Electrochemical Cells y3r2a

Electrochemical Cells Laboratory #15 Henry Ko AP Chemistry Dulaney High School March 12th, 2009

Abstract: In this experiment, a standard table of reduction potentials of a series of metal ions is constructed using copper, iron, lead, magnesium, silver, and zinc. These half cells are are connected by a salt bridge and all potentials are measured with respect to the zinc electrode. Also, the measured voltage of a nonstandard copper cell is calculated through the Nernst equation. The solubility product constant of AgCl is also determined through the Nernst equation. The Ksp value for AgCl was determined to be 7.33 × 10−11 , yielding a percent error of 59.3%. The voltage for the cell reaction was experimentally determined to be 0.81 V.

Theory: An electrochemical cell is produced when a redox reaction occurs. The resulting electron transfer between the reaction runs through an external wire. Because the oxidation and reduction reactions are physically separated from each other, these are called half-cell reactions. A half cell is prepared from with the metal with its solution of ions. Each element’s unique electron configuration allows each to develop a different electrical potential. The standard reduction potential is the voltage that a half-cell, under standard conditions (1 M, 1 atm, and 25◦ C), develops when combined with the standard hydrogen electrode, that is arbitrarily assigned ◦ to a potential of zero volts. A positive Ecell value indicates that the redox reaction in that particular cell is spontaneous. Calculations of nonstandard potentials can be made using the Nernst Equation:

E

= E◦ −

RT ln(Q) nF

(1)

where E is the measured cell potential, E ◦ is the standard cell potential, R is the gas constant (8.314 J/mol · K), T , is the temperature in K, n is the number of moles of electrons transferred as shown by the redox reaction, and F is the Faraday constant (9.65 × 104 C/mol). At STP, the Nernst equation can be simplified to

E

= E◦ −

0.0592 log(Q) n

(2)

Procedure: A wellplate is set up such that the first row contains approximately 2 mL of 1.0 M Zn(NO3 )2 solution in each well. In the second row, two mL of Cu(NO3 )2 , AgNO3 , Fe(NO3 )3 , Mg(NO3 )2 , and Pb(NO3 )2 are added in their respective wells. A salt bridge is used to connect to the two adjacent wells (made from filter paper soaked in KNO3 solution. A voltmeter is used to measure the potential difference for each of the 5 half cells. After, measure the potential difference between at least six combinations of various electrodes. Again, use the voltmeter to measure the potential difference. In part 2, Cu(NO3 )2 is diluted to 0.0010 M. It is added onto a wellplate and measured against the standard zinc half-cell. In part 3, 10 mL of 1.0 M NaCl solution is mixed with one drop of 1.0 M AgNO3 . After precipitation occurs, some of the solution is poured into the well plate and measured against the standard zinc half-cell.

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Data Analysis: Part 1 Voltage of Each Half-Cell versus the Zinc Electrode Voltage (V) 1.41 0.99 0.553 0.58 0.454

Zn versus Ag Zn versus Cu Zn versus Fe Zn versus Mg Zn versus Pb

Anode Zn Zn Zn Mg Zn

Cathode Ag Cu Fe Zn Pb

Predicted and Measured Cell Potentials Anode Mg Fe Fe Mg Pb Cu

Cathode Cu Cu Ag Pb Cu Ag

Equation for Cell Reaction Cu 2+ + Mg −−→ Cu + Mg 2+ 3 Cu 2+ + 2 Fe −−→ 3 Cu + 2 Fe 3+ 3 Ag+ + Fe −−→ 3 Ag + Fe 3+ Pb 2+ + Mg −−→ Pb + Mg 2+ Cu 2+ + Pb −−→ Cu + Pb 2+ 2 Ag+ + Cu −−→ 2 Ag + Cu 2+

Predicted Potential 0.99 + 0.58 = 1.57 0.99 + (-0.553) = 0.437 1.41 + (-0.553) = 0.857 0.58 + 0.454 = 1.034 0.99 + (-0.454) = 0.536 1.41 + (-0.99) = 0.42

