Bài giảng hoá phân tích galvanic cells

Experiment 32Galvanic Cells, the Nernst Equation • To measure the relative reduction potentials for a number of redox couples • To develop an understanding of the movement of electrons,

Experiment 32

Galvanic Cells, the

Nernst Equation

• 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

The following techniques are used in the Experimental Procedure:

Copper metal spontaneously oxidizes to copper(II) ion in a solution containing silver ion Silver metal crystals form on the surface of the copper metal.

Objectives

Techniques

Introduction Electrolyic cells are of two types, galvanic and electrolysis, both employing the

prin-ciple of oxidation–reduction (redox) reactions In galvanic (or voltaic) cells (this

experiment), redox reactions occur spontaneously as is common with all portable

bat-teries of which we are very familiar Electric cars, ashlights, watches, and power

tools operate because of a speci c spontaneous redox reaction Electrolysis cells

(Experiment 33) are driven by nonspontaneous redox reactions, reactions that require

energy to occur The recharging of batteries, electroplating and re ning 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 lose 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:

(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

oxi-dized state of the substance:

(32.2) (32.3)

2 Ag⫹(aq) ⫹ 2 e⫺l 2 Ag(s) reduction half-reaction (redox couple)

Cu(s) l Cu2⫹(aq) ⫹ 2 e⫺ oxidation half-reaction (redox couple)

Cu(s) ⫹ 2 Ag⫹(aq) l 2 Ag(s) ⫹ Cu2⫹(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

A galvanic cell is designed to take advantage of this spontaneous transfer of

elec-trons 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 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 ow, 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 Cu2⫹/Cu 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 NO3⫺anions must leave or cations must enter its half-cell to maintain neutrality

The electrode at which reduction occurs is called the cathode; the electrode at which oxidation occurs is called the anode Because oxidation releases electrons to the

electrode to provide a current in the external circuit, the anode is designated the nega-tive electrode in a galvanic cell The reduction process draws electrons from the circuit and supplies them to the ions in solution; the 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;

simi-larly, 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 (lose

electrons) or of their ions to reduce (gain electrons) Commonly, a measured reduction potential, the tendency for an ion (or molecule) to gain 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, Ecell, a value that represents the difference

between the tendencies of the metal ions in their respective half-cells to undergo reduc-tion (i.e., the difference between the reducreduc-tion potentials of the two redox couples)

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

one-half of the electrical circuit in a

galvanic cell

Cell Potentials

For the copper and silver redox couples, we can represent their reduction

poten-tials as and 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

poten-tial Since the cell potential, Ecell, is measured as a positive value, is placed

before in equation 32.4

The measured cell potential corresponds to the standard cell potential when the

concentrations of all ions are 1 mol/L and the temperature of the solutions is 25⬚C

The standard reduction potential for the Ag⫹(1 M)/Ag redox couple, E⬚Ag⫹,Ag, is

⫹0.80 V, and the standard reduction potential for the Cu2⫹(1 M)/Cu redox couple,

is ⫹0.34 V Theoretically, a potentiometer (or multimeter) would show the

difference between these two potentials, or, at standard conditions,

(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(NH3)4]2⫹and the precipitate CuS are

used to change the concentration of Cu2⫹(aq) in the Cu2⫹/Cu redox couple The

observed changes in the cell potentials are interpreted

The Nernst equation is applicable to redox systems that are not at standard conditions,

most often when the concentrations of the ions in solution are not 1 mol/L At 25⬚C,

the measured cell potential, Ecell, is related to E⬚celland ionic concentrations by

(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

concentra-tions, the reaction quotient, Q, equals the mass action expression for the cell reaction.

For the copper–silver cell (see equation 32.1):

In Part C of this experiment, we study in depth the effect that changes in

concen-tration of an ion have on the potential of the cell The cell potentials for a number of

zinc–copper redox couples are measured in which the copper ion concentrations are

varied but the zinc ion concentration is maintained constant

The Nernst equation for this reaction is

(32.7)

Rearrangement of this equation (where E⬚celland [Zn2⫹] are constants in the

exper-iment) yields an equation for a straight line:

Ecell⫽ E⬚cell⫺ 0.05922 log [Zn

2⫹] [Cu2⫹]

Zn(s) ⫹ Cu2⫹(aq) l Cu(s) ⫹ Zn2⫹(aq)

Q ⫽ [Cu2⫹] [Ag⫹]2

Nernst equation: Ecell⫽ E⬚cell⫺ 0.0592n log Q

E⬚cell⫽ E⬚Ag⫹,Ag⫺ E⬚Cu2⫹,Cu⫽ ⫹0.80 V ⫺ (⫹0.34 V) ⫽ ⫹0.46V

E⬚Cu2⫹,Cu,

ECu2⫹ ,Cu

EAg⫹ ,Ag

Ecell⫽ EAg ⫹ ,Ag⫺ ECu 2⫹ ,Cu

EAg⫹ ,Ag,

ECu2⫹ ,Cu

Silver jewelry is longer lasting than copper jewelry; therefore silver has a higher tendency to be in the reduced state, a higher reduction potential

