Determination of Electrode PotentialsNathalie D. Dagmang

Institute of Chemistry, University of the Philippines, Diliman, Quezon City, 1101 Philippines

Department of Food Sciences, College of Home Economics, University of the Philippines, Diliman, Quezon City 1101 Philippines

ABSTRACT

The two main objectives of the experiment are to (1) relate and apply the concepts of electrochemistry to actual experiments, (2) understand the processes and elements of an electrochemical cell and (3) determine the spontaneity of reduction-oxidation (redox) reactions based on standard reduction potential.

Different half-cells were prepared and connected to copper, which served as the reference electrode, to set up a voltaic cell. The volt-meter readings of the set-ups were then used to calculate for the standard reduction potentials of the variable half-cells. The results obtained from the experiment indicated the spontaneity of the redox reactions investigated, showing that the least spontaneous system is that connected to another copper half- while the most spontaneous system is that connected to the Zinc half-cell.

Introduction

In a redox reaction, an electron is being transferred from one reactant to another. This process is shown in the equation below, with the example of the redox reaction between Zinc and Copper:

Zn(s )+Cu(aq)2+¿→Cu(s )+Zn(aq )

2 +¿¿ ¿ [1]

An electrochemical process occurs when a spontaneous redox (or reduction-oxidation) reaction produces energy or a non-spontaneous reaction uses up energy.

This reaction can be prompted by directly immersing a Zinc solid in a CuSO4 solution. This reaction can also be set off even when the two reactants were separated, and their electrons are transferred not by direct contact but through a wire. In this case, a certain amount of work is done or used by the system. In equation [1], the anode, where the oxidation occurs (equation [2]), is zinc while the cathode, where the reduction occurs (equation [3]), is copper. These two components can be separated into what are called half-cells:

Zn(s )→Zn(aq)2+¿+2e−¿ ¿¿ [2]

Cu(aq )2+¿+2e−¿→Cu( s) ¿¿[3]

In equation [2], zinc with the less affinity for electrons undergoes oxidation wherein it losses electrons and causes copper to undergo reduction. This makes zinc the reducing agent, while the copper is the oxidizing agent.

This set-up, where the anode and cathode are separated, is called an electrochemical cell. There are two types of electrochemical cell: the voltaic cell, wherein work is done by the system, and the electrolytic cell, wherein work is needed to set off the reaction. The voltaic cell (also called galvanic cell), is shown in Figure 1.

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Figure 1. Voltaic cell

This can also be representation through a shorthand notation. In this case, the cell notation is:

Zn¿ [4]

wherein the reactant on the left is always the anode and the one on the right is always the cathode. The single vertical line represents a phase boundary while the double vertical line represents the two phase boundaries at both ends of the salt bridge.

In this set-up, a salt bridge provides ions to the two solutions to neutralize its charges by adding negative ions to the positive half-cell (Zinc) and positive ions to the negative half-cell (Copper). This prevents the reactants to react directly with one another but still maintains electrical contact between the two half cells.

The electrons produced from the Zinc rod passes through the wire, enter the copper rod and interact with the copper ions in solution. As the electrons travel through the wire, energy is produced and the bulb is lighted. In the experiment, a load like the light bulb was not connected to the wire, but a volt-meter. A volt-meter measures the voltage/ electric potential difference or the measure of

electromotive force, the amount that can be extracted from the system. While doing this, the volt-meter does not consume the energy produced as it has an infinite resistance. The voltage also serves as a parameter for the tendency of the reaction to proceed to an equilibrium state. As the reaction proceeds, the potential continues to decrease until it reaches 0.000 V.

