Experiment
32
Galvanic Cells, the
Nernst Equation
-.
Copper metal spontaneously oxidizes to copper(lll ion in a solution
containing silver ion. Silver metal crystals form on the surface of the
copper metal.
-5
=< -----
• To measure the relative reduction potentials for a number of redox couples
• To develop an understanding of the movement of electrons, anions, and cations in a
galvanic cell
• To study factors affecting cell potentials
• To estimate the concentration of ions in solution using the Nernst equation
OBJ E c TI v Es
The following techniques are used in the Experimental Procedure:
TE c HNI Q u Es
Electrochemical cells are of two types, galvanic and electrolytic, both employing the
principle of oxidation-reduction (redox) reactions. In galvanic (or voltaic) cells (this
experiment), redox reactions occur spontaneously as is common with all portable batteries of which we are very familiar. Electric cars, flashlights, watches, and power
tools operate because of a specific spontaneous redox reaction. Electrolytic cells
(Experiment 33) are driven by nonspontaneous redox reactions, reactions that require
energy to occur. The recharging of batteries, electroplating and refining of metals, and
generation of various gases all require the use of energy to cause the redox reaction
to proceed.
Experimentally, when copper wire is placed into a silver ion solution (see opening
photo), copper atoms spontaneously donate electrons (copper atoms are oxidized) to
the silver ions (which are reduced). Silver ions migrate to the copper atoms to pick up
electrons and form silver atoms at the copper metal-solution interface; the copper ions
that form then move into the solution away from the interface. The overall reaction that
occurs at the interface is:
INTRODUCTION
Cu(s)
+ 2 Ag+(aq)---> 2 Ag(s) + Cu 2+(aq)
(32.1)
This redox reaction can be divided into an oxidation and a reduction half-reaction.
Each half-reaction, called a redox couple, consists of the reduced state and the oxidized state of the substance:
+ 2 e-
oxidation half-reaction (redox couple)
(32.2)
2 Ag+(aq) + 2 e- ---> 2 Ag(s)
reduction half-reaction (redox couple)
(32.3)
Cu(s)---> Cu 2+(aq)
Interface: the boundary between two
phases; in this case, the boundary
that separates the solid metal from the
aqueous solution
Redox couple: an oxidized and
reduced form of an ion/substance
appearing in a reduction or oxidation
half-reaction, generally associated
with galvanic cells
Experiment 32
357
Potentiometer
Cu
Cu half-cell
Cu(s)- Cu 2 •(aq) + 2 e-
Ag
Ag half-cell
Ag•(aq) + e- -Ag(s)
Figure 32, 1 Schematic diagram of a galvanic cell
Half-cell: a part of the galvanic cell
that hosts a redox couple
External circuit: the movement of
charge as electrons through a wire
connecting the two half-cells, forming
one-half of the electrical circuit in a
galvanic cell
Salt bridge: paper moistened with a
salt solution, or an inverted tube
containing a salt solution, that
bridges two half-cells to complete the
solution part of an electrical circuit
Internal circuit: the movement of
charge as ions through solution from
one half.cell to the other, forming onehalf of the electrical circuit in a
galvanic cell
Cell Potentials
358
A galvanic cell is designed to take advantage of this spontaneous transfer of electrons.
Instead of electrons being transferred at the interface of the copper metal and the silver ions
in solution, a galvanic cell separates the copper metal from the silver ions to force the electrons to pass externally through a wire, an external circuit, for the reduction of the silver ions.
Figure 32.1 is a schematic diagram of a galvanic cell setup for these two redox couples.
The two redox couples are placed in separate compartments called half-cells.
Each half-cell consists of an electrode, usually the metal (reduced state) of the redox
couple, and a solution containing the corresponding cation (oxidized state) of the
redox couple. The electrodes of the half-cells are connected by a wire through which
the electrons flow, providing current for the external circuit.
A salt bridge that connects the two half-cells completes the construction of the
galvanic cell (and the circuit). The salt bridge permits limited movement of ions from
one half-cell to the other, the internal circuit, so that when the cell operates, electrical
neutrality is maintained in each half-cell. For example, when copper metal is oxidized
to copper(II) ions in the Cu 2+1cu half-cell, either No3- anions must enter or copper(II)
ions must leave the half-cell to maintain neutrality. Similarly, when silver ions are
reduced to form silver metal in its half-cell, either NO 3- anions must leave or cations
must enter its half-cell to maintain neutrality.
