• Author / Uploaded
• api-3856754

Citation preview

Experiment 8: GALVANIC CELLS Group 1 Lamayan, Ivy B. 2004-20483 Sison, Kevin Anthony S. 2005-73193 Chem. 157.1 DE Mr. Leo Yambot Department of Physical Sciences and Mathematics College of Arts and Sciences University of the Philippines Manila I.

Introduction Oxidation and reduction reactions involve the transfer of electrons. These types

of reactions can be carried in to two ways, one is both the oxidizing specie and reducing specie are put into contact and the other with both species separated into two connected compartments. The latter, involves the use of an electrochemical cell. In this cell, the oxidant and reductant are physically separated but has electrical contact by means of a salt bridge, it also consists

of two conductors called electrodes, and each of them is

immersed in an electrolyte solution. Of the two electrodes, the cathode is the part where reduction occurs, while oxidation occurs at the anode. There are two types of electrochemical cells; they are either galvanic or electrolytic. A galvanic cell converts chemical energy to electrical energy. On the other hand, an electrolytic cell requires an external source of electrical energy to make a nonspontaneous reaction to proceed. In a galvanic cell, at the left hand electrode “active” metals are oxidized to their respective cation and releases at the same time electrons. This electron travels through the conductor then to the right-hand side electrode where it is gained by the cations in the solution, thereby reducing it. The prolonged build-up of the charges due to oxidation and reduction is avoided by the migration of the cations and anions from the salt bridge. As electrons travel, a potential difference is made between the two electrodes and is given by εcell. ε cell is also a measure of the spontaneity of the reaction, as stated by : ∆G = -nFε cell if in the standard state: ∆G° = -nFε° cell = -RT lnKeq

by measuring the electrode potentials, thermodynamic quantities such as the Gibbs free energy can be measured. Equilibrium constants as well as activity coefficient for ions in solutions can be computed from ε cell measurements. II.

Methodology A. Preparation of Cu l Cu2+ Reference Electrode Tightly pack the tip of a 4-5 cm long pipet with cotton. Immerse the tip in a solution of KCL or KNO3 until fully soaked. Fill the pipet with 0.1 M CuSO4 solution.

Coil a copper wire in a metal rod with the diameter smaller than the pipet’s. Leave some wire uncoiled. Insert the coiled wire into the pipet. Fix the position of the wire and seal the pipet using clay. Alternate procedure A: Secure a 4-5 inch long copper wire and dip in a solution of 0.1 M CuSO4 solution Preparation of salt bridge: cut 1 x8 cm of filter paper and dip in a saturated solution of KCL or KNO3. Always prepare a fresh one for every solution. B. Determination of Electrode Potentials Assemble the following test half-cells: 2+

a. Zn l Zn electrode: dip metal zinc (1 x 5 cm) in a 50 ml beaker with 25 ml 0.1 M ZnSO4. b. Pb l Pb2+ electrode: dip Pb wire (10 cm long) in a 50 ml beaker with 0.1 M Pb(NO3)2. c. C l Fe2+, Fe3+ electrode: dip graphite rod in a 50 ml beaker with 12.5 ml 0.2 M Fe(NH4)2(SO4)2 + 12.5 ml 0.2 M FeNH4(SO4)2

d. Pb l PbSO4(s), SO42- electrode dip lead wire coated with PbSO4 in 50 ml beaker with 25 ml 0.1 M K2SO4 (to prepare lead wire coated with PbSO4: dip Pb wire in conc. H2SO4 until coated with white powdery substance ) Each of the prepared test electrode were coupled with the Cu l Cu2+ reference electrode. Having Cu l Cu2+ as the cathode (red terminal) and the test electrode as the anode. Respective voltages of the test electrodes were measured, with the reference electrode having a standard reduction potential of 0.34 V. C. Electromotive Force of Galvanic Cells Two test electrodes were coupled and connected through a salt bridge. Cells A to D were prepared and their respective potential differences measured by means of a voltmeter. Below is the schematic diagram for cells A to B: Cell A: Zn l Zn2+ ll Pb2+ l Pb Cell B: Zn l Zn2+ ll Fe2+ l Fe3+ l C

Cell C: Pb l Pb2+ ll Fe2+ l Fe3+ l C Cell D: Zn l Zn2+ ll PbSO4(s), SO42- l Pb D. Variation of Electrode Potential with Electrolyte Concentration Mixtures of varying concentrations of MnO4- and Mn2+ were prepared according to the following formulations: Mixture

mL of 0.02 M

mL of 0.05 M

mL of 6M H2SO4

1 2 3 4

KMnO4 30 35 20 25

Na2C2O4 5 10 15 20

15 15 15 15

Reduction potentials of each mixture was then measured by pairing it with the Cu l Cu2+ reference electrode as the cathode. E. Determination of Solubility Product Constant A Pb I Pb2+ II PbSO4(s), SO42- I Pb cell was prepared and its voltage was measured using a voltmeter.

