Problems with Electrolytes Ron Robertson r2 c:\files\courses\3620\ion activities.docProblems with Electrolytes Slide 1 Ion Activities Intro For non-electrolytes the interactions between solute particles are so weak that the replacement of activity with molality is justified. For electrolytes the interactions between ions is so strong that we must find an expression for an activity coefficient (γ) such that a = γ m/m° Mean activity and the activity coefficient Charge neutrality dictates that for every + ion in solution there is a negative counter ion. This means that the activity of a + ion will depend on the activity of the negative ion and makes it impossible for us to determine the activity of an isolated ion.Problems with Electrolytes Slide 2 For an ideal solution G = µ+ + µ-Problems with Electrolytes Slide 3 There is no way experimentally to disentangle γ+γ- so we define quantities γ±, m±, and a± Suppose we have a salt MpXq dissolved in waterProblems with Electrolytes Slide 4 Example – Calculate the mean activity of 8.25 x 10-4 m Al2(SO4)3 at 25°C given that the mean activity coefficient at this temp is 0.9913 and the compound dissociates completely.Problems with Electrolytes Slide 5 Debye-Huckel Limiting Law The interactions of the ions are coulombic in nature. The solution is electrically neutral, but near any given ion there is an excess of counter ions of opposite charge. This lowers the chemical potential and is quantified by RT ln γ±. At very low concentration (less than 0.001 m) the Debye-Huckel limiting law is log10 γ± = -z+z-A I1/2Problems with Electrolytes Slide 6 z = charge on ion A is a constant that involves Avogadro’s #, charge on the electron, the thickness of ionic atmosphere, the dielectric constant of solvent and the temp A = .509 at 25° I is the Ionic Strength I = ½ Σ zi2 mi/m° Example – What is I for a 0.100 m solution of CaCl2? Question for thought – What is the relationship between M (Molarity) and m (molality) at very low concentrations in aqueous solution?Problems with Electrolytes Slide 7Problems with Electrolytes Slide 8 To use this equation we assume 1. all ions have the same diameter 2. the dielectric constant is the same everywhere in the solution 3. the counter-ions form a spherical cloud 4. only long range electrostatic forces occur At slightly higher concentrations (0.0100 m) the extended Debye-Huckel Law is log10 γ± = -z+z-A I1/2 1 + B I1/2 The constant B includes a parameter for the closest approach of the ions to each other.Problems with Electrolytes Slide 9 Example – (long and tedious) Calculate the voltage of the cell below at 25°C. For the purpose of this example calculate the E° value for the cell from ∆Gf° values and use the Debye-Huckel limiting law to obtain activities for the reaction quotient. Zn(s) ZnSO4(aq) (3.00 x 10-3 m)  CuSO4 (aq) (1.00 x 10-3 m)