The silver electrode at which reduction occurs is called the cathode; the copper electrode
at which oxidation occurs is called the anode. Because an oxidation process donates electrons
to the copper electrode to provide a current in the external circuit, the anode is designated the
negative electrode in a galvanic cell. A reduction process accepts electrons from the circuit
and supplies them to the silver ions in solution; the silver cathode is the positive electrode.
This sign designation allows us to distinguish the anode from the cathode in a galvanic cell.
Different metals, such as copper and silver, have different tendencies to oxidize; similarly, their ions have different tendencies to undergo reduction. The cell potential of a
galvanic cell is due to the difference in tendencies of the two metals to oxidize (donate
electrons) or of their ions to reduce (accept electrons). Commonly, a measured reduction potential, the tendency for an ion (or molecule) to accept electrons, is the value
used to identify the relative ease of reduction for a half-reaction.
A potentiometer or multimeter, placed in the external circuit between the two
electrodes, measures the cell potential, Ece11, a value that represents the difference
between the tendencies of the metal ions in their respective half-cells to undergo reduction (i.e., the difference between the reduction potentials of the two redox couples).
Galvanic Cells, the Nernst Equation
For the copper and silver redox couples, we can represent their reduction potentials as Ecu" ,cu and EAg\ Ag• respectively. The cell potential being the difference of the
two reduction potentials is therefore
(32.4)
Experimentally, silver ion has a greater tendency than copper ion does to be in the
reduced (metallic) state; therefore, Ag+ has a greater (more positive) reduction potential. Since the cell potential, E,elh is measured as a positive value, EAg\Ag is placed
before Ecu" ,cu in equation 32.4.
The measured cell potential corresponds to the standard cell potential when the
concentrations of all ions are I mol/L and the temperature of the solutions is 25°C.
The standard reduction potential for the Ag+(! M)/Ag redox couple, E° Ag•,Ag• is
+0.80 V, and the standard reduction potential for the Cu2+(1 M)/Cu redox couple,
E°cu" ,Cu• is +0.34 V. Theoretically, a potentiometer (or multimeter) would show the
difference between these two potentials, or, at standard conditions,
E°cen =
E° Ag',Ag- E°cu" .Cu = +0.80 V - (+0.34 V) = +0.46V
Silver ;ewelry is longer lasting than
copper ;ewelry; therefore silver has a
higher tendency to be in the reduced
state, a higher reduction potential
(32.5)
Deviation from the theoretical value may be the result of surface activity at the
electrodes or activity of the ions in solution.
In Part A of this experiment, several cells are "built" from a selection of redox couples and
data are collected. From an analysis of the data, the relative reduction potentials for the
redox couples are determined and placed in an order of decreasing reduction potentials.
In Part B, the formations of the complex [Cu(NH 3) 4]2+ and the precipitate CuS are
used to change the concentration of Cu 2+(aq) in the Cu 2+1cu redox couple. The
observed changes in the cell potentials are interpreted.
Measure Cell Potentials
The Nemst equation is applicable to redox systems that are not at standard conditions,
most often when the concentrations of the ions in solution are not I mol/L. At 25°C,
the measured cell potential, £,en, is related to E°cen and ionic concentrations by
Measure Nonstandard
Cell Potentials
.
E cell
Nernst equat10n:
= c,=cell -
~~nl og Q
--n-
(32.6)
where n represents the moles of electrons exchanged according to the cell reaction. For
the copper-silver cell, n = 2; two electrons are lost per copper atom and two electrons
are gained per two silver ions (see equations 32. 1-32.3). For dilute ionic concentrations, the reaction quotient, Q, equals the mass action expression for the cell reaction.
For the copper-silver cell (see equation 32.1 ):
[Cu 2+]
Q= [Ag+]2
In Part C of this experiment, we study in depth the effect that changes in concentration of an ion have on the potential of the cell. The cell potentials for a number of
zinc---{:opper redox couples are measured in which the copper ion concentrations are
varied but the zinc ion concentration is maintained constant.
Zn(s) + Cu 2+(aq)-----, Cu(s) + Zn 2+(aq)
Mass action expression: the product
of the molar concentrations of the
products divided by the product of
the molar concentrations of the
reactants, each concentration raised
to the power of its coefficient in the
balanced cell equation
The concentrations (i.e., density) of
solids are constant and therefore do
not appear in mass action
expressions.