F. Determination of Activity Coefficient Solutions of 0.100 M, 0.080 M, 0.060 M, 0.040 M and 0.020 M FeSO4 were prepared. After which each solution was paired with a Pb l PbSO4(s) as a cathode forming the cell: Fe l FeSO4 (aq) (a), PbSO4(s) l Pb III.

Results A. Determination of Electrode Potentials Cathode: Cu2+ + 2e-  Cu (s)

ε°cell=0.34 V

Test

Reduction Half Reaction

εcell

εanode

Theoretical

electrode Zn l Zn2+ Pb l Pb2+

Zn2+ + 2e-  Zn (s) Pb2+ + 2e-  Pb (s)

0.468 V 0.3888

-0.128 V -0.0488

-0.7618 V -0.1265 V

C l Fe2+, Fe3+ Pb l PbSO4(s),

Fe3+ + e-  Fe2+ PbSO4(s) + 2e-  Pb (s) + SO42-

V -0.408 V 0.456 V

V 0.748 V -0.116 V

0.771 V -0.3546 V

SO42Sample computation:

ε°cell = ε°cathode - ε°anode For Zn l Zn2+ ll Cu2+ l Cu 0.468V =0.34 V - ε°anode

ε°anode = -0.128 V % error =l{[-0.128 – (-0.7618)]/-0.7618}l *100 = 83.20 % B. Electromotive Force of Galvanic Cells Cell A: Zn l Zn2+ ll Pb2+ l Pb Anode: Zn (s)  Zn2+ + 2e-

ε°= -0.7618 V

Cathode: Pb2+ + 2e-  Pb (s)

ε°= -0.1265 V

Cell: Zn (s) + Pb2+ Pb (s) + Zn2+

ε°theo

= -0.1265 V – (-0.7618 V) =

ε°theo = 0.6353 V ε°obs= 0.1092 V

Cell B: Zn l Zn2+ ll Fe2+ l Fe3+ l C Anode: Zn (s)  Zn2+ + 2e-

ε°= -0.7618 V

Cathode: 2(Fe3+ + e-  Fe2+)

ε°= 0.771 V ε°theo = 0.771 V –(-0.7618 V)

Cell: Zn (s) + 2 Fe3+ 2Fe2+ + Zn2+

ε°theo = 1.5328 V ε°obs= 9.33 x 10-4 V Cell C: Pb l Pb2+ ll Fe2+ l Fe3+ l C Anode: Pb (s)  Pb2+ + 2e-

ε°= -0.1265 V

Cathode: 2(Fe3+ + e-  Fe2+)

ε°= 0.771 V ε°theo = 0.771 V – (-0.1265 V)

Cell: Pb (s) + 2Fe3+  Pb2+ + 2 Fe2+

ε°theo = 0.8975V ε°obs= 8.02 x 10-4 V Cell D: Zn l Zn2+ ll PbSO4(s), SO42- l Pb

ε°= -0.7618 V

Anode: Zn (s)  Zn2+ + 2e-

Cathode: PbSO4(s) + 2e-  Pb (s) + SO42- ε°=-0.3546 V Cell:PbSO4(s) +Zn(s) Pb (s) + SO42- + Zn2+ ε°theo = -0.3546 V–(-0.7618V)

ε°theo = 0.4072V ε°obs= 0.385 V C. Variation of Electrode Potential with Concentration mixture

[MnO4-]

[Mn2+]

Log([MnO4-]/[Mn2+])

1 2 3 4

5.0 x 10-4 5.0 x 10-4 1.0 x 10-4 1.0 x 10-4

1.0 x 10-4 2.0 x 10-4 3.0 x 10-4 4.0 x 10-4

0.69897 0.39794 -0.477121 -0.6020599913

εcell -1.153 V 0.438 V 0.433 V -0.402 V

Variation of Electrode Potential with Electrolyte Concentration 1 y = 0.2248x - 0.733

0.5 εcell

Electrode Potential of [MnO4-] and [Mn2+] mixtures

0 -0.5

0

2

4

6

-1 -1.5 log([MnO4-] /[Mn2+]

Linear (Electrode Potential of [MnO4-] and [Mn2+] mixtures)