However, absolute electrode potentials cannot be measured. This is because all volt-meters measure only differences in potential between two half cells. Thus, the values of electrode potential used in calculations are only those of the half cells when these are reacted with a standard hydrogen electrode which has an assigned value of potential of 0.00 V. In this reaction, the standard hydrogen electrode serves as the anode while the electrode to be tested is the cathode. From this reaction, the standard reduction potential (E°) is measured. This value can then be used to compute for the standard potential of the whole electrochemical cell using the equation:

E ⁰cell=E ⁰cathode−E ⁰anode[5]

However, this standard potential only applies to solutions with the concentration of 1 M. In the experiment, it was assumed that the concentration of the halide ion did not significantly change with the electrolysis of the solution. But if the concentration was not 1 M, and other conditions such as the temperature and nature of the reactant were altered, the cell potential will be different from the standard potential. The effects of these factors are shown in the Nernst equation:

E=E°−RTnFlnQ [5]

Where R is the gas constant with a value of 8.314 J/molK, T is the temperature in Kelvin, n= number of moles of electrons that appear in the half cell reaction, and F is Faraday which is equal to 96, 485 Coulombs. The Q in the equation is the reaction quotient, given by the formula

Q= [ products]m

[r eactants ]n [6]

2

Volt-meter

+Cu

CuSO4

-Zn

ZnSO4

Salt bridg

e

e-

e-

2K+

SO4

2

-Zn(s) Zn2+

(aq) + 2e-

Cu2+ (aq) + 2e- Cu(s)Cathode

= Reductio

n

Anode = Oxidatio

n

Zn|Zn2+||

Cu2+|Cu

1

2

3

where m e the coefficients of the products and n are the coefficients of the reactants in the balanced equation. The values enclosed in brackets are the concentrations of the reactants and products.

Simplifying the Nernst equation by substituting the constant values and indicating that the temperature is at 25 C, the cell potential can be⁰ calculated from the formula:

E=E°−O .O592n

logQ [7]

According to Faraday’s law, the mass of the product formed or the reactant used is proportional to the amount of electricity that passes through the system. This relationship is shown in the equation:

C=At [8]

where C is the amount of electricity passing through the circuit, 1 coulumb being transported every second by each ampere. A is the current in ampere and t is time in seconds. 96,500 Coulomb per mole of electron is equivalent to 1 Faraday, which is the electrical charge contained in 1 mole electron. Using this formula, the concentration of the half-cell can be calculated and substituted to the Nernst equation.

The purpose of this experiment is to further understand and apply the concepts of electrochemistry and the processes and elements of an electrochemical cell to actual experiments and to determine the spontaneity of reduction-oxidation reactions based on standard reduction potential.

Experimental Detail

For the first part of the experiment, three half cells were prepared, with cell notations of Cu2+(1M)|Cu, Zn2+(1M)|Zn and Fe3+(1M),Fe2+(1M)|C. The first electrode was prepared by immersing a copper electrode in 1 M CuSO4. The second half cell was prepared by immersing a zinc electrode in 1 M ZnSO4. Lastly the third half cell was a mix of equal volumes of 2 M FeSO4 and 2 M FeCl3 with graphite as its electrode. An iron nail was not used due to the side reaction that might cause rust to form on the nail’s surface:

Fe3+¿→Fe2 +¿→FeO ¿¿[9]

Instead, a graphite electrode, which is a semi-conductor, was used. This is made of the electrically inert carbon that would not participate in the reaction.

These half cells were then connected with the wires of the volt-meter to a copper half cell prepared in the same manner. A salt bridge was made out of rolled filter paper soaked in saturated potassium nitrate and then each of its ends was soaked in one of the two half-cells. The set-ups for the first part of the experiment is shown in Figure 2.

Figure 2. Voltaic Cell Set-up

For the second part of the experiment, another 3 half cells were prepared with cell notations Cl-(1 M), Cl2| C, Br-(1 M), Br2| C, I-(1 M), I2| C. Like in the third half cell, a graphite electrode was used. Potassium halide (KX) solutions were electrolyzed by immersing two graphite electrodes into the solution and connecting these to a 1.5 V dry cell which serves as its energy source as shown in Figure 3. This was done for 1 minute, until the halide ions were oxidized to halogens, X2.

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Volt-meter

XCuSO4

Salt bridgeC

u X-

Figure 3. Electrolytic Cell Set-up

The prepared mixture of halogens and halide solutions were then connected to the copper half-cell like the set-up in Figure 2.

The volt-meter reading for the six voltaic cells prepared were recorded and used in calculations.

Results and Discussion

The measured voltages of the prepared voltaic cells are tabulated in Table 1.

