Measurement of the Charge on the Electron and the Gram Equivalent Weight of an Unknown Metal

Purpose

To measure the charge on the electron and the gram equivalent of an unknown metal.

Introduction

Gram Equivalent Weight

The gram equivalent weight (GEW) of a metal is the mass of the metal which reacts with or releases one mole of electrons in a redox reaction.   Consider the electrolytic cell below in which a metal M serves as the anode,   the cathode is made of copper, and the electrolyte is a dilute acid. 

Figure 1:  Electrolytic cell

The half-cell reactions are:                  

oxidation M(s) ® Mn+ + ne- (1)
reduction 2H3O+(aq)+2e-®H2(g)+2H2O(l)                (2)

At the anode, M is oxidized and it dissolves to form cations.  At the cathode hydronium ion is reduced with the formation of hydrogen gas. The number of electrons lost in oxidation must equal the number gained in reduction.  Therefore, to obtain the overall cell reaction, the oxidation half-reaction must be multiplied by two and the reduction half-reaction must be multiplied by n. The moles of electrons passed through the cell is 2n.   The overall cell reaction is

2M(s) + 2nH3O+ ® 2Mn+(aq) + nH2(g) + 2nH2O(l)                                                 (3)

The moles of hydrogen gas produced is  n and the moles of electrons passed is 2n. Therefore,

moles of electrons passed = 2 x moles of hydrogen gas formed                                         (4)

and

                                     (5)

and substituting (4) into (5) gives

                                     (6)

Thus, the GEW of M can be determined by measuring the mass loss of the anode, and the moles of hydrogen resulting from the cell reaction.  The detailed procedure for making these measurements is given below, and the apparatus is shown in Figure 2.

Figure 2: Experimental Apparatus

The Method

The hydrogen gas produced at the cathode is collected by displacing water in the inverted buret.  The moles of hydrogen gas is given by

(7)

                                                                                                

where PH2, VH2, and T are the pressure, in kPa, the volume, in L, and the temperature, in K, respectively, of the hydrogen gas. R is the gas constant, 8.31451 L kPa K-1 mol-1.

As shown in Figure 2, the gas pressure inside the buret is less than atmospheric.  If the inside pressure were equal to that of the atmosphere, the meniscus would be at the same level as the surface of the solution outside the buret. The pressure inside the buret, in kPa,  is

Pinside = Patm - dhg                                                                 (8)

where d is the density of the solution in kg m-3( assumed to be that of water, 1000. kg m-3), h is the height , in m, of the meniscus above the surface of the solution, and g is the acceleration of gravity, 9.81 ms-2.

The pressure inside the buret is due to hydrogen gas and water vapor.  Hence,

Pinside = PH2 + Pwater                                                           (9)

where Pwater is the vapor pressure of water, in kPa, at the temperature of the room. The pressure of hydrogen in kPa can be calculated by combining equations (8) and (9):

PH2 = Patm - dhg - Pwater                                                      (10)

The volume of hydrogen collected, VH2, is the total volume above the meniscus, and includes the volume labeled "V", in Figure 2.  The volume  "V" is "off-scale", and cannot be measured using the buret scale.  Its measurement is described in the Procedure.   The volume of collected hydrogen is given by

VH2 = V + 50.00 - (buret reading)                      (11)

where "buret reading" refers to the location of the meniscus on the buret scale.

 

The Charge on the Electron

The electron is a negatively charged subatomic particle found in all neutral atoms.  It was  discovered by the British physicist, J. J. Thomson in 1897.  The charge on the electron (symbolized by e, with units of coulombs),  was first measured by the American physicist, R.A. Millikan in 1909-1913.  Both Thomson and Millikan received the Nobel prize for their work.

The apparatus in Figure 2, can be used to determine the charge on the electron as well as the GEW of M.