Sample computation: 5(C2O42-  2CO2 + 2e-) 2(MnO4- + 8H+ + 5e-  Mn2+ + 4H2O) 5C2O42- + 2MnO4- + 16H+ + 10e-  10CO2+ 2Mn2+ + 8H2O + 10e5 NaC2O4 + 2KMnO4 + 8H2SO4  12MnSO4 + K2SO4 + 5NaSO4 + 8 H2O +10CO2 For mixture 1: Determining the limiting reactant: Considering KMnO4 0.030 L (0.02 mol KMnO4/ 1L) x (2mol MnSO4/2 mol KMnO4) = 6.0 x 10-4 mol MnSO4 Considering H2SO4 0.015 L(6mol H2SO4/1L) x (2mol MnSO4/8 mol H2SO4) = 0.0225 mol MnSO4 Considering NaC2O4 0.005L(0.05 molNaC2O4/1L) x (2mol MnSO4/5 mol NaC2O4)= 1.0 x 10-4 NaC2O4 Therefore NaC2O4 is the limiting reactant. Final concentrations: [MnO4-] = 6.0 x 10-4 - 1.0 x 10-4 = 5.0 x 10-4 / Vsoln [Mn2+] = 1.0 x 10-4/ Vsoln log([MnO4-]/[Mn2+]) = log (5.0 x 10-4/1.0 x 10-4) = 0.6989700042 MnO4- + 8H+ + 5e-  Mn2+ + 4H2O Writing the Nerns’t Equation,

εcell = ε° - (0.05916/n) log[Mn2+]/[MnO4-][ H+]8 εcell = ε° - (0.05916/n) {(log[Mn2+]/[MnO4-]) -log[ H+]8} =ε° - (0.05916/n) {log([MnO4-] /[Mn2+])-1 + 8pH} =ε° + (0.05916/n) {log([MnO4-] /[Mn2+]) – (8)(0.05916/n) pH }

εcell y

= (0.05916/n)

ε° – (8)(0.05916/n) pH }

{log([MnO4-] /[Mn2+]) +

m x Using linear regression,

+b

Slope = 0.2248 = (0.05916/n) Y-intercept = -0.733 = ε° – (8)(0.05916/n) pH D. Determination of Solubility Product Constant Pb I Pb2+ II PbSO4(s), SO42- I Pb Anode Half Reaction: -( Pb2+ + 2e-  Pb(s) )

ε°= -0.126 V

Cathode Half Reaction: PbSO4(s) + 2e-  Pb(s) + SO42-

ε°= -0.350 V

εcell°= -0.350 V-( -0.126 V) = -0.224 V

Cell Reaction: PbSO4(s) = Pb2+ + SO42Ksp = [Pb2+][ SO42-] = 1.6 x 10-8 Ksp from εcell°= 2.70665207 x 10-8 Ksp from experiment = 0.9618516805 Sample Computation:

∆G° = - RT ln K ln K = (∆G°/ -RT) = (-nF

εcell°/ -RT) = (-n 96485 εcell°/ -8.314 x 298.15)

log K = (nεcell°/0.05916) K = 10 ^ (nεcell°/0.05916) Ksp = 10 ^ (2 x (-0.5 x10-3)/0.05916) = 0.9618516805 F. Determination of the Activity Coefficient [FeSO4]

0.100 M 0.080 M 0.060 M 0.040 M

εcell° 0.0155 V 0.0698 V 0.0202 V 0.0292 V

ε°cell + 0.05916 log[FeSO4] -0.04366 4.91 x 10-3 -0.052 -0.054

√I 0.63245532 0.5656854249 0.4898979486 0.4

Activity Coefficient, γ 8.77 x 10-3 1.32 x 10-3 0.012 0.013

ε°cell + 0.05916 log[FeSO4]

0.020 M

-0.012 V

-0.11

0.2828427125

0.13

2.5 y = 0.1207x + 1.895

Experimental Results

2

Theoretical values

1.5 1 0.5 y = -0.0491x - 0.0066 0 0

0.5

1

Linear (Experimental Results) Linear (Theoretical values)

-0.5 √I Fe l FeSO4 (aq) (a), PbSO4(s) l Pb Anode: Fe2+ (a Fe2+) + 2e-  Fe (s)

ε°= -0.440 V

Cathode: PbSO4(s) + 2e-  Pb (s) + SO42- (aSO42-)

ε°= 1.455 V

Cell Rxn: Fe (s) + PbSO4(s)  Fe2+ (a Fe2+) + Pb (s) + SO42- (aSO42-) ε°= 1.895 V Since there is no liquid boundary: (a Fe2+)=(aSO42-), therefore Fe (s) + PbSO4(s)  FeSO4(aq) (a)+ Pb (s) εcell = ε° - (0.05916/2) log a a= (a Fe2+) x (aSO42-) = (γm )Fe2+(γm)SO42if m=conc. of FeSO4 = M FeSO4 m = mFe2+ = mSO42a= (γ+m ) (γ+m )= γ2m2 =(γm ) 2