Measured Potential 1.55 0.47 0.86 1.0 0.5 0.41

Part 2

Zn|Zn

2+

kCu

2+

|Cu

Equation for Cell Reaction Zn + Cu 2+ −−→ Zn 2+ + Cu

Voltage 1V

Anode Zinc

Predicted Potential 0.9012 V

Cathode Copper Measured Potential 1V

Part 3

Zn|Zn 2+ kAg+ |Ag Equation for Cell Reaction Zn + 2 Ag+ −−→ Zn 2+ + 2 Ag

Voltage 0.81 V

Calculated [Ag+ ] 7.33 ×10−11

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Anode Zinc

Cathode Silver

Calculated Ksp AgCl 7.33 ×10−11

Reported Ksp AgCl 1.8 ×10−10

Calculations: Part 1 1. Write reduction equations for each metal ion, arranging the equations in decreasing order of measured potential in the table below. Include zinc in the table, using 0.00 volts as the potential of the Zn — Zn 2+ half-cell. Record the accepted standard potentials using the hydrogen electrode as standard, and calculate the difference between the two standard values. ◦ ◦ Reduction Equation Standard Zinc, EZn Standard Hydrogen, E ◦ EZn − E◦ + – Ag + e −−→ Ag 1.41 0.80 0.61 2+ – Cu + 2 e −−→ Cu 0.99 0.34 0.65 Mg 2+ + 2 e – −−→ Mg 0.58 -1.18 1.76 Fe 2+ + 2 e – −−→ Fe 0.55 -0.44 0.99 Pb 2+ + 2 e – −−→ Pb 0.45 -0.13 0.58 Zn 2+ + 2 e – −−→ Zn 0 -0.76 0.76 2. Use the electrode potentials from the above table to predict the voltages of the six-half cell combinations selected in Part 1, step 10. Record thie value and which metal is the cathode and which is the anode in the Data Table above. Compare the predicted and measured potentials. The predicted and measured potentials were very similar to one another. Part 2 Write a balanced net ionic equation for the reaction occurring in the cell in Part 2. Record this equation in the Part 2 Data Table. Use the Nernst equation to calculate what the expected voltage should be. Record this value in the Part 2 Data Table. Compare this value to the measured voltage.

E

=

0.99 −

=

0.9017

0.0592 log 2



1 0.001



Part 3 1. Write the balanced net ionic equation for the reaction occurring the cell. Use the Nernst equation to calculate the concentration of the Ag+ ion. Record this value in the Part 3 Data Table.

0.81

= =

0.0592 1.41 − log 2



1 [Ag+ ]2



7.33 × 10−11

2. Calculate the value of the solubility product AgCl. Compare the calculated value to a reported value. Record this value in the Part 3 Data Table.

Ksp

= =

Percent Error :

