Chemistry 212 Lab, Spring 2009 Electrochemical Cells: Determination of Reduction Potentials for a Series of Metal/Metal Ion Systems, Verification of Nernst Equation, and Determination of Formation Constant of Cu(NH 3 ) 4 2+ Aqua Complex Purpose There are three parts in today s lab experiments. In part A, the purpose is to construct simple electrochemical cells, and measure cell potentials. Through these measurements, it will be possible to calculate the standard cell potential and confirm the observed "activity series" for some of the common metals. In part B, you will verify the Nernst equation by measuring the cell potential as a function of ion concentration in one of the half-cells. In part C, the measured cell potential, after addition of NH 3 as the complexing agent, in the Cu/Cu 2+ half-cell will be used to calculate the formation constant of a Cu(NH 3 ) 4 2+ aqua complex. Introduction You will need to rely heavily on the explanations of voltaic cells, concentration cells, and the Nernst equation that are provided in your lecture text. There is simply not enough space to cover all the necessary information here in the lab manual. This text is designed to help you to build the cells, take the experimental measurements, and suggest ways to interpret and quantify the information you will obtain while doing the experiment. For your information, an abbreviated table of standard reduction potentials is included as part of this text. Design of the Experiment: Standard and Non-Standard Reduction Potentials For Metal/Metal Ion Half-Cells Typical electrochemical cells are comprised of two half-cells, linked by a salt bridge (allowing transport of ions in both directions), with a voltmeter completing the circuit to measure the difference in voltage between the two halves. One half-cell has a reduction taking place (the cathode) while the other half-cell has an oxidation taking place (the anode). The cell potential, E cell, as measured by a voltmeter is a measure of the free energy change, G = -nfe cell, that occurs in the overall oxidation/reduction reaction. Electrons will move in response to this potential difference, with the flow going toward the cathode from the anode. Thus, the sign of the potential difference (as measured by a voltmeter) is sufficient for identifying which half-cell has the oxidation reaction and which has the reduction reaction. Standard half-cell reaction potentials are measured using the standard hydrogen electrode (SHE) as a reference point. The standard hydrogen electrode is assigned a value for 212 Echem Experiment_Text/7/12/11 1
potential of 0.00 V, and the half-cell reaction for the standard hydrogen electrode is the reduction of 1.00 M aqueous acid to gaseous hydrogen at 1 atm pressure on a platinum electrode: 2H + (aq, 1 M) + 2e - H 2 (g, 1 atm) All other half-cell reactions can be measured in tandem with the standard hydrogen electrode, which gives rise to the table of standard reduction potentials, an abbreviated version of which appears as part of this text. Measurements of standard half-cell potentials are supposed to be carried out at standard conditions i.e., at solution concentrations of 1.0 M and at 25 C. It is not always practical (or possible) to carry out electrochemical reactions at these conditions, as is the case in today's experiment. For all reversible reactions the cell potentials measured at non-standard conditions (E cell ) can be related to potentials at standard conditions (E cell ) by the Nernst equation: E cell = E o cell - (0.0591/ n) log Q (Q = equilibrium quotient) where, E o cell = E o oxidation + E o reduction Also, it is not practical to set up a standard hydrogen electrode for each of you to do your measurements. Instead, you will use the potential of the Ag + /Ag reduction half-reaction as your standard (+0.80 V). Using this value, and assuming it to be the cathode half-reaction, will allow you to determine half-cell potentials for the other systems you will study (half-cells of Cu, Sn, Pb, and Zn) whose general reduction half-reactions are of the form: M 2+ + 2e - M As an example of today's measurements, let us look at the half-cell reactions of Al/Al 3+ and Sn/Sn 2+ at standard conditions. The reduction half-reactions and potentials are as follows (from table of standard reduction potentials): Sn 2+ + 2e - Sn E o = 0.14 V Al 3+ + 3e - Al E o = 1.66 V To construct a complete electrochemical cell with a positive overall potential, it will be necessary to consider the aluminum half-cell not as a reduction, but as an oxidation. This requires writing the half-cell reaction shown above in reverse. It also requires changing the cell potential magnitude and sign to equal, but opposite, that of the reduction half-reaction. The new halfreactions, and the overall reaction are shown below. Oxidation (anode): (Al Al 3+ + 3e ) x 2 E o = +1.66 V Reduction (cathode): (Sn 2+ + 2e - Sn) x 3 E o = 0.14 V Overall Reaction: 2Al + 3Sn 2+ 2Al 3+ + 3Sn E cell = +1.52 V What you are being asked to do today is in a sense related to this, with the silver half-reaction as the standard potential. Taking this example further, you'd first have to correct for non-standard conditions. In today's experiment, solution concentrations are 0.1 M (temperature effects will not 212 Echem Experiment_Text/7/12/11 2