ε°cell= ε°- (0.05916/2)log(γm ) 2 ε°cell= ε°- 0.05916log(γm ) ε°cell + 0.05916 logm = ε°- 0.05916 logγ recall DHLL: logγ = -0.51 lZ+Z-l I1/2

I= ½ ΣCiZi2

ε°cell + 0.05916 log[FeSO4] = ε°- 0.05916(-0.51 lZ+Z-l y

ε - ε°

logγ=

b m 0.05916 logm -0.05916

+

-0.05916 γ= 10

ε°- ε

-

I1/2) x

log m

-0.05916

Sample Computations For [FeSO4] = 0.100 M

εcell (observed)= 0.0155 V ε°cell + 0.05916 log[FeSO4] = 0.0155 V + 0.05916 log0.100 M = 0.04366 I = ½Σcizi2 = ½{(0.1)(+2)2 + (0.1)(-2)2} = 0.4

√I = 0.63245532 Using Linear Regression, r = 0.79254755 slope = 0.2403598409 y-intercept = -0.1653431285 V = ε° γ= 10

ε°- ε

-

log m

γ= 10 -0.1653431285 –(-0.0155)

-0.05916

-

log

0.1 = 8.77 x 10-3

-0.05916

Theoretical Values

ε°cell + 0.05916

√I

γ

log[FeSO4] 1.971328781 1.963270538 1.95412402 1.94327456 1.929135269

0.632455532 0.5656854249 0.4898979486 0.4 0.2828427125

0.05126143034 0.07014580933 0.1001401371 0.1527566053 0.2648505443

r=1 slope = 0.1207 y-intercept = 1.895 =ε°

IV.

Discussion

A. Determination of Electrode Potentials The cell’s potential when it is connected at the cathode and the standard hydrogen electrode (SHE), a reference electrode is connected at the anode is called an electrode potential. According to IUPAC sign conventions, when there is no liquid junction the cell potential can be expressed as the difference of the cathode half-cell potential and the anode half-cell potential, that is

ε°cell = ε°cathode- ε°anode Take note that the values ε°cathode and ε°anode are expressed in standard reduction potentials to avoid any confusion. It is impossible to measure absolute electrode potentials, since neither oxidation nor reduction occurs alone. Also, what is of interest is the potential difference; this and not the absolute potential are measured by voltage measuring devices. To circumvent this problem a reference electrode is assigned at the anode having a half-cell potential of 0.000 V, for this purpose a standard hydrogen electrode is used. Using the equation above, when we pair our electrode in question with the SHE at the anode, the potential read by the meter is solely due to the potential of the electrode in question. In the experiment we paired electrodes of “unknown” electrode potentials with a Cu l Cu2+ reference electrode. The reference electrode is connected at the positive terminal or the cathode such that when the voltmeter gives the cell potential, the half-cell potential/ electrode potential of the electrode in question by subtraction following the equation given above. The standard electrode potential or ε° is defined as the electrode potential when the activities of all reactants and products are all unity, and that the pressure of any gas involved is 1 atm. Having a standard state allows us to obtain relative values of free energy, activity, entropy, and enthalpy. Take note that the electrode potential is an intensive property, i.e. it is not affected by the amount of matter but may vary when temperature and or concentration is changed, as what we will see in Nernst equation. B. Electromotive Force of Galvanic Cells

For current to move along a circuit, an electromotive force must be present. An emf causes differences of potential to exist between points in the circuit causing charges to move. An emf is associated only with reversible conversions of energy, whereas potential differences exist not only in sources of emf but also in resistors, which convert energy to heat irreversibly. In this part of the experiment, the equation given in part A is still applied to get the theoretical cell potential. The standard electrode potential measures the relative force tending to drive the half reaction from a state in which the reactants and products are at unit activity to a state in which the reactants and products are at their equilibrium activities. A positive electrode potential, gives a negative free energy, this means that this reaction is spontaneous relative to the SHE. The more positive the electrode potential, the greater is its tendency to be reduced; therefore it is a stronger oxidizing agent/ oxidant compared to that of the reference electrode. Electrons lost during oxidation at the anode flows from the anode to the cathode where it is gained by cations during reduction. When an external load such as a bulb, is added to Galvanic cell instead of a voltmeter, electrons would then through the bulb’s filament causing it to light. In addition all Galvanic cells have a positive cell potential; otherwise such cell is known to be electrolytic. C. Variation of Electrode Potential with Electrolyte Concentration When the concentration of the active species is other than unity, the Nernst equation is applied. This equation expresses emf in terms of the composition. ΔrG = ΔrG° + RT ln Q, where Q is the reaction quotient. Dividing both sides by –nF, ε = -( ΔrG°)/nF – {(RT)/nF} ln Q ε° = -( ΔrG°)/nF ε = ε° – {(RT)/nF} ln Q If the system is at equilibrium, Q = K, then ε = ε° – {(RT)/nF} ln K

