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Home Reading Skoog et al. Fundamental of Analytical Chemistry. Chapters 18, 19, 21 Overall error of measurement Overall error = Systematic Error + Random Error There are two schemes of summation of the errors: additive and quadratic Additive x syst t P , N x Errors are additive Quadratic x 2syst t P , N x 2 Variances are additive Electrochemical Analysis Electrochemical methods employ processes occurring in a system when electrical current passes through the system or the system is influenced by the electro-magnetic field to obtain information about its qualitative and quantitative composition. We will speak only about methods involving the passage of electrical current. All such methods imply a direct contact of two electrodes with a solution of an electrolyte. A vessel in which the electrodes contact with the solution is called an electrochemical cell. Cathode is the negatively charged electrode. It attracts cations . Anode is the positively charged electrode. It attracts anions General scheme of an electrochemical cell Conductometry Conductometry is a method of analysis based on the measurement of the conductivity of solutions. When difference of potentials is applied to the electrodes, the transfer of charged particles is initiated: cations go to the cathode, anions go to the anode. The conductance correlates with the concentration of charged species in the solution. The measured property is the resistance of the solution R [ohm]. Reciprocal resistance is called conductance G = 1/R. + ― + ― l l R S G 1 R l S – specific resistance l – distance between electrodes S – cross-sectional area + ― – specific conductance or conductivity + ― [R] = Ohm = W [G] = S = 1/W [] = S/m l The ratio l/S can be measured with scale for solid conductors but it is NOT so easy to do with liquid conductors. Then this ratio (cell constant) is to be found by Kcell l calibration with a standard solution. S G K cell Conductivity = Observed conductance × cell constant Conductance depends on the total concentration of charged particles in a solution. G K cell ( water ) i i Molar conductivity m ,i i 1000 ci [c] = mol/L The total conductivity of an electrolyte solution is additive with respect to ions’ conductivities only for strongly diluted solutions, so called at infinite dilution. This is not true for concentrated solutions of electrolytes. c b c The Kohlrausch law Conductance and concentration G K cell Overall concentration 1000 c c c b c c 1000 1000 c b c G K cell We cannot measure separately the conductivity of ions. We can only measure the total conductivity. So, the conductometry is a method of the determination of total salinity. Nowadays, it is used for the determination of total salinity in pipelines, in water purification systems and so on. Measurement of conductance Modified Wheatstone bridge circuit Conductivity cell Conductometers Desktop conductometer On-line conductometer Portable conductometer Water purification system with molded on-line conductometer Potentiometry Potentiometry is a method of analysis based on the measurement of the potential of electrochemical cells, in which one electrode is selective to a certain sort of ions, called potential determining ions. Theory of potentiometry Cu|Cu2+ (0.02M)||Ag+ (0.02M)|Ag Anode Copper is dissolving Cu = Cu2+ + 2e- Cathode Silver is reducing Low resistance circuit e- Salt bridge Ag+ + e- = Ag Reductant Oxidant Copper electrode Silver electrode CuSO4 solution AgNO3 solution Cu + 2Ag+ = Cu2+ + 2Ag Transfer of charge from an electrode to the solution and from the solution to an electrode by dissolving copper ions from the anode into the solution and by transfer of electrons from silver cathode onto silver cations in the solution. As a result of electrochemical reaction electrons leave copper electrode and it is charged positively. Electrons are accumulated on the silver electrode and it is charged negatively. Potentials are formed on each electrodes. Difference of these potentials determines the electromotive force of this electrochemical cell. Conductor e- _ + Ag+ e- Ag Cu Cu2+ Electrolyte solution e- Conductor _ Half-reaction + Ag+ e- Ag Cu Cu2+ 0.02M CuSO4|| 0.02M AgNO3 E = 0.287 E = 0.698 Ecell = emf = Ecat – Eanod = 0.698 – 0.287 = 0.411 Half-reaction Nernst equation Potential of electrode relates to the concentrations of the reactants and the products of a half-reaction through the Nernst equation. Consider the following reversible half-reaction aA+bB = cC+dD c d RT C D 0 EE ln a b nF A B E0 = standard electrode potential R = gas constant, 8.314 J/mol K T = temperature, K n = number of electrones F = Faraday constant, 96500 coulombs Cu2+ + 2e- = Cu(s) Ag+ + e- = Ag(s) AgCl(s) + e- = Ag(s) + Cl- EE 0 Cu 2 Cu EE 0 Ag Ag EE 0 AgCl Ag RT 1 ln 2 F Cu 2 RT 1 ln F Ag RT ln Cl F Standard electrode potential E0 is a potential of a half-reaction when the concentrations of all participants are equal to 1. Values of the standard potential for a number of common Red/Ox reactions are tabulated. (c) Skoog et al. Fundamentals of analytical chemistry emf of an electrochemical cell is a difference of the potentials of two electrodes E C1 , C2 E 0 hr1 RT RT 0 ln C1 Ehr 2 ln C2 nF nF Half-reaction 1 Half-reaction 2 In order to make the instrumental signal a function of the analyte concentration, we have to fix the potential of the second electrode. We need one electrode to be the reference electrode, an electrode with a constant potential . E C1 E 0 hr1 RT ln C1 E reference nF Potentiometry A principal scheme of a potentiometric cell Reference electrode|Salt bridge|Analyte solution|Indicator electrode Hydrogen reference electrode Salt Bridge Ag Indicator electrode Reference electrodes 1. Calomel Electrodes Hg I Hg2CI2 (sat'd), KCI(x M) II Half-reaction: 2. Silver/Silver chloride electrodes Ag I AgCI(sat'd), KCI(x M) II Half-reaction: *Reference electrodes can contain a KCl solution of different concentration. Most frequently x = 0.1; 1, saturated. Silver/Silver chloride reference electrode Silver wire AgCl on Ag wire KCl solution Ceramic quartz or glass fiber junction One-beaker potentiometric cell Indicator electrodes Type of indicator electrode Determined ions Metallic Metal cations Membrane Inorganic cations; Organic and inorganic anions lon-Sensitive Field Effect Transistors (ISFETS) Inorganic cations and anions; solvated gases pH – electrodes. pH-metry Glass membrane electrodes Insulated connection cable Silicate glass structure Shielding Lead wire Mercury connection Internal reference electrode pH-responsive glass membrane Internal electrolyte solution (c) G. A. Perley, Anal. Chem., 1949, 21, 395. Examples of pH-electrodes Measurement of pH with glass electrodes Potentiometric cell for pH measurement Ag/AgCl Ej EIRE Eb = E2 – E1 EERE Eb = boundary potential E1, E2= potentials at the surface of the glass membrane Ej = junction potential C H 1 2.303RT Eb E2 E1 log 1F C H 2 Measurement of pH with glass electrodes C H 1 2.303RT Eb E2 E1 log 1F C H 2 C(H+)2 = concentration of the internal solution; C(H+)2 = constant Eb E2 E1 2.303 8.314 298 log C H 1 constant 96500 log CH = - pH Eb E2 E1 L 0.0592pH (T = 250C) Eb E2 E1 L 0.0592pH Include EIRE, EERE, Ej Ecell E 0 cell 0.0592pH Calibration plot Ecell slope = 0.0592 0 Ecell pH (250C)
