the experiment to Determine Faraday’s Constant through Electrochemistry

The aim of this experiment report is to provide a comprehensive description of water electrolysis, including the collection and measurement of the gaseous oxygen and hydrogen released, as well as the pressure and temperature at the electrodes. The number of moles, electron moles, current, and coulombs calculated from the products evaluated. The moles of electrons that were used to calculate the F- value from water hydrolysis to determine the Faraday’s constant value. Second, the galvanic cell’s electromotive force (emf) was calculated and compared to the referential potential of silver/silver ion (Ag/Ag+). And thirdly, the measured emf of galvanic cell potential compared to the referential literature potential values. The Lab Report of the experiment to Determine Faraday’s Constant through Electrochemistry
Introduction
Electrochemistry is an interplay between chemical reactions and electricity particularly in solutions. The electrolysis of water produces both oxygen and hydrogen gases which can be utilized as an alternative source of energy. The decomposition of water molecules requires energy to produce the products. The equation below illustrates the decomposition of water to oxygen and hydrogen gas in an endothermic reaction.
2 H2O (g) ( 2H2 (g) + O2 (g) ( H= 285.84 kJ/mol (endothermic)
The endothermic implies that the external electrical source of energy is required to drive the production of oxygen and hydrogen gases as products(Cullen & Pentecost, 2011). The produced hydrogen gas requires being stored in specialized high pressured reinforced tanks or as a condensed liquid in insulated containers which are expensive compared to the current liquid fuels such as gasoline and ethanol.

In the lab, the experiment of producing hydrogen is a relatively cheap and straightforward (electrolysis of water), since acidified water, inert platinum electrodes source of electricity and means of gas collection are only required.

Figure 1: illustrations of the apparatus used for water electrolysis in the lab.
From the figure above, it can be noticed that for every two moles of hydrogen gas collected/ produced only one mole of oxygen produced. The indication of twice the volume of hydrogen gas compared to oxygen confirms. The selected platinum electrodes are unreactive; thus, they are not reduced or oxidized or reduced in the progress of the experiment. The value of Faraday’s constant was determined from the number of moles of electrons(Hirose, 2001). Faraday’s constant is equal to the amount of charge contained in 1 mole of electrons. As established, 1 electron has a charge of 1.602 x 10-19 coulombs ©. Thus, the charge carried in 1 mole could be calculated.

1 F = (6.02214 x 1023) x (1.60218 x 10-19 C) = 96485 C (96485 C/mole)
1 mole of electrons charge of 1 electron

The Faraday’s constant was determined experimentally, through the known number of moles of charge (one) and the total amount of charge (Q) in coulombs. The formula for calculating the value of Faraday’s constant can be expressed as F = Q/ne.
The amount of the total charge was determined through the known electric current (I) and the total time (t) of the flow of current. The amount of charge that flows via a wire per second is coulombs per second or merely the electrical current. The current in amperes can be expressed in the formula of I (amperes) = Q (Coulombs)/ time (seconds).
Therefore, the Q (Coulombs)= time (seconds) x I (amperes) Q- the total charge. Most often charge is constant
In the cathode reaction of water electrolysis results to the production of hydrogen gas due the reduction of H+ collected using water displacement technique to enable calculation of the total number of moles of electrons. The hydrogen gas volume was determined through reading the gas level inside the burette considering the space that space that was initially in the burette graduated scale as the burette’s dead volume
The ideal atmospheric pressure P atm is the pressure of the gas inside the burette. However, water vapor reduces the contribution of H2s towards the total pressure as the weight of water suspended inside the burette. The calculation of hydrogen pressure was achieved through the formula; PH 2= Patm – PH2O vapor – P suspended. The atmospheric pressure recorded at the barometer, vapor pressure of water and suspended pressure calculated by measuring the height of the sodium sulfate solution. The suspended pressure can be converted as
P suspended (torr) = height (mm) x 0.73555923 (torr/mm)
The ideal gas law, the adjusted pressure, and the total gas volume was then used to calculate the number of moles of gas collected. The number of moles of electrons was also determined to utilize the reaction that occurred at the cathode and the ngas.
The galvanic cell (example a non-rechargeable battery) has the positive charge at the cathode. The galvanic cell is electrochemical whereby the reduction-oxidation reactions taking place spontaneously within the cell derive electrical energy. A typical galvanic cell comprises two pieces of metal each immersed each in a solution composed of the dissolved salts of the corresponding. Then the two separate solutions are connected to each other through a porous that allows ions to diffuse through but prevents them from rapid mixing.

