EXPERIMENT 8 POTENTIOMETRY: DIRECT-MEASUREMENT OPTION I. INTRODUCTION This experiment introduces the direct-measurement approach to potentiometry. Principal purposes of the study are a) to understand quantitative relationships between electrode potential and concentration and b) to use that information to understand how absolute and relative concentration errors depend on errors in measured potentials. A secondary purpose is to use potential measurements to quantify the hydrogen peroxide concentration in an unknown sample and to determine the confidence interval for the results. II. OVERVIEW A. Chemical reactions The half reactions involved in this experiment are as follows: + O + 2 H + 2 e 2 H O (1a) H2 2 2 I I + 2 e (1b) Hydrogen peroxide is reduced to water and iodide is oxidized to triiodide. The net reaction is the sum of these two half reactions as follows: + - O + I + 2 H I 2 H O (1c) H2 2 + 2 This reaction is slow in the absence of a catalyst but quite fast in the presence of catalysts such as molybdate (Mo(VI)) and an excess of iodide that forces the reaction to completion by the formation of triiodide, I -. B. Rationale In the presence of a high iodide concentration, changes in triiodide concentration can be monitored potentiometrically. Accordingly, hydrogen peroxide concentration can be quantified potentiometrically by measuring the potential of an inert electrode immersed in the solution and using a calibration relationship to compute triiodide concentration, which is then converted to hydrogen peroxide concentration. C. Standardization In practical situations, the hydrogen peroxide concentration should be standardized. However, the main thrust of this experiment focuses on characteristics of potentiometric methods. Accordingly, to save time and to permit you to focus on the main thrust of the experiment, you will use the nominal concentration of the hydrogen peroxide in a % solution. D. Potentiometric detection It will be helpful to review some features of potentiometric detection before proceeding with the experimental discussion. 1. General. Potentiometry exploits electrochemical properties of chemical systems. In potentiometry, the aim is to measure the potential of a system without drawing any current from it, e.g. to measure the potential without causing electrochemical reactions that would change the concentration at the electrode surface. Typical examples of potentiometric sensors include the glass electrode used for ph measurements and ion-selective electrodes used for a variety of ionic analytes such as sodium, potassium, calcium, sulfide, etc. Relationships between electrode potential and concentration are described by the Nernst equation (see text). Potentiometry is frequently used in one of two modes, namely a direct-measurement mode where electrode potential is measured and used to compute concentration and a titrimetric mode where electrode potential is used to detect the end point in a titration. This experiment involves the direct-measurement mode. 1
2. Electrode potential. Potentiometric detection of triiodide at an inert (e.g. platinum) electrode is based on the fact that reaction 1b is reversible. The Nernst equation for this reaction is: E I/I = E 0 I/I + (RT/nF)ln(C I /C I ) = E 0 I/I - (RT/nF)lnC I + (RT/nF)lnC I (2) where E is the electrode potential, E 0 I/I is the standard reduction potential (See text) for reaction 1b, R is the ideal gas constant, T is temperature ( 0 K), n is the number of electrons involved in the reaction (n = 2 in this case), F is Faraday s constant, and C I and C I are the molar concentrations of triiodide and iodide, respectively. Because the iodide concentration is present in large excess and does not change significantly, it can be incorporated into the formal electrode potential, E 0. Substituting E 0 I/I = E 0 I/I - (RT/nF)lnC I, Eq. 2 can be simplified to: E I/I = EI/I 0 + (RT/nF)ln C I (). Cell voltage. The potential described above is the potential expected at an inert electrode immersed in a solution containing iodide and triiodide. Unfortunately, this potential can not be measured independently but must be measured relative to a reference electrode. The reference electrode used in this study is the saturated calomel (SCE) electrode and has a potential of 0.244 V vs. the normal hydrogen electrode(nhe) at 25 0 C. The cell voltage you will measure is the difference between the indicator and reference electrodes. E Cell = E I/I - E SCE = E I/I - 0.244 V @ 25 0 C (4a) Substituting from Eq. we have: E Cell = E 0 I/I - E SCE + (RT/nF)ln C I (4b) Because both E 0 I/I and E SCE are constants, Equation 4b can be simplified to: E Cell = α + β ln C I (4c) where α = E 0 I/I - β ln C