Determining Avogadro’s Constant and Faraday’s Constant

List of Apparatus

Name of Apparatus

Quantity

Uncertainty

Electronic Stopwatch

1

±0.2s

Ammeter

1

±0.01A

Wires with crocodile clips

1

–

D.C power source

1

±0.01V

300cm3 Beaker

3

–

Copper strips

2

–

Sand paper

1

–

Graphite rod

2

–

pH probe/data-logger

1

±0.2

Electronic weighing balance

1

±0.001

DATA COLLECTION:
The electrolytic cell used in this investigation is illustrated in Fig 1:

Fig 1 Diagram of electrolytic cell used in investigation
In this investigation, a current is passed through the solution with copper as the cathode and graphite as the anode. After a set amount of time, the circuit is disconnected and the mass of the cathode is measured. Following which, calculations are made so as to determine the Avogadro’s and Faraday’s constant.
Qualitative Observations
When the D.C power source was turned on, bubbles were formed at the Graphite anode. As the reaction progresses, powdery substance gets suspended in the solution and a black solid deposits can be found at the bottom of the beaker and there is a visible decomposition of the graphite electrode. As the reaction progress, a pink layer of copper forms on the copper strip. The copper strip is originally brown in colour while the graphite electrode is black in colour. Eventually, as the graphite electrode decomposes, the graphite molecules will turn the copper (II) sulphate solution from blue to black in colour. However, when the copper sulfate solution is filtered, it is noted that there is a decrease in the intensity of the blue colour in the filtrate after the electrolysis. The initial pH of the solution is 2.75, after the electrolysis is carried out, the pH decreases to 2.10.
Data Collection
Constant variables

Time Interval/s(±0.2)

300

Voltage/V

4V

Current/A(±0.01)

0.25

Cathode

 

Trial 1

Initial mass/g (± 0.001 g)

1.315

Final mass/g (± 0.001 g)

1.279

Change in mass/g (± 0.002 g)

0.036

Chemical equation for reaction at the anode:
2H2O (l) O2 (g) + 4H+ + 4e– (aq)
Chemical equation for reaction at the cathode:
Cu2+ (aq) + 2e–  Cu (s)
Calculations for cathode

Calculations

Error Propagation

Change in mass(Cu) = 0.036g
Mols of (Cu) =
=5.7 x 10-4 mol
 
Number of mol of electrons-
Using mol ratio
Cu2+ (aq) + 2e–  Cu (s)
Number of mol of electrons =11.4 x 10-4
 
 
Charge flowing through circuit

Number of electron charges in circut=
Where is the elementary charge, the charge of one electron
Number of electron charges in circuit
=

Number of mol of electrons

Where L is the Avagandro’s constant
Equating the number of mols of electrons obtained form the copper mass data and the number of mol of electrons from the current-

Faraday’s constant =

= 67000 C

%±Δ Mol of Cu =
%±Δ Mol of Cu =
= 5.6 %
% Uncertainty of number of mol of electrons
=
% uncertainty of Mass(Cu) =5.6%
% uncertainty of number of mol of electrons =5.6%
%±Δ charge flowing in circuit =

Percentage error
Percentage error for Faraday’s Constant =
=
= 30%
Percentage uncertainty of faraday’s constant =5.9%
Percentage systematic error in Faradays’ constant =%error-%random error
= 24.1%
Percentage error for Avogadro’s Constant =
= 30%
Percentage uncertainty of Avogadro’s Constant =5.9%
Percentage systematic error in Avogadro’s Constant =%error-%random error
= 24.1%
Conclusion
In conclusion, the calculated value of Faraday’s constant is mol-1 and Avogadro’s constant is.
As seen above, the percentage error for both Faraday’s constant and Avogadro’s constant are both 30% and after subtracting the error due to instrumental uncertainty, the % systematic error obtained is 24.1%. This shows that the experimental values calculated differ greatly from the literature values, indicating that there has been a significant amount of systematic error, which has caused the calculated value to be much different from the literature value. As percentage error of both Faraday’s constant and Avogadro’s constant are much larger than their respective percentage uncertainties, this indicates that the sources of systematic error are significant and cannot be ignored
Evaluation

Type of error

Limitation

Improvement

Systematic

Oxidation of copper occurs naturally when the copper strip is exposed to oxygen and when it is heated in the oven. Even when sand paper is used to scratch off the layer of copper oxide on the surface of the, it is difficult to completely rid of all the copper oxide. The formation of copper oxide will affect the reaction when electrolysis occurs and will affect the change in mass of the copper electrode, which is the dependent variable in this experiment. Even when the copper strip is immersed in the copper (II) sulphate solution, after a period of time, it will eventually start to form a layer of copper (II) oxide which will not be involved in the electrolysis reaction. This will reduce the amount of copper which will undergo reaction, causing it to reduce the eventual calculated Faraday’s and Avogadro’s constant.