(7.33 × 10−11 )(1.0) 7.33 × 10−11

7.33 × 10−11 − 1.8 × 10−10 = 59.3% 1.8 × 10−10

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Conclusion: In this experiment, a standard table of reduction potentials of a series of metal ions is constructed using copper, iron, lead, magnesium, silver, and zinc. These half cells are are connected by a salt bridge and all potentials are measured with respect to the zinc electrode. Also, the measured voltage of a nonstandard copper cell is calculated through the Nernst equation. The solubility product constant of AgCl is also determined through the Nernst equation. The Ksp value for AgCl was determined to be 7.33 × 10−11 , yielding a percent error of 59.3%. The voltage for the cell reaction was experimentally determined to be 0.81 V. Contamination was a huge source of error in this experiment. Because the cells were based in wellplates, any spillage or mixture of two cells could result in a mixing of the concentration of different solutions. This would have produced a different redox reaction than what was intended, and which would have yielded a different voltage with respect to the zinc electrode. This would have severely impacted calculations concerning the predicted and measured cell potentials, which are used in other parts of the lab. Concentration contaminations could impact the cell reaction because a different amount of electrons would have been transferred via the salt bridge, creaing a different voltage. Another error that was a factor was the voltmeter. Because the voltmeter has a reading that is constantly fluxuating, there is no clear moment in which the measurement should have been taken. Therefore, the measurement for each cell varied with respect to their individual times. This could cause some errors in the experimentally determined voltage, which could have impacted the future calculations. Overall this experiment is neither accurate nor precise. Only one set of trials was used, meaning that there is no basis for comparison and the result could have varied widely. Also the precision and accuracy depended heavily on the voltmeter used. Human judgement in the reading, as well as the accuracy of the voltmeter, makes the reading variable. This experiment could have been improved in equipments. A more accurate/precise voltmeter could have been used, as well as cleaner and more accurate pipets (in transferring solutions) could have been used to for better results. Pre-Lab Questions 1. Which ion is most easily reduced? Copper 2. Which metal is most easily oxidized? Aluminum 3. The copper and aluminum electrodes are connected to form a battery. a. Which is the anode? Aluminum b. Which is oxidized? Aluminum c. What will be the battery voltage? 0.62 + 1.38 = 2 V d. Write a balanced net ionic equation for the reaction that takes place. 3 Cu 2+ + 2 Al −−→ 2 Al 3+ + 3 Cu 4. A soltuion is prepared in which trace or small amounts of Fe 2+ is added to a much larger amount of solution in which the [OH – ] is 1.0 × 10−2 M. Some Fe(OH)2 precipitates. The value of Ksp for Fe(OH)2 is 8.0 × 10−10 . a. Assuming that the hydroxide ion concentration is 1.0 × 10−2 M, calculate the concentration of Fe 2+ ions in the solution. 8.0 × 10−10 [Fe 2+ ] = = 8.0 × 10−8 M 1.0 × 10−2 4

b. A battery is prepared using the above solution with an iron wire dipping into it as one half-cell. The other half-cell is the standard nickel electrode. Write the balanced net ionic eqaution for the cell reaction. Ni 2+ + Fe −−→ Ni + Fe 2+ c. Use the Nernst equation to calculate the potential of the above cell.

E

= =

0.0592 0.15 − log 2



8 × 10−8 1 × 10−2



0.3 V

Post-Lab Questions 1. What is an electrode potential? An electrode potential is the difference between the charge on an electrode and the charge in the solution. The electrode potential depends on the concentration of substances and the temperature, according to the Nernst equation. 2. Did the ranking of reduction equations agree with that in the published chart of E ◦ values? The ranking of the reduction equations should agree with that in a published chart of E ◦ values. However, the obtained “standard” table of reduction potentials did not exactly compare with the accepted table. The order of the metals in decreasing reduction potentials was silver, copper, magnesium, iron, lead, and zinc. For the expected values, the order was copper, lead, iron, zinc and magnesium. 3. How should the values found using the zinc electrode as a standard compare with those in the E ◦ table that are based on the standard hydrogen electrode? Did they? The values found using the zinc electrode as a standard should be greater than the values in the E ◦ table by approximately 0.76 V, which are based on the standard hydrogen electrode. This is because the zinc electrode was used as the standard, with the voltage preset to 0. However, when the hydrogen electrode is used as the standard, the voltage for the zinc electrode is not zero; in fact it is -0.76 V. 4. What factors can cause a difference between experimental and reported values? See Conclusion. 5. What does a negative value for a standard potential indicate? A negative value for standard potential indicates that the cell is not galvanic, meaning that the oxidation reaction is more likely to occur than the reduction. 6. How did the change in concentration of the copper ions in Part 2 affect the cell potential? Is this change in agreement (qualitatively) with that which would be predicted by LeChatelier’s Principle? Did the calculated and measured values agree? The electrode potential depends on the concentration of substances and the temperature (according to the Nernst equation). In this case, the concentration of copper was reduced from 1.0 M to 0.001 M. For one molar solution, the reduction potential was 0.99 V, whereas the 0.001 M solution had a potential of 0.81 V. This is in agreement with LeChatelier’s Principle because when the concentration of copper was reduced, the amount of volts generated by the reaction was also reduced. The calculated and measured potential values differed by approximately 0.1 volts. 7. Explain how the AgCl solubility product was determined. The AgCl solubility product was determined using the Nernst equation in conjunction with the equation for Ksp . The unknown in this case, was the concentration of Ag+ . Therefore, with the standard and nonstandard measures of potential known through the experiment, the concentration of of Ag+ was found. Because the amount of Cl – was known to be approximately 1, the Ksp was also equal to the concentration of Ag+ .

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