The Nemst equation for this reaction is
E
_ E°
cell -
cell -
2
0.0592 lo [Zn +]
2
g [Cu 2+]
(32.7)
Rearrangement of this equation (where E°cen and [Zn 2+] are constants in the experiment) yields an equation for a straight line:
E cell -_ £ 0cell
y=
-
0.0592
- Iog [Z n2+ ] +
--
2
b
+
0.0592
2 log [Cu2+]
m
(32.8)
x
Experiment 32
359
To simplify,
pCu = -log {Ctl•j
Ece 11
= constant -
0.0592
- -- pCu
2
(32.9)
A plot of Ece 11 versus pCu for solutions of known copper ion concentrations has a negative slope of 0.0592/2 and an intercept b that includes not only the constants in equation
32.8 but also the inherent characteristics of the cell and potentiometer (Figure 32.2).
The E,. 11 of a solution with an unknown copper ion concentration is then measured;
from the linear plot, its concentration is determined.
Procedure Overview: The cell potentials for a number of galvanic cells are measured and the redox couples are placed in order of decreasing reduction potentials. The
effects of changes in ion concentrations on cell potentials are observed and analyzed.
Perform the experiment with a partner. At each circled superscript@ in the procedure, stop and record your observation on the Report Sheet. Discuss your observations with your lab partner and your instructor.
EXPERIMENTAL
PROCEDURE
A. Reduction Potentials of
Several Redox Couples
The apparatus for the voltaic cell described in the Experimental Procedure may be different in your laboratory. Consult with your instructor.
1. Collect the electrodes, solutions, and equipment. Obtain four small (-50 mL)
beakers and fill them three-fourths full of the 0.1 M solutions as shown in Figure
32.3. Share these solutions with other chemists/groups of chemists in the laboratory.
Polish strips of copper, zinc, magnesium, and iron metal with steel wool or sandpaper, rinse briefly with dilute (--0.1 M) HNO 3 (Caution!), and rinse with deionized
water. These polished metals, used as electrodes, should be bent to extend over the lip
of their respective beakers. Check out a multimeter (Figure 32.4) (or a voltmeter) with
two electrical wires (preferably a red and black wire) attached to alligator clips.
2. Set up the copper-zinc cell. Place a Cu strip (electrode) in the CuSO4 solution
and a Zn strip (electrode) in the Zn(NO 3) 2 solution. Roll and flatten a piece of filter paper; wet the filter paper with a 0.1 M KNO 3 solution. Fold and insert the ends
of the filter paper into the solutions in the two beakers; this is the salt bridge
shown in Figures 32.1 and 32.3. Set the multimeter to the 2000-mV range or as
appropriate. Connect one electrode to the negative terminal of the multimeter and
the other to the positive terminal.'
Chemists often use the "red, right,
plus" rule in connecting the red wire
of the multimeter to the right-side
positive electrode (cathode) of the
galvanic cell
3. Determine the copper-zinc cell potential. If the multimeter reads a negative
potential , reverse the connections to the electrodes. Read and record the (positive)
cell potential. Identify the metal strips that serve as the cathode (positive terminal)
Multimeter
Cell Potential vs. pCu
1.150
1.100
1.050
1l 1.000
LU 0.950
0.900
0.850
0.800
0
2
8
6
4
1(
pCu
Figure 32,2 The variation of E,. 11 versus the pCu
Figure 32,3 Setup for measuring the cell potentials of six
galvanic cells
1
You have now combined two half-cells to form a galvanic cell.
360
Galvanic Cells, the Nernst Equation
and the anode. Write an equation for the half-reaction occurring at each electrode.
Combine the two half-reactions to write the equation for the cell reaction.<D
4. Repeat for the remaining cells. Determine the cell potentials for all possible galvanic cells that can be constructed from the four redox couples. Refer to the Report
Sheet for the various galvanic cells. Prepare a new salt bridge for each galvanic cell.<%>
5. Determine the relative reduction potentials. Assuming the reduction potential
of the Zn 2•(0. l M)/Zn redox couple is -0.79 V, calculate the reduction potentials
of all other redox couples.2®
[I]
6. Determine the reduction potential of the unknown redox couple. Place a
0.1 M solution and electrode obtained from your instructor in a small beaker.
Determine the reduction potential, relative to the Zn2+(0. I M)/Zn redox couple, for
your unknown redox couple.©
1. Effect of different molar concentrations. Set up the galvanic cell shown in
Figure 32.5, using IM CuSO 4 and 0.001 M CuSO4 solutions. Immerse a polished
copper electrode in each solution. Prepare a salt bridge (Part A.2) to connect the
two half-cells. Measure the cell potential . Determine the anode and the cathode.
