8.1. Measurement of the electromotive force of an electrochemical cell

Transcription

1 8.. Measurement of the electromotive force of an electrochemical cell Ojectives: Measurement of electromotive forces ( the internal resistances, investigation of the dependence of ) and terminal voltages of galvanic cells, determination of on the electrolyte concentration. 2 Theoretical acground: The cell diagram of the Daniell cell: s Zn s aq. ZnSO 4 c ZnSO 4 salt ridge saturated KNO 3-solution SO 4 c SO 4 aq. s 2. The electromotive force, terminal voltage, and the internal resistance of a galvanic cell The method for the measurement of the potential difference (terminal voltage or terminal potential difference) of a galvanic cell can e represented y a simple electric circuit (Fig. 8...). According to Ohm s law the current flowing through the resistances given as: (internal resistance) and I The voltage etween the terminals of the cell i.e. the potential drop e also easily calculated using Ohm s law: Fig (load resistance) can e (8...) across the load resistance can I (8..2.) Measurement of the potential difference of the electrochemical cell (terminal voltage)

2 After rearranging eq. (8..2.) we have: (8..3.) It can e seen from the aove equation, that for a galvanic cell the terminal voltage is always smaller than the electromotive force, however, the smaller and is. In the limiting case current flowing through the cell is zero. and the greater is, the smaller the difference etween,. It also means, that the limiting value of the (In other words: In case of discharging of an electrochemical cell, the terminal potential difference cannot e greater than the difference ecomes equal to the resistance voltage eceeds the.) of a cell ut in the asence of the internal resistance, the terminal potential, the terminal potential difference of a cell. In case of charging of an electrochemical cell having internal of the cell is greater than its. Here, the terminal of a cell y the term I. If there is no internal resistance then = 0, then 2.2 Measurement of the electromotive force with a voltmeter of high internal resistance According to the aove considerations, the of a cell can e measured with a voltmeter, provided that the internal resistance of the voltmeter is high enough. But what is high enough? Oviously, the current passing the cell must e low enough to ensure the electrochemical equilirium at oth electrodes, i.e. it should e much smaller than the echange current of either electrode. Of course, in duious cases this should e checed with adequate eperiments. 2.3 Determination of electromotive force y compensation technique The determination of the advantage that the of a cell using a potentiometer is a classic eperiment. This eperiment has the of a cell can e measured without drawing any current from the cell, in short the measurement can e done as if it was done with a voltmeter of infinite resistance. Figure presents a compensation coupling with which the electromotive force of a voltage source (galvanic e.g. cell) can e measured. is the cell under test and T (= + 2 ) is the total resistance of the potentiometer in the circuit. N is a standard cell. A standard cell is a galvanic cell whose voltage is accurately nown and remains sufficiently constant for instrument caliration purposes (e.g. the Weston standard cell has a voltage of volts at 20 C). 2

3 Fig Principle of the compensation method I If the S switch is open, the current in the circuit containing the voltage source (the voltage is /. If cvs 2 cvs U cvs ) equals U is constant and 2 is also constant, then I remains constant during the measurement. The cell under test is connected parallel to the resistor in series with the switch S and a galvanometer G. (A galvanometer is a very sensitive ammeter.) The value of the resistor (the resistance) should e set so that the current passing the galvanometer is zero ( I G 0 ), even if the switch is closed. (If the value of is decreased, the value of 2 should e increased in order to have a constant 2.) The value of corresponding to this situation is where In this case the voltage drop across is given as: equals to the electromotive force of the cell under test.. I. (8..4.) Correspondingly, after replacing the cell under test with a standard cell, in case of I G 0 the electromotive force of the standard cell ( ) can e epressed as N n I. (8..5.) In eq. (8..5.) N is the value of if the current passing the galvanometer is zero ( I G 0 ), even if the switch is closed. From eqs. (8..4.) and (8..5.) we get: n n (8..6.) n 3

4 (The switch S should e switched on only for very short time periods, in order to avoid the polarization of the electrodes.) Of course, in the practice of signal processing it is impossile to deal with zero currents, in reality a non-zero current is flowing through the cell. The intensity of this near-zero current depends on the sensitivity of the galvanometer (in our case the sensitivity of the galvanometer is of the order of magnitude of 0 6 A). 2.4 Determination of y etrapolation There is another possiility for the determination of the electromotive force if we follow the measuring instruction given in the definition of. The method is the following: In order to measure the internal resistance we add different load resistances in parallel with the cell, and the voltmeter of high input impedance (see Fig ). Fig Circuit for the etrapolation method ( : load resistance; B : input resistance of the voltmeter; : internal resistance of the galvanic cell; : electromotive force) In this case a current I passes through the electrochemical cell. Using Kirchhoff s laws (Kirchhoff's laws: pair of laws stating general restrictions on the current and voltage in an electric circuit. The first of these states that at any junction of paths, or node, in a networ the sum of the currents arriving at any instant is equal to the sum of the currents flowing away. The second states that at any given instant the sum of the voltages around any closed path, or loop, in the networ is zero) the terminal voltage can e epressed as: From Ohm s law the current I flowing in the aove circuit is equal to I (8..7.) 4

