8.1. Measurement of the electromotive force of an electrochemical cell
1 Objectives:
Measurement of electromotive forces ( EMF ) and terminal voltages of galvanic cells, determination of
the internal resistances, investigation of the dependence of EMF on the electrolyte concentration.
2 Theoretical background:
The cell diagram of the Daniell cell:
salt bridge
Cu s 
Zns 
ZnSO4 aq.
saturated
cZnSO4
KNO3-solution
CuSO 4 aq.
cCuSO4
Cu s 
2.1 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 be represented by a simple electric circuit (Fig. 8.1.1.). According to Ohm’s
law the current flowing through the resistances Rb (internal resistance) and Rk (load resistance) can be
given as:
I
EMF
Rb  Rk
(8.1.1.)
The voltage between the terminals of the cell  i.e. the potential drop E k across the load resistance Rk  can
be also easily calculated using Ohm’s law:
Ek  I  Rk 
EMF
 Rk
Rb  Rk
Fig. 8.1.1.
Measurement of the potential difference of the electrochemical cell (terminal voltage)
1
(8.1.2.)
After rearranging eq. (8.1.2.) we have:
EMF Rb  Rk

Ek
Rk
(8.1.3.)
It can be seen from the above equation, that for a galvanic cell the terminal voltage is always smaller than
the electromotive force, however, the smaller Rb and the greater Rk is, the smaller the difference between
E MF and E k is. In the limiting case Rk   , Ek  EMF . It also means, that the limiting value of the
current flowing through the cell is zero.
(In other words: In case of discharging of an electrochemical cell, the terminal potential difference E k
cannot be greater than the E MF of a cell but in the absence of the internal resistance, the terminal potential
difference becomes equal to the E MF of a cell. In case of charging of an electrochemical cell having internal
resistance Rb , the terminal potential difference E k of the cell is greater than its E MF . Here, the terminal
voltage exceeds the E MF of a cell by the term I  Rb . If there is no internal resistance then Rb = 0, then
EMF  Ek .)
2.2 Measurement of the electromotive force with a voltmeter of high internal resistance
According to the above considerations, the E MF of a cell can be measured with a voltmeter, provided that
the internal resistance of the voltmeter is “high enough”. But what is high enough? Obviously, the current
passing the cell must be low enough to ensure the electrochemical equilibrium at both electrodes, i.e. it
should be much smaller than the exchange current of either electrode. Of course, in dubious cases this should
be checked with adequate experiments.
2.3 Determination of electromotive force by compensation technique
The determination of the E MF of a cell using a potentiometer is a classic experiment. This experiment has the
advantage that the E MF of a cell can be measured without drawing any current from the cell, in short the
measurement can be done as if it was done with a voltmeter of infinite resistance.
Figure 8.1.2. presents a compensation coupling with which the electromotive force of a voltage source
(galvanic e.g. cell) can be measured. RT (= R1 + R2 ) is the total resistance of the potentiometer in the circuit.
E x is the cell under test and E N is a standard cell. A standard cell is a galvanic cell whose voltage is
accurately known and remains sufficiently constant for instrument calibration purposes (e.g. the Weston
standard cell has a voltage of 1.018636 volts at 20°C).
2
Fig. 8.1.2.
Principle of the compensation method
If the S switch is open, the current in the circuit containing the voltage source (the voltage is U cvs ) equals
I  Ecvs / R1  R2  . If U cvs is constant and R1  R2 is also constant, then I remains constant during the
measurement. The cell under test is connected parallel to the resistor R1 in series with the switch S and a
galvanometer G. (A galvanometer is a very sensitive ammeter.)
The value of the resistor R1 (the resistance) should be set so that the current passing the galvanometer is
zero ( I G  0 ), even if the switch is closed. (If the value of R1 is decreased, the value of R2 should be
increased in order to have a constant R1  R2 .) The value of R1 corresponding to this situation is Rx .
In this case the voltage drop across Rx is given as:
Ex  I k  Rx .
(8.1.4.)
where Ex equals to the electromotive force of the cell under test.
Correspondingly, after replacing the cell under test with a standard cell, in case of I G  0 the
electromotive force of the standard cell ( E N ) can be expressed as
En  I k  Rn .
(8.1.5.)
In eq. (8.1.5.) R N is the value of R1 if the current passing the galvanometer is zero ( I G  0 ), even if the
switch is closed.
From eqs. (8.1.4.) and (8.1.5.) we get:
E x  En 
Rx
Rn
3
(8.1.6.)
(The switch S should be 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 impossible 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 10–6 A).
2.4 Determination of E MF by extrapolation
There is another possibility for the determination of the electromotive force if we follow the measuring
instruction given in the definition of E MF . 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. 8.1.3.).
Fig. 8.1.3.