Figure 2: Diagrammatical representation of a galvanic cell
Galvanic cell converts chemical energy in redox reactions into electrical energy, comprising of an electrochemical cell.
Materials and methods
The required materials include rubber squeeze bulb, 50 ml gas burette, burette clamp, 250ml beaker, ring stand and 10ml volumetric pipette. Also, pipette helper, low voltage power supply, the current sensor, stopwatch, barometer, ruler, wires were required.
Procedure A
The burette’s stopcocks were opened and raised the leveling bulb to an extent at which the burettes were filled by the electrolyte solution. Then the stopcocks were closed, and current turned on and adjusted to 0.1-0.2 amperes. The electrolyte solution was then saturated with oxygen and hydrogen gases by passing current through the apparatus for 2 minutes. The stopcocks were then opened after turning off the current and then raised the leveling bulb again to fill the burette with the electrolyte solution. The stopcocks were closed, and current turned on and the time was noted precisely when this was done. The process of electrolysis was carried out until 40 mL of H2 was collected then turned off the current recording the time taken to collect the 40 ML of hydrogen gas. The volume for both O2 and H2 were measured. The temperature of the electrolyte solution was also measured and also recorded the barometric pressure. Lastly, we obtained the vapor pressure of water at the temperature of the electrolyte solution for a table reference. The data of time the current was turned on and off, current, the volume of H2 and O2 collected, electrolyte temperature, barometric pressure and vapor pressure of water were tabulated.

Procedure B
The electrochemical cell was rinsed several times with distilled water before the solutions were added to each compartment of the cell. The metal electrodes were immersed into the solutions, and then black lead from the voltmeter was connected to electrode A. the red wire was then attached to electrode B. The readings were recorded and the next combination followed on various electrode/solution pairs.

Results
Part A
Time current turned on = 265.95
Time current turned off = 322.62 minutes
Current: 66 Amps final 62
Volume of H2 collected -Initial =1.3 mL Final 31.0 mL
Volume of O2 Collected – initial = 1.2 mL Final 15.8 mL
Electrolyte temperature = 21.6o C
Barometric pressure – initial =756 mmHg final =753 mmHg
Vapor pressure –initial = 756 and final 753