be considered) and not the 1.0 M of "standard conditions". Thus the Nernst equation that would be needed to "correct" the cell potential of the above example to non-standard conditions is: E cell = E o cell - (0.0591 / n) log ([0.1] 2 / [0.1] 3 ) Where, n = 6 (the overall number of electrons required to balance the reactions) E cell = 1.52 - (0.0099) = 1.51 V This is what you should observe on the voltmeter The above principle can be used to measure the standard potential of an unknown redox couple if the cell potential is measured and if one half of the couple has known standard reduction potential (in this case aluminum). Continuing the above example, if you know the "standard" reduction potential for the aluminum half cell (-1.66 V from Table), you then measure the overall cell potential with the voltmeter, and solve for the half-cell potential for tin. It plays out like this. Assume the following to be true: (Oxidation and reduction are abbreviated as ox and red) Standard reference half-cell potential: E o ox = +1.66 V (for the Al 3+ /Al half-cell as anode) Measured overall cell potential: E cell = +1.50 V Solution concentrations: [Sn 2+ ] = 0.01 M and [Al 3+ ] =0.01 M +1.50 = E o cell - (0.0591 / 6) log ([0.01] 2 / [0.01] 3 ) E o cell = + 1.52 V = E o ox + E o red E o red = 0.14 V (Non standard reduction potential for Sn 2+ + 2e Sn) So the actual objective is to determine half-cell potentials for Sn, Pb, Cu and Zn at nonstandard conditions, using the Ag + /Ag half-reaction as your standard reference and examining the all-possible combinations of half-cells. Notes on Experimental Procedure and Precautions There are 15 sets of pre-assembled and labeled weighing boat setup's located on the various benches. Obtain one of these for use by your group of two students. There are also several sets of solutions placed around the room on the benches. These are used by those students occupying a given bench space, so please use what you need and leave the sets where you found them so that others may also get what they need. No one should have to cross the lab to find a reagent they need. Treat the ph meters (being used here as voltmeters) with care, and return them to the cabinets when you are finished. Waste bottles for silver and lead salts generated during this experiment are in the hoods. Please carefully follow the waste disposal directions. You must not spill silver solution on your skin, clothes or on the bench; it may produce a semi-permanent mark where spilled. Promptly clean and wash the spilled area with plenty of water. 212 Echem Experiment_Text/7/12/11 3
Experimental Procedure A. Measurement of Non-Standard Reduction Potentials Place 5.0 ml of the following solutions into the labeled weighing boats. IT IS IMPORTANT TO PUT THESE SOLUTIONS INTO THE CORRECT PLACE, OR YOUR RESULTS WILL BE UTTERLY USELESS. 0.10 M KNO 3 into the boat labeled "Salt Bridge" 0.10 M AgNO 3 into the boat labeled "Ag" 0.10 M Zn(NO 3 ) 2 into the boat labeled "Zn" 0.10 M Cu(NO 3 ) 2 into the boat labeled "Cu-1" 0.01 M Cu(NO 3 ) 2 into the boat labeled "Cu-2" 0.001 M Cu(NO 3 ) 2 into the boat labeled "Cu-3" Salt bridge: filter paper soaked in KNO3 Cu Cell: Plastic weighing cup Ag PH/ mv Meter Schematic diagram of the electrochemistry cell setup. To construct "salt bridges", dip one end of a piece of filter paper into the boat containing KNO 3 solution, and the other into a boat containing a metal ion solution. A total of 5 such pieces of filter paper must start from the KNO 3 boat, and end up in each of the 5 different solutions. Do not let the salt bridges dry. Keep a medicine dropper handy to put a few drops of KNO 3 on the filter paper whenever necessary. Obtain pieces of Cu, Ag, and Zn metals to use as electrodes. Place each metal strip into its corresponding metal ion solution (copper metal into the copper nitrate solution, etc), bending each 212 Echem Experiment_Text/7/12/11 4
strip as needed to allow a portion to stick above the solution surface for potential measurements. It is important to handle these strips as little as possible, and never with bare fingers. Attach electrical leads to the ph meter by carefully inserting the connector and giving a slight twist. Making sure the meter is set to "mv", turn on the meter and connect the two leads (alligator clips) to one another. A voltage reading of zero should result. If not, use the calibration knob to set the voltage to zero. Digital meters usually autozero by itself. Attach one lead to the end of the strip of zinc metal, the other lead to the strip of silver metal and make sure that the metal strips remain dipped in solution. If the voltage is negative, reverse the leads to obtain a positive