We've  seen in equation (4), that the moles of electrons passed through the electrolytic cell, n e, is twice the moles of hydrogen produced.  The total electrical charge, q, in coulombs (C), passed through the cell is given by

q = I t                                                                                          (12)

where I is the average current during the electrolysis, in C s -1, (1C s -1is called an ampere), and t is the length of time in seconds that current is passing through the cell.  If  n e mole of electrons is passed through the cell, then the number of electrons passed is n e x NA.  Where NA is Avogadro's Number.  The charge on the electron is

 (13)

The current I is measured with the "meter" in Figure 2. 

Procedure

Note to Instructor:  Set the voltage on the lab DC power supply to 7 volts.

1. Students will work in pairs.  Obtain from the stockroom: a buret (an expensive item), a multimeter, wire and an unknown metal sample .   Weigh the metal to 0.001g and record its mass in your notebook.

2. Determine the volume of the uncalibrated portion of the buret ("V" in Figure 2) as follows:  Weigh to 0.001 g, a clean, dry 50 mL beaker and record the mass in your notebook. Add water to the buret, and drain it until the meniscus is exactly at the 50 mL mark.  The remaining water in the buret now fills the volume "V".  Carefully drain this water into the preweighed 50 mL beaker.  Drain only the water in volume "V", and  not the water in the tip.  Weigh the beaker plus water to 0.001 g and record.  The volume "V" is obtained by dividing the mass of water by its density. Make three measurements of "V".

3.  Assemble the apparatus shown in Figure 2.   Use a 250 mL beaker.  Make sure that all of the exposed copper wire (wire without insulation) of the cathode is inside the buret.  Also make sure that the buret stopcock does not leak.  Otherwise, some hydrogen gas will escape from the buret.

4.  Using a wire with an alligator clip connect the anode (unknown metal) to the negative terminal of the multimeter.  Connect the other meter terminal to the positive terminal of the DC power supply at your desk.  Connect the cathode( the wire going into the buret) to the negative terminal of the DC power supply.  

5. Into the beaker pour about 200 mL of a solution containing 0.1 M acetic acid and 0.5 M Na2SO4.  Do not allow the solution to come into contact with the alligator clip. Why ?

6.  Fill the buret with electrolyte solution as follows:  with the buret stopcock closed, attach one end of a piece of rubber tubing to the tip of the buret.  Attach the other end to an aspirator.  Turn "ON" the water through the aspirator, and slowly open the buret stopcock.   Draw solution into the buret until it is just filled.  Close the stopcock. Avoid drawing water into the tip.  Turn "OFF" the water and disconnect the tubing.

7.  Adjust your multimeter to read millampere (mA).   Use the range 0-200 or 0-250 mA.  You can measure the time with a wrist watch or the clock on the wall. Turn "ON" the current to your apparatus, and record the time in your notebook.  During the electrolysis, the current may fluctuate.  In order to obtain a meaningful average current you should record the current value at 5 min intervals. Continue the electrolysis until the volume of H2 collected is about 25 mL.  Turn "OFF" the current and again record the time.

8.  Once, the current has been turned "OFF",   read the buret to 0.01 mL, measure h, the height of the meniscus above the surface of the external solution, measure the temperature and the barometric pressure.

9.  Carefully disconnect the alligator clip from the unknown metal sample, wash the metal with deionized water, rinse it with acetone, let it dry on a paper towel for at least five minutes, and weigh it to 0.001g.

10.  Repeat the experiment at least once.

Data

A summary of the data to be collected follows:

1. initial and final mass of anode.

2. current at 5 min intervals

3. electrolysis time

4. final buret reading

5. height of solution column, h.

6. mass of water corresponding to the volume "V"

7. temperature

8. atmospheric pressure

Calculations

Clearly show your calculations of the following quantities for each trial.  Include units in your calculations, and specify the units of all calculated quantities.

1.  PH2

2.  the average value of "V"

3. VH2

4. moles of hydrogen

5. GEW of the unknown metal

6. Average current

7.  The charge on the electron

Sample Calculation

Conclusion

In your conclusion report:

1. The average GEW of your unknown metal.

2. The average value for the charge on the electron.   Compare your value with the accepted value.  What is your source of the accepted value?  What is the percent error of your value?

3. Why is it important that the alligator clip attached to the anode  not touch the electrolyte solution.