Part B
Experiment Solution A Electrode A Solution B Electrode B Volts DCV ∆Eo standard potentials 1 Cu2+ Cu Zn2+ Zn -1.04 20 + 1.10 2 Pb2+ Pb Cu2+ Cu 0.45 20 -0.96 3 Fe2+ Fe Zn2+ Zn -0.48 20 0.08 4 Sn2+ Sn Cu2+ Cu 0.55 20 0.197 5 Cu2+ Cu 0.1MKCl Ag wire -0.04 20 0.891 6 Pb2+ Pb 0.1MKCl Ag wire 0.37 20 0.428 7 Zn2+ Zn 0.1MKCl Ag wire 1.0 20 -0.206 8 Sn2+ Sn 0.1MKCl Ag wire 0.50 20 0.414 9 Fe2+ Fe 0.1MKCl
(+0.334) Ag wire
(0.222) =0.554 0.49 20 0.44
Table 2: showing the E cell measured and the calculated E cell from Ag/Ag+ and their respective percentage Errors
Experiment E cell measured E cell calculated from Ag/Ag+ Error 1 2 3 4 Table 2: showing the E cell measured and the calculated E cell from H2/H+ and their respective percentage Errors
Experiment E cell measured E cell calculated from H2/H+ Percentage Error 1 -1.04 + 1.10 94.5% 2 0.45 -0.96 46.9% 3 -0.48 0.08 6% 4 0.55 0.197 27.9% 5 -0.04 0.891 4.4% 6 0.37 0.428 86.5% 7 1.0 -0.206 485.5% 8 0.50 0.414 120.7% 9 0.49 0.44 111.36%
Calculations
96,500/ mol = F = C/ mol
2 H2O (g) ( 2H2 (g) + O2 (g)
Total Charge in Coulombs = time in seconds x Current (Amperes)
Time in seconds = final – initial = 322.62-265.95, = 56.67 minutes
Change time from minutes to seconds 56.67x 60 seconds
= 3400.2 seconds
217.61C = 3400.2 s X I (A)
I (A) = 0.06399917 A = 64 x 10-3 Amperes
Volume of Hydrogen Gas collected = final – initial
31.0 mL – 1.3 mL
29.7 mL of H2 gas collected
Ideal gas law equation PV = nRT = n = PV/RT
Pext = PH2 + P H2O
PH2 = Pext – PH2O = 753 mmHg – 19.9 mmHg
Pressure of H2 gas = 733 mmHg
ngas H2 = (733.1 mmHg*133.322 Pa x 29.7* 10-6 m3)/ (R x temperature in Kelvin= (21.6+273))
= (733mmHg*133.322 Pa x 29.7* 10-6 m3)/ (8.31441JK-1 mol-1* 294.6K)
Number of moles of H2 gas = 0.001184944moles
Calculating the number of electrons, 1 mole = 6.02214 x 1023 electrons
0.001184944moles moles =?
Number of electrons = 7.135902 * 1020
1F = Number of electrons * charge per electrons
(7.135902 * 1020) *(1.60218 x 10-19 C)
F = 96485

Discussion
Electrochemistry is often interested in the number of electrons that have flow through a cell in association to the products formed and the mass of the reactants consumed. Whats measured in the lab is current and not charge, with current = charge/ over time. From the equation with a known current and time, then the charge can be calculated. 1 ampere (A) = 1 Coulomb (C) per second and thus the equation can be rearranged to calculate the time taken to get specific charge given current or total charge.

Faraday’s constant can be derived from converting the charge to a number of electrons since the Faraday’s constant is defined from coulombs of 1 mole of electrons. With the faraday’s constant being estimated to be 96,485 C mol-1, F can be calculated by multiplying the charge on one electron (1.602 x 10 -19) by Avogadro’s constant (6.22x 10 23).
Balanced equations are used in stoichiometry to calculate charge. For instance, the cell of Zn | Zn 2+ || Ag+ | Ag, = Zn (s) + 2 Ag+ Zn 2+ + 2 Ag (s)
From this equation, the number of electrons that flow per Zinc is 2, Oxidation-reduction reaction.
Zn (s) Zn 2+ + 2 e- (Oxidation)
Ag+ + 2 e – 2 Ag (s) (Reduction)
The number of electrons from the above reaction is 2, illustrating that for every mole of Zinc reacting, it produces two moles of electrons. Since every mole has (F) coulombs of charge,
For electrochemical cell of Cu | Cu2+ | Cu, the reaction taking place at the anode
Cu(s) Cu2+ (aq) + 2e Eo red = 0.34 V
The two half-cell equations at the cathode and anode are
Cu2+ +2e- Cu(s) (Cathode)
Cu(s) Cu2+ +2e- (Anode)
At the cathode, the reaction that took place was the reduction reaction that did not produce solid copper but the reduction of hydrogen ions to produce Hydrogen gas as the equation below
2 H+ (aq) + 2e- H 2 (g)
The measurement of emf of the electrochemical cell is carried out by the following formula.
Eo cell = Eo red (cathode) – Eo red (anode)
In a Galvanic cell, -spontaneous Eo red (cathode) is always more positive than Eo red (anode)

Conclusion

Reference
Cullen, D. M., & Pentecost, T. C. (2011). A model approach to the electrochemical cell: An inquiry activity. Journal of Chemical Education, 88(11), 1562–1564. https://doi.org/10.1021/ed101146u
Hirose, K. (2001). A Practical Guide for the Determination of Binding Constants. Journal of Inclusion Phenomena and Macrocyclic Chemistry, 39, 193–209. https://doi.org/10.1023/2FA-3A1011117412693