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Home Reading Skoog et al. Fundamentals of Analytical Chemistry. Chapter 10, 21 Eb E2 E1 L 0.0592pH Include EIRE, EERE, Ej Ecell E 0 cell 0.0592pH Calibration plot Ecell (250C) slope = - 0.0592 0 Ecell 0 Ecell Ecell 0.0592log CH pH Concentration and activity 0 Ecell Ecell 0.0592pH pH = -logCH+ Diluted solutions 0 Ecell Ecell 0.0592 log CH [C] = mole/L Concentration and activity 0 Ecell Ecell 0.0592pH pH = -logCH+ Diluted solutions Concentrated solutions 0 Ecell Ecell 0.0592 log CH 0 Ecell Ecell 0.0592 log CH 0 Ecell Ecell 0.0592 log aH Activity (Apparent concentration) Concentration and activity 0 0.0592pH By convention we accept that equation Ecell Ecell is true at any concentration. 0 Ecell Ecell 0.0592 log aH Ecell E 0 cell 0.0592pH pH = -logaH+ Operational definition of pH pH log aH 0 Ecell Ecell 0.0592 Concentration and activity 0 Ecell Ecell 0.0592 log aH aH H C H H activity coefficient 1 C 0 For diluted solutions a = C Activity coefficient of an individual ion is a theoretical quantity. Ions exist in solutions only in combinations with oppositely charged co-ions. Therefore we cannot experimentally measure the activity coefficient of an individual ion. In experiment, we can only able to determinate the mean activity coefficient, averaged by all the ions in the solution. The mean activity coefficient of the electrolyte KmAn is defined as m n 1 m n Experimental Value Theoretical value m n 1 m n For a 1:1 electrolyte KA the mean activity coefficient is equal to 12 Calculation of the activity coefficient The total concentration of ions in a solution is characterized by a quantity called ionic strength (I) 1 I Ci zi2 2 i Ci = molar concentration of ionic species i zi = charge of ionic species i Example: Calculate ionic strength of 1M solution of HCl 1 I Ci zi2 2 i CH = 1M; CCl = 1 M; zH = 1; 1 I 112 112 1 2 zCl = 1 Debay – Hückel equation Azi2 I log i 1 Bri I A and B are coefficients depending on the solvent and temperature. For water solutions at T = 25 oC A = 0.51, B = 3.3 ri = effective diameter of the hydrated ion i in nanometers. It is close to 0.3 nm for most single charged ions. Ion-selective electrode Ion-selective electrodes measure the activity of ions. Correspondingly the potentiometric equation for them reads 0 Ecell Ecell 0.0592pX pX = -logCX Ion-selective electrode Glass electrodes Liquid membrane electrodes Solid-state crystalline electrodes Li+, Na+, K+, NH4+ Ca2+, K+, Water hardness (Ca2+ + Mg2+), Cl-, NO3- Cu2+, Cd2+, Pb2+, Ag+/S2-, Cl-, F-, I-, CN- Ion-sensitive glass electrodes H+ responsive glass Na+ responsive glass H+ Na+ H+ Na+ H+ Na+ H+ Na+ Ion-sensitive glass electrodes Cole-Parmer® potassiumselective electrode Ion-sensitive glass electrodes Ion conductive glasses are ion-exchangers. When such glass is brought to contact with a solution of electrolyte, equilibrium is established: Glass-A+ + B+ = Glass-B+ +A+ soln soln Any aqueous solution contains hydrogen-ions. So, most frequently, this ion- exchange equilibrium is between H+ and a metal cation. Glass-H+ + B+ = Glass-H+ +A+ soln soln Ion-sensitive glass electrodes Eb = L‘ + 0.0592log(a+kH,Bb) Ej EIRE Eb = E2 – E1 EERE a, b = activity of hydrogen-ion and the cation in the solution kH,B = selectivity coefficient The selectivity coefficient is a measure of the response of an ion-selective electrode to other ions. Eb = L‘ + 0.0592log(a+kH,Bb) 1. kH,B ≈ 0 Eb ≈ L‘ + 0.0592log(a)=L‘ - 0.0592pH pH-glass 2. kH,B >> 0 Eb ≈ L‘ + 0.0592log(kH,Bb)=L‘‘ - 0.0592pB L ‘‘ = L ‘ + 0.0592*log(kH,B) Ion-selective glass Ion-sensitive glass electrodes Liquid membrane electrodes Ag wire Plastic tubing Liquid ionexchanger Aqueous solution sat’d AgCl + B+ Porous plastic membrane holding liquid ion-exchanger Liquid membrane electrodes Solid-state electrodes Solid-state electrode has principally the same design as glass membrane electrodes except the membrane is made from cast pellets of crystalline material rather than from conducting glass. Solid membrane must contain mobile ions, to which it is responsive. Material Selective ion AgF, LaF F- AgCl Cl- AgI I+ Ag2S S2+, Ag+ CdS/Ag2S Cd2+ PbS/Ag2S Pb2+ Solid-state electrode Potentiometric titration Potentiometric titration is a titration technique. It differs from classic titration only in a method of indicating the titration endpoint. Can be used for Benefits: 1. Acid/base titration 1. More sensitive 2. Red/Ox titration 2. Can be automated 3. Complexometry 3. Can be used for turbid or strongly coloured solutions 4. Can be used if there is no suitible indicator Set-up for potentiometric titration Burette Potentiometer Electrode Automatic titration Pump-burette Electrodes Reservoirs Cell There are two distinguishable situation in potentiometric acid/base titration: 1. Titration of a strong electrolyte by a strong electrolyte 2. Titration of a weak electrolyte by a strong electrolyte Titration of a strong acid by a strong base 13 12 11 10 pH 9 Veq 8 7 6 5 4 3 0 5 10 15 20 Volume NaOH (mL) 25 30 35 Titration of a weak acid by a strong base Consider the following graph: 13 12 11 10 Veq pH 9 8 7 6 pKa 5 Veq/2 4 3 0 5 10 15 20 Volume NaOH (mL) 25 30 35 Consider the following graph: 13 12 11 10 pH 9 8 7 6 5 4 3 0 5 10 15 20 25 30 35 Volume NaOH (mL) In this region H+ dominates, the small change in pH is the result of relatively small changes in H+ concentration. Consider the following graph: 13 12 11 10 pH 9 8 7 6 5 4 3 0 5 10 15 20 25 30 35 Volume NaOH (mL) In this region, relatively small changes in H+ concentration cause large changes in pH, The midpoint of the vertical region is the equivalence point. Consider the following graph: 13 12 11 10 pH 9 8 7 6 5 4 3 0 5 10 15 20 25 30 35 Volume NaOH (mL) In this region OH- dominates, the small change in pH is the result of relatively small changes in OH- concentration.