It is impossible to prevent the oxidation of copper from happening however, this systematic error can be minimised. Other than ensuring that the layer of copper oxide is scratched off by rubbing the copper strip excessively with sandpaper. The time for which the copper stays in the oven can be minimised or hair dryer can be used instead to blow the water off.

Systematic

When the graphite electrode starts to disintegrates as the reaction progresses, fragments of graphite will be dispersed throughout the entire solution. As copper (II) ions move towards the copper strip to plate it, some of the graphite fragments may end up attached to the copper strip as well and are unable to fall off as a layer of copper plates over the graphite fragments. This can be observed in the experiment when the copper strip is removed at the end of the experiment; black fragments of graphite are observed on the copper strip.

The graphite fragments would easily reach the copper strip mainly because they were quite near each other. Hence, the graphite fragments could easily move towards the copper strips and attach to them. In order to minimise this from happening, the experiment should be conducting in a 500cm3 beaker, with the copper strip and the graphite electrode held further away from each other. Also, the graphite electrode should be positioned below the copper strip so that as the graphite electrode disintegrates, the graphite fragments will simply sink towards the bottom of the beaker, hence it will be less likely for the graphite fragments to accidentally coat onto the copper electrode

Systematic

Fluctuations in the current. Whenever the 2 electrodes were moved, the current of the circuit changes. Hence, whenever the copper electrode was moved in order to be weighed, the current would fluctuate, resulting in an inconsistent current throughout the experiment. If the current deviates from the stated 0.25, the resulting Faraday’s constant and Avogadro’s constant will be affected as well. An increase in current will result in an increase in the Faraday’s constant and Avogadro’s constant calculated while a decrease in current will result in a decrease in the Faraday’s constant and Avogadro’s constant calculated.

In order to prevent fluctuations in the current as a result of the shifting electrodes, a retort stand can be used to hold the electrodes in place and prevent them from moving. This is much more reliable than just using hands to hold the electrode, resulting in a reduction in the fluctuation of the current
A rheostat can be used and included in the circuit in order to adjust the amount of resistance of the circuit so that the desired current can be achieved. As current is inversely proportionate to resistance according to Ohm’s law, the resistance of the circuit can be adjusted in order to ensure a consistent current of 0.3 throughout the experiment.

Systematic

Also, another source of systematic error in this experiment would come from the fact that, the reading on the ammeter does not indicate the actual electric current flowing through the electrodes and the electrolyte as this value may decrease due to power losses in the wires. That is the electrical energy would be converted to heat. However the resistance of the wires in the circuit was assumed to be negligible in this experiment for simplicity. This would lead to systematic error as we would consistently overestimate the magnitude of the current flowing through the electrolyte.

This error can be avoided if the values of the resistance of the wires as well as the internal resistance of the power source were known and included in the calculations made.

Systematic

The copper electrode may undergo a process called passivation[1] where the metal forms a protective layer on its surface to protect it from outer factors such as water or air to prevent corrosion. Such a protective layer will result in a high resistance which will lead to a voltage delay. This process may also occur on the graphite electrode.
During the reaction, in the presence of passivation, the initial rate of the increase in mass of the copper electrode will be slowed down; ultimately affecting the total gain in mass by the copper electrode, affecting the Faraday’s constant and Avogadro’s constant calculated.

This process of passivation can be removed by allowing the reaction to progress for 5 minutes to avoid a voltage delay. 5 minutes was chosen because too short a time will be insufficient to remove the protective layer on the electrode and too long a time will result in the disintegration of the graphite electrode even before the collection of data has begun. As mentioned above, if there is too much graphite fragments in the copper (II) sulphate solution, they may come into contact with the copper electrode and affect its final mass as copper ions plate over the graphite fragments on the copper electrode.

Random Error

Due to time constrains, only one set of data was collected. This will result in the fluctuation of the value of the Faraday’s and Avogadro’s constant.

In order to reduce the error, perhaps more sets of data can be collected, so that a graph of metal deposited against time can be plotted and the gradient will enable the determination of the two constants.

[1] Metal passivation-en.w,wikepedia.org/Passivation_(Chemistry). Accessed- 26/2/2014)