CONDUCTOMETRIC TITRATIONS. Reading: 1. Skoog, Holler and Nieman: Chapter 22 A. INTRODUCTION. A.1 Classification of Electroanalytical Methods

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1 Reading: 1. Skoog, Holler and Nieman: Chapter 22 A. INTRODUCTION A.1 Classification of Electroanalytical Methods Electroanalytical methods are methods of analysis which rely on electrical properties of analytes, including their ability to donate and receive electrons (oxidation and reduction) and their ability to conduct electricity. Electroanalytical methods utilize electrochemical cells, which in their simplest form comprise two electrodes: a cathode, where reduction takes place and an anode where the oxidation takes place and the solution of the analyte. When reactions are spontaneous, the cell generates electrical energy and is called a galvanic cell. When the cell draws electrical energy from an external source to cause reactions, it is called an electrolytic cell. Analytical information about analytes is obtained from the measurements of potentials and/or current flow across the electrochemical cell. Electroanalytical methods are divided into two major categories: interfacial methods or bulk methods, with the former being the most widely used methods. Interfacial methods rely on phenomena occurring at the interface between electrode surfaces and the thin layer of solution surrounding the electrode. Interfacial methods are classified as static or dynamic. Static methods such as potentiometry and potentiometric titrations are based on the measurements of potential in the absence of current flow through the cell. Dynamic methods depend on the flow of current through the cell. Voltammetry, for example, is a dynamic method in which the potential is varied and the current measured as a function of applied potential. Bulk methods such as conductometric titrations rely on phenomena occurring in the bulk of the solution. A.2 Conductometry (Reference 3) Unlike interfacial electroanalytical methods, conductometry is not concerned with either equilibria or reactions at electrodes. In conductometry and conductometric titrations, the electrical conductivity of the solution of the analyte is measured and related to the concentration of the analyte. The electrical conductivity of a solution depends not only on the concentration of ionic species but also on their mobility. Mobility of an ion describes the ease with which it moves therefore its current carrying capacity. If two relatively large platinum electrodes are immersed in a solution of a nonelectroactive salt and a potential difference is applied between them, a small current will flow simply to charge the electrodes to the applied potential. After the electrodes have been charged, nothing more happens unless the voltage is sufficient to bring about an electrochemical change, which will generate faradaic currents. If the direction of the applied potential is reversed well before the 1

2 charge has been built up on the electrodes, then the current (that is charging current) will begin to flow in the opposite direction. Thus an applied alternating potential produces an alternating current totally associated with charging of the electrodes. Under the desired conditions this is nonfaradaic current. Provided the electrical capacitance between the two electrodes is relatively small, then the current that flows depends on the resistance of the solution (Reference 3). Since all ions in solution contribute to the conductivity, measurements of resistance give nonspecific information. The resistance of the solution is related to the conductance according to: 1 1 G = ( Ω R ) (mho) The property of the ion that gives quantitative information about its relative contribution to the conductance is its mobility. The mobility of an ion is the rate at which it moves under the influence of an external force such as an electric field. In dilute solutions, when the concentration of an ion is doubled, its contribution to conductance is doubled. When its mobility is doubled, its contribution to conductance is also doubled. Accordingly, for a given ion or salt a linear relation exists between the measurement of conductivity and concentration. Most applications of conductance involve aqueous solutions. Pure water is a poor conductor; being only slightly dissociated, the contribution of hydrogen ions and hydroxyl ions to the conductance is slight even though their mobilities are high. In analysis, the conductance method is typically used in the form of a titration for systems where the conductance differs significantly between components of the original solution and the products of reaction or the titrant. Conductance measurements are also useful for assessing the degree of dissociation of the acids, complexes, etc. Conductance changes linearly on addition of reagent, provided dilution is properly accounted for. Incomplete reactions result in curvature in plots of conductance against titrant volume, in the region of the end point. The relation between conductance, concentration of ions and cell properties 1 A G = = k( λ a Ca + λbcb + λccc +...) = k' R l 1 G : conductance in mho ( Ω ) R : resistance in ohm (Ω) λ : equivalent ionic conductance ( Ω cm eq ) 2 A: cross sectional area of electrode ( cm ) l : distance between electrodes (cm ) 1 1 k': specific conductance ( Ω cm ) 2