I - - E SCE and β = (RT/nF). In other words, the cell potential is expected to vary linearly with the logarithm of the molar concentration of triiodide ion. 4. Numerical values of constants. Using R = 8.14 J K -1 and F = 96,485 coulombs it follows that β = RT/nF = 8.62 x 10-5 T/n. Assuming n = 2 (See reaction 1b) and T = 298, it follows that β = 1.284 x 10-2. Given E 0 I/I = 0.56 V, E SCE = 0.244 V, and β ln C I - = 1.284 x 10-2 ln (0.2) = -0.062, it follows that α = 0.56 V - 0.244 V - (-0.062 V) = 0.54. Accordingly, at 25 0 C, the cell potential is expected to vary with triiodide concentration as follows: E Cell (V) = 0.54 V+ 1.284 x 10-2 ln C I (4d) This expression gives potentials in Volts, V. The ph meter you will use reads potential in millivolts, mv. The above expression is expressed in millivolts as follows: E Cell (mv) = 54 mv+ 12.84 ln C I (4e) with C I expressed in mol/l. In practice, the cell voltage is expected to vary linearly with the logarithm of concentration (Eq. 4c) but the constants are expected to be somewhat different than those in Eqns. 4d and 4e. 5. Concentration vs. potential. Equation 4c is easily rearranged to be explicit in concentration. The relationship is E α C = exp( ) Cell (5) β In other words, the relationship between concentration and potential is an exponential function. Theoretical values of the constants for T = 298 and n = 2 are given above, with magnitudes depending on whether voltages are expressed in volts or millivolts. III. INSTRUMENTATION AND SOLUTIONS A. Extra glassware In addition to supplies in your drawers, each group will need twelve 100-mL volumetric flasks, twelve 100-mL beakers and a thermometer good to at least 0.1 degrees Celcius. 2
B. Instrumentation A ph meter equipped with a platinum indicator electrode and a saturated-calomel reference electrode pair will be used to measure potentials. Potentials will be measured and entered into laboratory notebooks manually. C. Solutions All solutions are to be prepared in deionized water and glassware should be rinsed in deionized water. 1. Solution provided Buffer/catalyst solution. For each liter of solution, add 0.1 g of (NH 4 ) 6 Mo 7 O 24 4H 2 O, 0 g of KH 2 PO 4, and 14 g of K 2 HPO 4 H 2 O to 1 L of water and stir until the salts are completely dissolved (600 ml/group). 2. Solutions you must prepare a. Composite reagent (1 L required). Prepare this solution fresh by dissolving 67 g of potassium iodide in about 500 ml of the buffer/catalyst solution and dilute to about 1L with DI water. Because the dissolution of KI is endothermic and light enhances air oxidation of iodide, place the solution in your desk to warm to room temperature in the dark while you prepare hydrogen peroxide solutions described below. b. Stock solutions of hydrogen peroxide. Three stock solutions of hydrogen peroxide will be used to prepare diluted solutions containing nominal hydrogen peroxide concentrations over a wide concentration range. The nominal molar concentration of hydrogen peroxide in a % solution is C H2O2 = (1000 ml/l) x 1g/mL x 0.0 (g/g) /4 g/mol = 0.882 mol/l. i. Stock 1 (0.0882 M). Pipet 10 ml of % hydrogen peroxide into a 100-mL volumetric flask, dilute to volume with water and mix thoroughly. ii. Stock 2 (0.00882 M). Pipet 25.00 ml of the Stock 1 solution into a 250-mL volumetric flask, dilute to volume with water and mix thoroughly. iii. Stock (0.000882 M). Pipet 25.00 ml of Stock 2 hydrogen peroxide solution into a 250-mL volumetric flask, dilute to volume with water and mix thoroughly. IV. PROCEDURES Turn on the ph meter and set the mode switch to mv at least 20 min before you will begin to measure potentials. Briefly, the procedure involves reaction of hydrogen peroxide with iodide to produce triiodide and detection of the triiodide potentiometrically using a platinum indicator electrode and a saturated calomel reference electrode. Three sets of data will be obtained for each solution. A. Calibration Standards/Unknown. Stock solutions described above are used to prepare two sets of calibration standards covering a 150-fold concentration range. Do NOT dilute the following solutions to volume at this point. 1. Calibration standards (Set 1). Label five 100-mL volumetric flasks A-E. Using a buret, add 2.00, 5.00, 10.00, 20.00, and 0.00 ml of Stock solution to flasks labeled A-E, respectively. Set these flasks aside and proceed with the next step. 2. Calibration standards (Set 2). Label four 100-mL volumetric flasks F-I. Using a second buret, add 5.00, 10.00, 15.00 and 0.00 ml of Stock 2 solution to flasks labeled F-I, respectively. Set these flasks aside and proceed with the next step.. Unknown. See instructions for Unknown for Experiment 8 on page 8.