Table 1. Volt-meter Readings

Set-up #

Cell Notation Volts

1 Cu|Cu2+||Cu2+|Cu 0.0896

2 Zn|Zn2+||Cu2+|Cu 1.08

3 Cu|Cu2+||Fe3+|Fe 0.414

4 C|Cl-,Cl2||Cu2+|Cu 0.468

5 C|Br-,Br2||Cu2+|Cu 0.269

6 C|I-,I2||Cu2+|Cu 0.121

The potentials measured from the experiment are the potentials of the whole voltaic cell set-ups while the given potential of the reference electrode, Cu2+/Cu, is 0.34 volts. From these data, the experimental value of potential of the different half cells connected to the copper half-cell can be calculated using equation [5].

If the copper served as the anode in the voltaic cell, the formula for the potential of the variable half-cell is calculated from:

Ecathode=Ecell+0.34 [10]

Otherwise, the potential of the half cell will be

Eanode=0.34−Ecell [11]

For set-ups 1, 2, 4, 5 and 6, the reference electrode, Cu, served as the anode. Thus, given the E⁰red of Cu as 0.34, the standard potential of the cathode was calculated from equation [10]. The first set-up should have yielded a voltage reading of 0.00 V because both half-cells supposedly have the same content and concentration. Because of this, the Eanode

and Ecathode should have the same value and the Ecell

should be equal to 0.00 V. However, a difference in concentration can also add to the potential difference, so even a slight error in the volume measurements can add to the error of the results.

Set-ups 4, 5 and 6 were affected by the concentration. However, in the experiment, it was assumed that the change in concentration due to the hydrolysis was negligible and was not taken into account in the calculations.

Because in set-up 3, copper served as the cathode, the value calculated for was the standard potential of the anode. This was computed from equation [11].

Using these equations, the resulting experimental value for the standard reduction potentials of the variable half-cells are as follows:

Table 2. Calculated standard potential

Set-up #

Variable Half-Cell Notation

Calculated Volts

Book Value

% Error

1 Cu|Cu2+ 0.2504 0.00 26 %

2 Zn|Zn2+ - 0.74 - 0.763 3.01 %

3 Fe3+|Fe 0.754 0.771 2.2 %

4

1 M KX

C C

batt

4 C|Cl-,Cl2 0.808 1.359 40.54 %

5 C|Br-,Br2 0.609 1.087 43.97 %

6 C|I-,I2 0.461 0.615 25.04 %

These values were compared to the book value and yielded percentages of error within the range of 2.2%-43.97%.

The percent error were highest for the last three set-ups for these were calculated without taking into account the changes in concentration due to the electrolysis done prior to setting up the voltaic cell.

If the change in concentration was taken into account, the current (in Amperes) and time length of the electrolysis should be measured. For example, in the experiment, Cl- is converted into Cl2. which follows the reaction:ly

2Cl(aq)−¿→2e−¿+Cl

2( s) ¿¿ [12]

The Cl- solution was electrolyzed for 4 minutes and 30 seconds and the measured current was 0.065 Amperes. Substituting these values to equation 8, the calculated amount of electricity is 17.55 Coulombs. This is then converted to mole e- by dividing 17.55 by 96,500. Using stoichiometry, the number of moles of Cl- is calculated, hence, also the concentration of Cl- in the solution. This new concentration can be substituted to equation [7] and

since Q=[Cl2]¿¿¿

and the activity of Cl2 is taken as 1,

Q is only equal to 1¿¿¿

.

The measured voltage of the voltaic cell, which is 0.468 V, was then used to calculate the potential of the Chloride half-cell:

Ecathode=0.468+0.34=0.808V

The n, calculated Q, and potential of the cathode was substituted in the Nernst equation to get the standard reduction potential of the cathode:

E=E°−0.05922

log1

[0.00364]2

0.808=E°−0.1444

E°=0.9524 V

By using this method of calculation, the percent error will decrease from 40.54% to 29.92%.

These calculated reduction potentials can serve as a parameter for the spontaneity of a reaction.

If the calculated values for the potentials of the half-cells are more positive than 0.34, the reactants of that half-cell are stronger oxidizing agents. If the potential difference is positive, the reaction follows a forward direction. Otherwise, the backward reaction is favored and work is needed to stimulate the forward reaction. An electrolytic cell set-up is used in this experiment to initiate a reaction like this, namely the halide half-cells.