voltage. Measure the instantaneous cell voltage and record two more readings immediately after that. Take the average of the three as the measured cell potential. At this point, the silver electrode is acting as the cathode (i.e., reduction is occurring at the silver metal). Leaving the connection to the silver electrode intact, move the other lead to the other metals in any sequence you wish and take reading. Obtain voltage values for all possible combinations of two metals. Convert your readings to volts (if you have been taking them in millivolts) and use the Nernst equation to find half-cell potentials for the Zn 2+ /Zn and Cu 2+ /Cu half-cells. Remember, Ag + /Ag half-cell as the reference, assuming it to be the cathode, with a potential of E o red = + 0.80 V (+0.7993 V to be exact). Table 1. Determination of Reduction Potentials. Cell # Electrode 1 (Cathode) Reduction Electrode 2 (Anode) Oxidation 1 Ag Zn 2 Ag Cu 5 Zn Cu E cell (V) Measured E o cell, (V) Nernst E o cell(v) Standard Explanations First, identify the anode (Ox) and cathode (Red) and place them in proper columns. Placement shown in table may not be correct. E o Cell Nernst is obtained from the Nernst equation, (E o Cell Nernst = E cell, Measured + (0.0591/n) log Q). This is the non standard cell potential. You must write a balanced redox reaction to find n. E o Cell Standard is the standard cell potential = E o ox + E o red. Standard potentials are listed in Table 2 as obtained from table of standard reduction potentials in your textbook. 212 Echem Experiment_Text/7/12/11 5
Table 2. Calculated standard reduction potentials Half Cell Reaction E o red (V) E o red (V) Percent error Non standard Table value Ag+ + e - Ag +0.7993 na Cu 2+ + 2e Cu +0.339 Zn 2+ + 2e Zn -0.762 Note: Knowing the E o cell, Nernst from Table 1 and given the E o Ag/Ag+ one can calculate the nonstandard reduction potential. B. Verification of Nernst equation for Cu/Cu 2+ half-cell by changing [Cu 2+ ] Measure cell potentials for all Cu/Cu 2+ (0.1, 0.01, and 0.001 M) // Ag + (0.10 M)/Ag cells. You should have three measurements for three different copper concentrations (0.1, 0.01, and 0.001M). For the overall cell reaction: 2Ag + + Cu (s) Cu 2+ + 2Ag (s), according to Nernst equation: E cell = E o cell (0.0591/2) log ( [Cu 2+ ]/ [Ag + ] 2 ) a plot of E cell vs. log ( [Cu 2+ ]/ [Ag + ] 2 ) should be a straight line with a slope = -0.0295 V (per tenfold change in concentration) and an intercept, E o cell. By knowing standard reduction E o for Ag/Ag + and the E o cell, you can calculate the standard reduction potential for Cu/Cu 2+. Compare the calculated value with that of the literature. 212 Echem Experiment_Text/7/12/11 6
C. Determination of Formation Constant, K f, of Cu(NH 3 ) 4 2+ Aqua Complex In this experiment you will use the cell: Ag/Ag + (0.10 M) // Cu 2+ (0.10 M)/Cu for the above measurement. Measure the cell potential as you have done earlier to ensure the cell is working. With a graduated cylinder, add 5.0 ml of 6.0 M NH 3 into the copper solution to form a deep blue complex. Stir the solution with a glass rod to mix well and measure the new cell potential. The free [Cu 2+ ] in the cell after complexation can be calculated from the cell potential by using the Nernst equation. Calculation of K f The formation of the complex is given by the reaction Cu 2+ (aq) + 4 NH 3 (aq) Cu(NH 3 ) 4 2+ (aq) K f = [Cu(NH 3 ) 4 2+ (aq)] / ([Cu 2+ (aq)] x [NH 3 (aq)] 4 ) Here, we have added excess NH 3 so that initial [Cu 2+ ] = [Cu(NH 3 ) 4 2+ (aq)] at equilibrium. The free [NH 3 (aq)] can be obtained from mass balance and the free [Cu 2+ (aq)] can be obtained from Nernst equation as follows: Cu 2+ (aq) NH 3 (aq) Cu(NH 3 ) 2+ 4 (aq) 5.0 ml, 0.1 M 5.0 ml, 6.0 M Initial mols (M x V) 0.10 x 0.005 = 0.0005 6.0 x 0.005 = 0.03 0 Equilibrium mols To be calculated 0.03-4 x 0.0005 = 0.028 0.0005 Equilibrium conc., M Use Nernst and Cell Pot 0.028/0.01 = 2.8 0.0005/ 0.01 = 0.05 Total volume = 10.0 ml or 0.01 L Assuming the following cell reactions: Oxidation : Cu Cu 2+ + 2e E o ox = 0.34 V Reduction : 2Ag + + 2 e 2Ag E o red = + 0.80 V The measured cell potential is, E cell = E o cell (0.0591/2) log ([Cu 2+ ]/[Ag + ] 2 ). Given, E o cell = E o ox + E o red and [Ag + ] = 0.10 M, one can solve for [Cu 2+ ]. Use this value of [Cu 2+ ] along with other equilibrium concentrations in the equilibrium expression to calculate the K f. Write your K f value on the chalkboard for the class to copy. Compare your result with that of the literature K f = 6.6 x 10 12. Waste Disposal and Clean Up Place two drops of concentrated HCl (or H 3 PO 4 ) into the Pb and Ag solutions, and stir briefly. Allow the solid formed to settle, and decant the solution into the drain. Place the solid slurries of PbCl 2 (or Pb 3 (PO 4 ) 2 ) and AgCl (or Ag 3 PO 4 ) into their appropriate containers in the hood. All other solutions may be rinsed down the drain. Return the metal strips to the containers near the balances 212 Echem Experiment_Text/7/12/11 7