B. Reaction step Pipet 50.00 ml of the composite reagent into each of the 100-mL volumetric flasks containing calibration standards and unknowns. Dilute each to volume using deionized water and mix thoroughly. Wait approximately 5 min after preparing these solutions before making measurements. Note and record the appearances of the solutions. C. Measurement step Label several clean dry 100-mL beakers A-I and U. Transfer approximately 50 ml of each of the calibration standards and unknown solutions into each of the 100-mL beakers. Rinse the platinum/saturated calomel electrode (SCE) pair with deionized water and pat dry with lint-free tissue. 1. Calibration solutions Wipe the electrodes gently with a lint-free tissue (do not wash with water) and Immerse them in the most dilute of the calibration standards. Swirl briefly let stand until the potential stabilizes, and record the potential. (The potential should approach a steady-state value very quickly in this and the other standard solutions). Repeat this process for each of the calibration standards, working from the more dilute to the more concentrated solutions to minimize effects of carry-over among the solutions. Measure and record the temperature of at least three of the solutions. 2. Unknown solution After measuring the potential of the calibration standards, rinse the electrodes thoroughly with deionized water, pat them dry, and measure and record the potential of the unknown solution.. Replicate measurements Repeat the measurement process twice for each standard and unknown. You should have at least three complete sets of data for potential vs. concentration before you quit. D. Least significant digit Note and record the least significant digit (LSD( )) on the ph meter used to measure voltages. The least significant digit is the smallest voltage resolved by the readout scale on the ph meter. The precision of replicate measurements with a digital device can be no better than one half of the LSD (i.e. SD 0.5 LSD). V. DATA PROCESSING/ANALYSIS Principal emphasis here is on relationships between potential and concentration and error analysis. In all of the discussion below, it is assumed that signals are expressed in Volts (not mv) and that concentrations are expressed in mol/l (M). Note: The ph meter you will use reads cell voltage in millivolts. Although it is possible to work with millivolts (See Eq. 4e), there will be less confusion in some calculations if you change voltages to volts by multiplying by 1 x 10 - V/mV before you proceed with other calculations (See Eq. 4d). 4
A. Mean values and imprecision Calculate the mean values and standard deviations of cell voltages for the replicate measurements of the calibration standards. Use the individual standard deviations to calculate the pooled standard deviation (s E,p, See text) for all the data. Compare the pooled standard deviation to the least significant digit (Part IV-D). If the pooled standard deviation is greater than one half the least significant digit (s E,p 0.5 LSD), use the pooled standard deviation as the voltage error, s E, in calculations below. If the pooled standard deviation is less than 0.5 LSD, use 0.5 x LSD as the voltage error, s E, in calculations below. B. Potential/Concentration relationships Potential/concentration data will be plotted in three formats to help you visualize more completely the nature of the relationship. 1. Potential vs. concentration Potential (V) vs. concentration (M) will be plotted in two formats, on linear coordinates and as a semilogarithmic plot. a. Linear coordinates. Plot mean values of Potential (V) vs. Concentration (M) on linear coordinates. Using suitable software (e.g. Origin), fit an equation in the form of Eq. 4c to the data. A suitable syntax for the equation in Origin is: P 1+ P2* LN( X ) (6) where P1 is α and P2 is β (Eq. 4c). Use numbers in Eq. 4d (assuming data are in Volts) as initial estimates of P1 and P2. Include this graph and least-squares statistics in your report as Figure 1. Compare values of P1 = α and P2 = β to expected values in Eq. 4d. b. Semilogarithmic plot. Calculate values of the natural logarithms of concentrations (ln C I ) of the standards and prepare a plot of potential vs. ln C I. Fit a linear model to these data. Include this graph and least-squares statistics in your report as Figure 2. 