3 However, for analytical applications, knowledge of absolute values of conductance is not required. Since the change in conductance is what enables extrapolation to obtain the end-point, only relative values are important. A titration of hydrochloric acid with sodium hydroxide, may be written H + Cl + Na + OH Na + Cl + H2O Before the end point, the solution composition is changing as hydrogen ions are being replaced by sodium ions. The hydrogen ion has a mobility about seven times ( x 10 7 m/s at 25 C) that of the sodium ion (50.11 x 10 7 m/s at 25 C) (Reference 2), causing the conductance to decrease sharply. After the equivalence point, the conductivity increases sharply because both sodium ions and hydroxyl ions are being added in increasing amounts When a weak acid HA is titrated with sodium hydroxide, the reaction is + + HA + Na + OH Na + A + H2O If the acid is so weak that ionization is negligible, the conductivity increases throughout the titration, but more sharply after the end point because the hydroxyl ion has a higher conductivity than does the anon of any weak acid. In precipitation reaction such as + Na Cl + Ag + NO3 AgCl( s) + Na + NO3 the conductivity changes but slightly throughout the reaction and then increases after precipitation is complete. B. EXPERIMENT SUMMARY Conductance will be measured during the following titrations, to determine the concentration of HCl, acetic acid and sulfuric acid. 1. Titration of HCl with NaOH 2. Titration of acetic acid with NaOH 3. Titration of H 2 SO 4 with barium hydroxide 3

4 C. EQUIPMENT The instrument used for this experiment is a Beckman Model RC-18A Laboratory Conductivity Bridge. Figure 1, copied from the Beckman instruction manual, shows the front panel of the instrument and the bridge circuit. The six dial knobs in the middle adjust the resistance of the 6-decade resistor. Figure 1: Front panel of the Beckman Model RC-18A conductivity bridge and the bridge circuit as used for resistance measurements 4

5 Measurement of the resistance of the cell is obtained by balancing the bridge. At balance, the potential difference between point x and y is zero and no current flows between the two points. For this condition to be met the voltage drop across the Cell (I 2 xr cell ) must be equal to the voltage drop across resistor A (I 1 xr A ); and the voltage drop across the 6 decade variable resistor (I 2 x R dec ) must be equal to the voltage drop across resistor (I 1 xr B ). i 2 RCell = i1 R A (1) i 2 Rdec = i1 R B (2) Rearranging (1), we obtain i R 1 Cell = RA (3) i2 Rearranging (2), we obtain i1 i2 = Rdec RB (4) Substituting (4) into (3), we obtain R R dec Cell = RA (5) RB Substituting RA = RB = 1K into (5), we obtain R Cell = Rdec (6) This means that at balance, the Cell resistance is equal to the variable resistance. Just to prove to yourself that is the case, a standard resistor (nominal value =10 K= 10 x 10 3 Ω) will be connected to the bridge in the Cell position, and you will dial/ measure the resistance required to balance the bridge. The bridge is balanced when the trace on the oscilloscope is a straight line along the horizontal middle line on the screen. D. EXPERIMENTAL D.1. Solutions 1) 0.10 N NaOH standard solution 2) 1.0 N NaOH standard solution 3) ~0.1 N HCl 4) ~0.1 N acetic acid 5) M Ba(OH) 2 6) ~0.05 M H 2 SO 4 5

6 D.2 Measuring the resistance of the 10K resistor Connect the 10 K resistor instead of the cell and balance the bridge. Record the resistance measured. D.3 Titration of hydrochloric acid with sodium hydroxide Transfer 5.00 ml HCl into a 250-ml beaker. Dilute with deionized water to approximately 150 ml. Measure the resistance. Titrate with 0.10 N NaOH using 0.50 ml increments till 4.5 ml, 0.2 ml increments to the end point and 0.5 ml increments up to 2 ml after the end point. Correct the resistance reading for dilution. D.4 Titration of acetic acid with sodium hydroxide Transfer ml of 0.1 M acetic acid into a 250 ml beaker. Dilute with deionized water to approximately 150 ml. Measure the resistance. Titrate with 1.0 N NaOH using 0.50-mL increments up to 4.0 ml after the end point. Correct the resistance readings for dilution D.4. Titration of sulfuric acid with barium hydroxide Transfer 5.00 ml of 0.05 M Ba(OH) 2 into a 250 ml beaker. Dilute with deionized water to approximately 150 ml. Measure the resistance. Titrate with 0.05M H 2 SO 4 using 0.50-mL increments up to 4 ml after the end point. Correct the resistance readings for dilution and calculate the conductance at each titration point. E. DATA PROCESSING AND QUESTIONS 1. For each titration, calculate the corrected conductance at each point, using the corrected resistance. 2. Plot the titration curves using corrected conductance. 3. Locate the end points for the three titrations. 4. Calculate the concentration of HCl, acetic acid and sulfuric acid. 5. Comment on the differences between the shape of the titration curve of HCl, acetic acid, and sulfuric acid. 6

7 F. REFERENCES 1. Skoog, Holler and Crouch, Chapters R.P. Franenthal in Handbook of Analytical Chemistry, L. Meits, Ed., McGraw- Hill, 1963, pp W.E. Harris and B. Kratochvil, An Introduction to Chemical Analysis, Saunders College Publishing, 1981, pp