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

Measure Cell Potentials

Measure Nonstandard Cell Potentials

To simplify,

(32.9)

A plot of Ecellversus pCu for solutions of known copper ion concentrations has a

nega-tive 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 Ecellof 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 mea-sured 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 1–12 in the

pro-cedure, stop and record your observation on the Report Sheet Discuss your

observa-tions with your lab partner and your instructor

The apparatus for the voltaic cell described in the Experimental Procedure may be differ-ent in your laboratory Consult with your instructor

1 Collect the electrodes, solutions, and equipment Obtain four small (⬃50 mL)

beakers and ll 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 sand-paper, rinse brie y with dilute (⬃1 M) HNO3(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 CuSO4solution and a Zn strip (electrode) in the Zn(NO3)2solution Roll and atten a piece of lter

paper; wet the lter paper with a 0.1 M KNO3solution Fold and insert the ends of

the lter 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 appropri-ate Connect one electrode to the negative terminal of the multimeter and the other

to the positive terminal.1

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)

Ecell⫽ constant ⫺ 0.05922 pCu

Experimental

Procedure

A Reduction Potentials of

Several Redox Couples

Chemists often use the “red, right,

plus” rule in connecting the red wire

to the right-side positive electrode

(cathode) of the galvanic cell

Figure 32.2 The variation of E cell 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.

pCu ⫽ ⫺log [Cu2⫹]

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.1

4 Repeat for the remaining cells Determine the cell potentials for all possible

gal-vanic 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.2

5 Determine the relative reduction potentials Assuming the reduction potential

of the Zn2+(0.1 M)/Zn redox couple is ⫺0.79 V, determine the reduction

poten-tials of all other redox couples.2 3

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⫹(0.1 M)/Zn redox couple,

for your unknown redox couple.4

1 Effect of different molar concentrations Set up the galvanic cell shown in

Figure 32.5, using 1 M CuSO4and 0.001 M CuSO4solutions 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.5

2 Effect of complex formation Add 2–5 mL of 6 M NH3to the 0.001 M CuSO4

solution until any precipitate redissolves.3(Caution: Do not inhale NH3.) Observe

and record any changes in the half-cell and the cell potential.6

3 Effect of precipitate formation Add 2–5 mL of 0.2 M Na2S to the 0.001 M

CuSO4solution now containing the added NH3 What is observed in the half-cell

and what happens to the cell potential? Record your observations.7

1 Prepare the diluted solutions Prepare solutions 1 through 4 as shown in

Figure 32.6 using a 1-mL pipet and 100-mL volumetric asks.4Be sure to rinse the

pipet with the more concentrated solution before making the transfer Use

deion-ized water for dilution to the mark in the volumetric asks Calculate the molar

concentration of the Cu2⫹ion for each solution and record.8

2 Measure and calculate the cell potential for solution 4 Set up the experiment as

shown in Figure 32.7, page 356, using small (⬃50 mL) beakers

The Zn2⫹/Zn redox couple is the reference half-cell for this part of the

experi-ment Connect the two half-cells with a new salt bridge Reset the multimeter to the

B Effect of Concentration Changes on Cell Potential

2 Note: These are not standard reduction potentials because 1 M concentrations of cations at 25 ⬚C

are not used.

3 Copper ion forms a complex with ammonia: Cu 2⫹ (aq) ⫹ 4 NH 3 (aq) l [Cu(NH 3 ) 4 ] 2⫹ (aq)

4 Share these prepared solutions with other chemists/groups of chemists in the laboratory.

M M

Figure 32.5 Setup for measuring the cell

potential of a Cu 2⫹ concentration cell

Figure 32.4 A modern

multimeter

C The Nernst Equation and an Unknown Concentration

Figure 32.6 Successive

quantitative dilution, starting with 0.1 M CuSO 4

lowest range (⬃200 mV) Connect the electrodes to the multimeter and record the

potential difference, Ecell, expt.9 Calculate the theoretical cell potential Ecell, calc (Use a table of standard reduction potentials and the Nernst equation.)10

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

4 Plot the data Plot Ecell, expt and Ecell, calc (ordinate) versus pCu (abscissa) on the

same piece of linear graph paper (page 362) or by using appropriate software for the four concentrations of CuSO4 (see data from Part A.3 for the potential of solution 1) Have your instructor approve your graph.11

5 Determine the concentration of the unknown Obtain a CuSO4solution with an unknown copper ion concentration from your instructor and set up a like galvanic

cell Determine Ecellas in Part C.2 Using the graph, determine the unknown cop-per(II) ion concentration in the solution.12

CLEANUP: Rinse the beakers twice with tap water and twice with deionized water Discard the rinses in the Waste Metal Solutions container