Write an equation for the reaction occurring at each electrode.'2>
B. Effect of Concentration
Changes on Cell Potential
2. Effect of complex formation. Add 2-5 mL of 6 M NH 3 to the 0.001 M CuSO4
solution until any precipitate redissolves. 3 (Caution: Do not inhale NH 3.) Observe
and record any changes in the half-cell and the cell potential.®
3. Effect of precipitate formation. Add 2-5 mL of 0.2 M Na 2S to the 0.001 M
CuSO4 solution now containing the added NH 3• What is observed in the half-cell
and what happens to the cell potential? Record your observations.CD
1. Prepare the diluted solutions. Prepare solutions I through 4 as shown in
Figure 32.6 using a 1-mL pipet and 100-mL volumetric flasks.4 See Prelaboratory
Assignment, question 3. Be sure to rinse the pipet with the more concentrated solution before making the transfer. Use deionized water for dilution to the mark in the
volumetric flasks. Calculate the molar concentration of the Cu 2+ ion for each solution and record.®
C. The Nernst Equation
and an Unknown
Concentration
2. Measure and calculate the cell potential for solution 4. Set up the experiment as
shown in Figure 32.7, page 362, using small (-50 mL) beakers.
Multimeter
1 M CuS04
0.001 M CuS0 4
Figure 32.5 Setup for measuring the cell
Figure 32.4 A modern
potential of a Cu 2• concentration cell
multimeter
Data Analysis, A
l"".
1 ml
1 ml
1 ml
i
"'----0.1 M CuS04
Figure 32.6 Successive
quantitative dilution, starting with
0.1 MCuSO 4
'Note: These are not standard reduction potentials because l M concentrations of cations at 25°C
ore not used.
3
Copper ion forms a complex with ammonia: Cu 2•(aq) + 4 NH 3 (aq) -> [Cu(NH 3) 4] 2•(aq)
4
Share these prepared solutions with other chemists/groups of chemists in the laboratory.
Experiment 32 361
Multimeter
Cu
Cu 2+
(4)
so/Figure 32.7 Setup to measure the effect that
Cu
Cu
(3)
diluted solutions have on cell potentials
[I]
The Zn 2•rzn redox couple is the reference half-cell for this part of the experiment. Connect the two half-cells with a new salt bridge. Reset the multimeter to the
lowest range (~200 mV). Connect the electrodes to the multimeter and record the
potential difference, Ec,u. expt~ Calculate the theoretical cell potential Ec,u. calc· (Use a
table of standard reduction potentials and the Nemst equation.)®
3. Measure and calculate the cell potentials for solutions 3 and 2. Repeat Part C.2
with solutions 3 and 2, respectively. A freshly prepared salt bridge is required for
each cell. See data from Part A.3 for the potential of Solution 1.
Data Analysis, F, G
4. Plot the data. Plot Ec,u. expt and Ec,u. calc (ordinate) versus pCu (abscissa) on the
same piece of linear graph paper (page 368) or by using appropriate software for
the four concentrations of CuS04 . Have your instructor approve your graph~
5. Determine the concentration of the unknown. Obtain a CuS04 solution with an
unknown copper ion concentration from your instructor and set up a like galvanic
cell. Determine Ec,u as in Part C.2. Usii the graph, determine the unknown copper(II) ion concentration in the solution.
[I]
Disposal: Dispose of the waste zinc, copper, magnesium, and iron solutions
in the Waste Metal Solutions container. Return the metals to appropriately
marked containers.
CLEANUP: Rinse the beakers twice with tap water and twice with deionized water.
Discard the rinses in the Waste Metal Solutions container.
The Next Step
362
Galvanic cells are the basis for the design of specific ion electrodes, electrodes that sense
the relative concentration of a specific ion (e.g., hydrogen ion) relative to the electrode
that has a fixed concentration. Part C of this experiment could be the apparatus for measuring concentrations of Cu2+ in other samples. According to equation 32.8, the pCu
(negative log of [Cu 2+]) is proportional to the Ec,u! Research specific ion electrodes, their
design, and their application. Design an experiment in which a specific ion electrode,
other than the pH electrode, can be used to systematically study an ion of interest.
Galvanic Cells, the Nernst Equation