes are tabulated on page 154 of HarrisOverall charge on ion is more diffuse if:1. Larger the radius2. The lower the chargeSo…More diffuse the overall charge, the less it will affect the activityCHM 320 Lecture 10 Chap 8Debye-Hückel Equation:In 1923, P. Debye and E. Hückel used the ionic atmosphere model to derive a theoretical expression that permits the calculation of activity coefficients of ions from their charge and their average size. This is called Debye-Hückel Equation:CHM 320 Lecture 10 Chap 8Points concerning the Debye-Hückel Equation• The constants A and B are applicable to aqueous solutions at 25℃. • The equation works fairly well for μ≤0.1M. • α is the effective hydrated radius of the ion and its tightly bound sheath of water molecules. • As ionic strength increases, the activity coefficient decreases.For all ions, γ approaches unity as μ approaches zero.• As the charge of the ion increases, the departure of its activity coefficient from unity increases. Activity corrections are much more important for an ion with a charge of ±3 than for one with a charge of ±1.• The smaller the hydrated radius of the ion, the more important activity effects become.CHM 320 Lecture 10 Chap 8Does γ really matter?• The solubility of Ca3(PO4)2(s) is measured in pure water and in aqueous solutions of NaNO3• The behavior on the right is foundCHM 320 Lecture 10 Chap 8Points concerning Activity (A):• Concentration of ions (ionic strength, μ) is important.• Charge on ions (z) is important.• Size of ions (α) is important.• Molar concentrations are an approximation for activity of solution species.• “Activity” (A) should be used for exact work.• The activity coefficient (γx)of a species is a measure of the effectiveness with which that species influences an equilibrium. • In very dilute solutions (μ is small), this effectiveness becomes constant and the activity coefficient is unity. The activity and molar conc. of the species is equal.CHM 320 Lecture 10 Chap