Galvanic cells are the basis for the design of speci c ion electrodes, electrodes that sense the relative concentration of a speci c ion (e.g., hydrogen ion) relative to the electrode that has a xed concentration Part C of this experiment could be the apparatus for mea-suring concentrations of Cu2⫹in other samples According to equation 32.8, the pCu (negative log of [Cu2⫹]) is proportional to the Ecell! Research speci c ion electrodes, their design, and their application Design an experiment in which a speci c ion electrode, other than the pH electrode, can be used to systematically study an ion of interest

Disposal: Dispose of the waste zinc, copper, magnesium, and iron solutions

in the Waste Metal Solutions container Return the metals to appropriately marked containers

Figure 32.7 Setup to measure the effect that

diluted solutions have on cell potentials

Appendix C

The Next Step

Experiment 32 Prelaboratory Assignment

Galvanic Cells, the Nernst Equation

Date Lab Sec Name Desk No

1. In a galvanic cell,

a. reduction occurs at the (name of electrode)

c. anions ow in solution toward the (name of electrode)

d. electrons ow from the (name of electrode) to (name of electrode) _ _

2 a. What is the purpose of a salt bridge? Explain

b. How is the salt bridge prepared in this experiment?

3. Experimental Procedure, Part C.1 A 1-mL pipet is used to transfer 1.0 mL of a 0.10 M CusO4solution to a 100-mL volumetric ask The volumetric ask is then lled to the mark with deionized water What is the molar concentration

of the diluted solution? Show calculations expressing the concentration with the correct number of signi cant guers

4. Refer to Figure 32.2 and equations 32.8 and 32.9

a. What is the value of the cell constant?

b. What is the [Cu2⫹] if the measured cell potential is 0.96 V?

c. What should be the cell potential if the [Cu2⫹] is 1.0 ⫻ 10⫺3mol/L?

5. Consider a galvanic cell consisting of the following two redox

couples:

a. Write the equation for the half-reaction occurring at the

cathode

b. Write the equation for the half-reaction occurring at the anode

c. Write the equation for the cell reaction

d. What is the standard cell potential, E⬚cell, for the cell?

e. Realizing the nonstandard concentrations, what is the actual cell potential, Ecell, for the cell? See equation 32.6

Hint: What is the value of n in the Nernst equation?

*6 The extent of corrosion in the steel reinforcing rods (rebar) of concrete is measured by the galvanic cell shown in the

diagram of the instrument The half-cell of the probe is usually a AgCl/Ag redox couple:

AgCl ⫹ e⫺l Ag ⫹ Cl⫺(1.0 M) E⬚ ⫽ ⫹0.23 V

Corrosion is said to be severe if the cell potential is measured

at greater than 0.41 V Under these conditions, what is the

iron(II) concentration on the rebar? See equation 32.6

Fe2⫹⫹ 2 e⫺l Fe E⬚ ⫽ ⫺0.44 V

Cr3⫹(0.010 M) ⫹ 3 e⫺l Cr(s) E⬚ ⫽ ⫺0.74 V

Ag⫹(0.010 M) ⫹ e⫺l Ag(s) E⬚ ⫽ ⫹0.80 V

Rebar Concrete

Cr3+(0.010 M )

Cr

M

Experiment 32 Report Sheet

Galvanic Cells, the Nernst Equation

Date Lab Sec Name Desk No

A Reduction Potentials of Several Redox Couples

Fill in the following table with your observations and interpretations from the galvanic cells

_ _

1Cu–Zn _ _

2Cu–Mg _ _ Cu–Fe _ _

Zn–Mg _ _

Fe–Mg _ _

Zn–Fe _ _

1. Write balanced equations for the six cell reactions.

2. What is the oxidizing agent in the Zn–Mg cell?

3. Compare the sum of the Cu–Zn and Zn–Mg cell potentials with the Cu–Mg cell potential Explain.

4. Compare the sum of the Zn–Fe and Zn–Mg cell potentials with the Fe–Mg cell potential Explain.

5. Complete the table as follows:

• EcellMeasured: Re-enter the values from Part A, Column 2

• Reduction potential (experimental): Enter the reduction potential for each redox couple relative to ⫺0.79V for the

Zn2⫹(0.1 M)/ Zn redox couple Use EM2⫹/M⫽ Ecell, measured⫹ (⫺0.79V), assuming Zn as the anode

• Reduction potential (theoretical) Enter the reduction potential for each redox couple (M2⫹/ M) as calculated from a table of standard reduction potentials and the Nernst equation (equation 32.7) for [M2+] = 0.10 M.

• % Error See Appendix B

_ _ _ _

_ _ _ _

_ _ _ _

_ _ _ _

_ _ _ _

_ _ _ _

6. 4Reduction potential of the unknown redox couple:

B Effect of Concentration Changes on Cell Potential

1. 5Cell potential of concentration cell:

Anode reaction: _

Cathode reaction:

Explain why a potential is recorded.

2. 6Cell potential from complex formation:

Observation of solution in half-cell

Explain why the potential changes as it does with the addition of NH3(aq).

3. 7Cell potential from precipitate formation:

Observation of solution in half-cell

Explain why the potential changes as it does with the addition of Na2S