5 By sustituting I from eq. (8..8.) into eq. (8..7.): If is constant (i.e. it is independent on I), the line equals the internal resistance I. (8..8.) (8..9.) vs. plot yields a straight line. The slope of the multiplied y, and the intercept gives the value of. It should e noted, that the current-voltage characteristics of electrochemical cells are typically nonlinear. However, if the current is low enough, the current vs. potential curve can e well approimated y a linear function. In such cases can e treated as sustantially constant. 3 periments Procedure esults sheet : In each case, lael the diagram appropriately to descrie the cell you have constructed. 3. Constructing a galvanic cell. ach of the students should construct a galvanic cell, using 0. M zinc sulfate solution, 0. M copper sulfate solution, a piece of copper metal (copper rod), a piece of zinc metal (zinc rod) and saturated potassium nitrate solution for the salt ridge. The connector tues must e filled ule free, the polished section of glass joints and stopcocs should e moistened with the electrolyte solution. It is foridden to luricate joints with a laoratory grease. 3.2 Measuring the terminal voltages and the. First, the of the galvanic cell has to e measured with a high-impedance voltmeter. ecord the measured voltage in your la noteoo. Net, a load resistance ( ) has to e connected in series with the Daniell-cell, and the terminal voltage should e measured with a high-impedance voltmeter. Using different load resistances measure and record the voltage for each. Use resistances ranging in value of aout 0 ohms up to aout 0 Mohms. (esistances uilt in the connector o can e used.) The measurement should e carried out oth with the glass stopcoc (valve) in closed (first measurement series) and open position (second measurement series). The load resistances should e used in ascending order, i.e. starting with the highest resistance. Don t change the position of the plug of the stopcoc during a measuring series, ecause the value of depends on the resistance of the electrolyte solution in the glass stopcoc (there is a thin layer of electrolyte solution etween the shell and the plug). 3.3 Determination of y the compensation method 5

6 The potentiometer is formed from a length ( l T ) of uniform resistance wire attached to a DC source ( U CVS ) such as a lead acid accumulator (Fig ). If a standard cell whose is nown (e.g. a Weston standard cell) is used as one of the cells then the potentiometer can e calirated, the standard cell is wired in series with a galvanometer etween B and a moveale proe, the galvanometer will give a zero reading at point N. Then distance BN ( l N ) is measured. The eperiment should e repeated to find point X where a zero current reading ( l X ) is otained for the unnown cell. Fig Then the of the unnown cell can e calculated using l X N (8..6.) ln The switch S should e switched on only for very short time periods, in order to avoid the polarization of the electrodes. The stopcocs of the electrode vessels should e in the open positions. 3.4 Concentration dependence of the Prepare serial dilutions (at least 5 solutions) of the stoc miture (0. mol/dm 3 SO 4-solution) in the range of 0.00 mol/dm 3 to 0. mol/dm 3. Values of the concentrations must e selected at nearly equidistant intervals in the logarithmic (concentration) scale. The stoc solution should e diluted with MgSO 4 solution of 0. mol/dm 3 (instead of water), in order to maintain constant ionic strength. (At constant ionic strength the mean activity coefficients ( ) are approimately constant.) Using the SO 4-solutions construct galvanic cells according to the cell diagram saturated calomel electrode SO 4 (aq) c SO 4 6

7 and measure the of the cell with a high-impedance digital voltmeter. ecord the measured voltage in your la noteoo (at least 5 data pairs in a tale lie the tale elow). c / V -3-3 c 2 / mol dm lg 2 / mol dm 4 valuation of the measured data 4. Measurement of the electromotive force with a voltmeter of high internal resistance Present the eperimental results with uncertainties. 4.2 Determination of y etrapolation Plot the vs. / curves using the two data series measured: with the glass stopcoc in closed (first measurement series) and open position (second measurement series). According to (8..9.) the electromotive force and the internal resistance of the cell can e otained y linear regression of slope of the curve is, and the intercept gives the value of. Perform a statistical analysis of the results. against /. The 4.3 Determination of y the compensation method Calculate the electromotive force with the help of eq.(8..6.): n (8..6.) n 4.4 Concentration dependence of Plot the -3 / V vs. lgc 2 / mol dm data, and fit the data with a straight line. The two parameters of the line, the slope and the intercept, provide the two constants in Nernst s equation. Perform a statistical analysis of the results. 4.5 stimate the Gis energy change of the cell reaction. Use the values from 4., 4.2 and 4.3. Perform a statistical analysis of the results. GGL_204 7