Consider the cathode iron half-cell in set-up 3 where the following reduction reaction occurred:

Fe3+¿+e−¿→Fe 2+ ¿¿¿¿ [13]

When the chemically inert electrode, graphite, was inserted to the solution, a continuous exchange in electrons occurs between the electrode and the oxidizing and reducing substances that came in contact with it. At equilibrium, when Q = Keq, reaction [13] and its reverse reaction occur at the same rate, making the composition of the solution near the electrode, constant. The equilibrium potential, or the potential of the electrode with respect to the solution, can be calculated from the Nernst equation:

Eeq=E°−O .O 592n

log¿¿ [14]

If the given potential of the electrode, E’, exceeds the Eeq, the wire is not in equilibrium, thus electrons are still exchanged between the components of the solution until the potentials of the solution and the electrode are equal. The value of the

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ratio ¿¿ increases to lessen the value of E’ and the ferric iron tends to be reduced (reaction [13]). On the other hand, if E’ is less than Eeq, the ratio decreases and reverse reaction predominates.

Consider the electrolysis of a Chloride solution in part B:

2Cl−¿→Cl 2+2e−¿¿ ¿ [15]

In the electrolytic cell, voltage is applied to the two chemically inert graphite electrodes, one of which serves as the cathode, the other, the anode. The voltage applied can be calculated from the formula:

V applied=Eanode−Ecat hode [16]

If a potential applied to the cathode, Ecathode, is less than Eanode, the system is not in equilibrium. This causes the Ecathode to increase and the Eanode to decrease until Ecell = 0, producing work instead of consuming it from the energy input (dry cell). So if the passage of current or electrolysis is aimed to occur, the Eanode should be greater than Ecathode.

The potential at the anode of the cell and the reduction potential of the cathode can also be calculated from the Nernst equation:

Ecat hode=E°−O .O592

nlog

[Cl2]¿¿¿ [17]

Eanode=E°−O .O592

nlog ¿¿¿ [18]

Referring to the aforementioned concept, as the produced Cl2 increases, the oxidation potential decreases. Conversely, the reduction potential of the cathode increases with the increase of Cl2. This causes the potential needed by the system to decrease until it reaches equilibrium and making the reaction more spontaneous. After the electrolysis of the system, it can already be connected to the copper half-cell to produce a galvanic cell. It now acts as the cathode because of the high amount of Cl2 which tend to be reduced to Cl-.

Conclusions

The three main objectives of the experiment, namely to (1) relate and apply the concepts of electrochemistry to actual experiments, (2) understand the processes and elements of an electrochemical cell and (3) determine the spontaneity of reduction-oxidation (redox) reactions based on standard reduction potential, were all achieved in the experiment.

From the read voltages, the spontaneity of the reactions was measured. It can be concluded based on the data gathered and values calculated that the spontaneity of the reactions with respect to a copper half-cell in decreasing order is:

Set-up # 2 > # 4 > # 3 > # 5 > # 6 > # 1

This was concluded using the knowledge that a higher potential difference or Ecell produces a more spontaneous reaction and more work that can be done by the system. This means that the farther the value of the standard reduction potential (SRP) of the half-cell is from the SRP of copper, the more spontaneous the reaction would be. Individually, the standard reduction potentials of the half-cells, when at a higher value, also indicate a higher tendency to be reduced and serve as a cathode in the voltaic cell and as an anode in an electrolytic cell.

To further understand the concepts of electrochemistry, it is recommended that in the second part of the experiment, the change in concentration due to electrolysis is taken into account. This can be done by measuring the amperes and recording the time of the duration of electrolysis.

Also, the effect of concentration differences between the half-cells can also be investigated by setting up two half-cells containing the same solutions but in different concentrations.

References

[1] Belcher, R. Quantitative Inorganic Analysis, 1970

[2] Christian, G.D. Analytical Chemistry, 1986

[3] Day, Underwood, et al. Quantitative Analysis, 1967

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[4] Haenisch, Pierce, et al. Quantitative Analysis, 1958

[5] Skoog, et al., Fundamentals of Analytical Chemistry, Eighth edition, 2004

[6] http://academic.pgcc.edu/psc/chm103/103_manual.pdf

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