Circuit for the extrapolation method
(Rk: load resistance; RB: input resistance of the voltmeter; Rb: internal resistance of the galvanic
cell; EMF: 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 network 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 network is zero) the terminal voltage can be expressed as:
Ek  EMF  Rb  I
From Ohm’s law the current I flowing in the above circuit is equal to
4
(8.1.7.)
I
Ek
.
Rk
(8.1.8.)
By substituting I from eq. (8.1.8.) into eq. (8.1.7.):
Ek  EMF  Rb 
Ek
Rk
(8.1.9.)
If Rb is constant (i.e. it is independent on I), the Ek vs. Ek Rk plot yields a straight line. The slope of the
line equals the internal resistance Rb multiplied by –1, and the intercept gives the value of EMF .
It should be 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 be well approximated by a
linear function. In such cases Rb can be treated as substantially constant.
3 Experiments
Procedure
Results sheet : In each case, label the diagram appropriately to describe the cell you have constructed.
3.1 Constructing a galvanic cell.
Each of the students should construct a galvanic cell, using 0.1 M zinc sulfate solution, 0.1 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 bridge. The connector tubes must be filled bubble free, the polished
section of glass joints and stopcocks should be moistened with the electrolyte solution.
It is forbidden to lubricate joints with a laboratory grease.
3.2 Measuring the terminal voltages and the EMF.
First, the E MF of the galvanic cell has to be measured with a high-impedance voltmeter. Record the
measured voltage in your lab notebook.
Next, a load resistance ( Rk ) has to be connected in series with the Daniell-cell, and the terminal voltage
should be measured with a high-impedance voltmeter. Using different load resistances measure and record
the voltage for each. Use resistances ranging in value of about 10 kohms up to about 10 Mohms.
(Resistances built in the connector box can be used.) The measurement should be carried out both with the
glass stopcock (valve) in closed (first measurement series) and open position (second measurement series).
The load resistances should be used in ascending order, i.e. starting with the highest resistance. Don’t change
the position of the plug of the stopcock during a measuring series, because the value of Rb depends on the
resistance of the electrolyte solution in the glass stopcock (there is a thin layer of electrolyte solution
between the shell and the plug).
3.3 Determination of EMF by the compensation method
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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. 8.1.4.). If a standard cell whose EMF is known (e.g. a Weston standard
cell) is used as one of the cells then the potentiometer can be calibrated, the standard cell is wired in series
with a galvanometer between B and a moveable probe, the galvanometer will give a zero reading at point N.
Then distance BN ( l N ) is measured. The experiment should be repeated to find point X where a zero current
reading ( l X ) is obtained for the unknown cell.
Fig. 8.1.4.
Then the EMF of the unknown cell can be calculated using
E x  EN 
lX
lN
(8.1.6.)
The switch S should be switched on only for very short time periods, in order to avoid the polarization of the
electrodes. The stopcocks of the electrode vessels should be in the open positions.
3.4 Concentration dependence of the EMF
Prepare serial dilutions (at least 5 solutions) of the stock mixture (0.1 mol/dm3 CuSO4-solution) in the
range of 0.001 mol/dm3 to 0.1 mol/dm3. Values of the concentrations must be selected at nearly equidistant
intervals in the logarithmic (concentration) scale.
The stock solution should be diluted with MgSO4 solution of 0.1 mol/dm3 (instead of water), in order to
maintain constant ionic strength. (At constant ionic strength the mean activity coefficients (   ) are
approximately constant.)
Using the CuSO4-solutions construct galvanic cells according to the cell diagram
CuSO 4 (aq)
cCuSO4
saturated calomel
electrode
6
Cu
and measure the E MF of the cell with a high-impedance digital voltmeter. Record the measured voltage in
your lab notebook (at least 5 data pairs in a table like the table below).
lg  cCu2 / mol dm -3 
cCu2 / mol dm-3
EMF / V
4 Evaluation of the measured data
4.1 Measurement of the electromotive force with a voltmeter of high internal resistance
Present the experimental results with uncertainties.
4.2 Determination of E MF by extrapolation
Plot the Ek vs. Ek / Rk curves using the two data series measured: with the glass stopcock in closed (first
measurement series) and open position (second measurement series). According to (8.1.9.) the electromotive
force and the internal resistance of the cell can be obtained by linear regression of Ek against Ek / Rk . The
slope of the curve is  Rb , and the intercept gives the value of EMF .
Perform a statistical analysis of the results.
4.3 Determination of E MF by the compensation method
Calculate the electromotive force with the help of eq.(8.1.6.):
E x  En 
Rx
Rn
(8.1.6.)
4.4 Concentration dependence of E MF


Plot the EMF / V vs. lg cCu2 / mol dm -3 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 Estimate the Gibbs energy change of the cell reaction.
Use the EMF values from 4.1, 4.2 and 4.3.
Perform a statistical analysis of the results.
GGL_2014
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