2. Concentration vs. potential Plot Concentration (M) of standards as ordinate vs. Potential (V) as abscissa and fit a model similar to Eq. 5 to the data. The model in Origin syntax is: EXP(( X P1) / P2) (7) Symbols have the same significance (and approximate numerical values) as in Eq. 6. Include this graph and least-squares statistics in your report as Figure. C. Error analysis A primary purpose of this experiment is to understand how measurement errors, s E, are translated into absolute and relative concentration errors (s C and s c /C). We shall approach this both graphically and mathematically. Recall that the absolute concentration error is the measurement error divided by the sensitivity. The measurement error was quantified above (Part V-A). Accordingly, the next step in our error analysis is to determine the sensitivity. Error equations are summarized at the end of this experiment. 5
1. Sensitivity (Eq. EEP-5) Recall that the sensitivity is the slope of a plot of the dependent variable vs. the independent variable. In this case, it is the slope of a plot of cell voltage vs. concentration. (See Eq. EEP-5 in attached equations). Use the numerical value of β calculated above (Part V-B-1-a) to calculate values of sensitivity as a function of concentration. Prepare a plot of sensitivity vs. concentration, do a least-squares fit of EEP-5 (P1/X in Origin syntax) to the data and include this plot in your report as Figure 4. Rationalize the shape of this plot using the linear-coordinate plot of potential vs. concentration (Part V-B-1-a). 2. Concentration error (Eq. EEP-6) Calculate the concentration error (Eq. EEP-6) for each standard concentration. Prepare a plot of concentration error (mol/l) vs. concentration, fit Eq. EEP-6 to the data and include the plot in your report as Figure 5.. Relative concentration error (EEP-7) Use equation EEP-7 to describe how relative concentration error is expected to vary with concentration in direct-measurement potentiometry. D. Unknown concentration Use the relationship in Eq. 7 (Part V-B-2) to calculate the concentration (mol/l) of your unknown. Use this value to calculate the hydrogen peroxide concentration in the 250 ml volumetric flask after the first dilution. Report this concentration, the standard deviation, and the 95 % confidence interval in the usual way. Target values for unknown concentrations are 0.0 to 0.09 mol/l. VI. REPORT In addition to the usual information, your report should include a tabulation of all calculations, figures, and least-squares results requested above, and a discussion of each. Also, compare relationships between absolute and relative concentration errors vs. concentration in direct-measurement potentiometry and direct-measurement spectrophotometry with fixed transmittance error (Experiment 4). 6
ERROR EQUATIONS POTENTIOMETRY This paper summarizes an approach to the development of error equations for direct-measurement potentiometry. Sensitivity The symbol, Φ E,C, represents the sensitivity of potential, E, to changes in concentration, C. The sensitivity is quantified either as the slope of a plot of potential vs. concentration or the first derivative of a mathematical relationship between potential and concentration. Indicator reaction I + 2 e I (EEP-1) Equilibrium electrode potential [I 0 RT ] E = E + ln E - Ref nf [I ] (EEP-2) Constants R = 8.14 Coul/ 0 K mol, F = 96,485 Coul/Eq, n = 2, T = 298 0 K, E Ref = 0.244 V, [I - ] = 0.20 mol/l Simplified equation E = 0.54V + 0.0128 ln[ I ] (EEP-) E = α + β ln C (Note: α = 0.54 V, β = 0.0128 V) (EEP-4) Sensitivity de d(α + βlnc) β d( k lnu) 1 du Φ E, C = = = (Note: = k ) (EEP-5) dc dc C dx u dx Concentration error se se C sc = = = se,c (EEP-6) ΦE,C β / C β (Note: Absolute concentration error increases linearly with concentration). Relative concentration error (RCE) sc 1 C 1 = s E,C = se,c (EEP-7) C C β β (Note: Relative concentration error is independent of concentration). 7
Instructions for Unknown for Experiment 8 Peroxide is somewhat unstable in air and must be diluted immediately prior to analysis. Therefore, you will need to do two dilutions of your unknown to get it into the proper concentration range for analysis by this procedure. Dilute unknown to volume in the 250 ml flask with distilled water and mix thoroughly. Pipet 25 ml of this into a clean 250 ml volumetric flask. Dilute to volume with composite reagent and mix thoroughly. Pipet 10 ml of this dilution into a clean 100 ml volumetric flask and proceed with the reaction step. 8