D. Determination of Solubility Product Constant Equilibrium constants can be evaluated from the standard cell potential by applying the Nernst equation. Since our system is at equilibrium ε = 0, therefore 0 = εcell° – {(RT)/nF} ln K {(RT)/nF} ln K = εcell° ln K = (nF εcell°)/RT K = exp((nF εcell°)/RT) Consider a saturated solution of a slightly soluble solute which is in contact with the undissolved solid. Cell reaction : AxBy (s) = x Ay+(aq) + yBx-(aq) Ka = a(Ay+)x a(Bx-)y , in very dilute solutions, the activity coefficient is almost equal to 1.00 and activity is taken to be equal to molar concentration Ksp = [Ay+]x[Bx-]y The Ksp can be solved from the cell potential of the cell reaction given above. E. Determination of Activity coefficient The cell constructed is an example of a galvanic chemical cell without transference. This chemical cell, is composed only of one compartment containing only one solution, such that the activities of the cation is equal to that of the anion. Fe l FeSO4 (aq) (a), PbSO4(s) l Pb Anode: Fe2+ (a Fe2+) + 2e-  Fe (s)

ε°= -0.440 V

Cathode: PbSO4(s) + 2e-  Pb (s) + SO42- (aSO42-)

ε°= 1.455 V

Cell Rxn: Fe (s) + PbSO4(s)  Fe2+ (a Fe2+) + Pb (s) + SO42- (aSO42-) ε°= 1.895 V Since there is no liquid boundary: (a Fe2+)=(aSO42-), therefore Fe (s) + PbSO4(s)  FeSO4(aq) (a)+ Pb (s) εcell = ε° - (0.05916/2) log a a= (a Fe2+) x (aSO42-) = (γm )Fe2+(γm)SO42-

if m=conc. of FeSO4 = M FeSO4 m = mFe2+ = mSO42a= (γ+m ) (γ+m )= γ2m2 =(γm ) 2

εcell= ε°- (0.05916/2)log(γm ) 2 εcell= ε°- 0.05916log(γm ) εcell + 0.05916 logm = ε°- 0.05916 logγ recall DHLL: logγ = -0.51 lZ+Z-l I1/2 I= ½ ΣCiZi2

εcell + 0.05916 log[FeSO4] = ε°- 0.05916(-0.51 lZ+Z-l y logγ=

ε - ε°

+

-0.05916 γ= 10

ε°- ε

-

b m 0.05916 logm -0.05916

I1/2) x

log m

-0.05916

The activities calculated on the basis of the equation just above is tabulated in the results. Experimental activity coefficients agree with the trend that is followed by their theoretical counterparts. Recall that in a concentrated solution counter ions surround ions thereby decreasing their activity. This results to a lower activity coefficient. By plotting εcell + 0.05916 log[FeSO4] vs (I1/2) we obtained a straight line, which when extrapolated to the y-axis gives a y-intercept equal to ε°, this constant would then be used to calculate the activity coefficient. The activity coefficient could also be obtained from the colligative properties. V.

Answers to Questions 1.

Does the plot obtained conform to the Nernst equation? Why Support your answer. The plot obtained does not conform to the Nernst equation, but theoretically it should. Plotted points did not correspond to a line as predicted by the equation

2.

What is the significance of the slope of the line? How does it compare with the theoretical value?

Theoretically, the slope of the line corresponds to 2.303RT/nF. The obtained slope was much higher about 38 times as large as that of the expected. 3.

What is the significance of the value of the y-intercept obtained in your plot? How does it compare with the theoretical value? The y-intercept is equal to ε° – (8)(0.05916/n) pH. The theoretical value cannot be obtained because it requires knowing the pH of the solution which was not obtained during the experiment.

VI.

Reference(s) Fundamentals of Analytical Chemistry 8th ed. Skoog, West, and Holler Physical Chemistry 3rd ed. Laidler and Meiser Physical Chemistry 7th ed. Atkins and de Paula College Physics 5th ed. Weber, Manning, White, and Weygand Learning modules in Gen. Chemistry 2 2002 ed. Engle and Ilao