Data Collection and Processing
Raw data:-
- Initial mass of anode (zinc electrode): 31.29 ±0.01g
- Initial mass of cathode (copper electrode): 32.05 ±0.01g
Table 1 – Mass of anode and cathode obtained from different time intervals
Note*
- Uncertainties:
The average reaction time was ±0.5s even though it did alter from interval to interval. Note that there is also a ±0.01s time uncertainty in the stopwatch itself. The uncertainty for mass is inscribed on the top pan balance as well.
Data Processing:
We must now calculate the mass changes which have taken place due to experimenting with different time intervals. (Different time intervals would result in a different mass change)
This can be calculated simply by doing the following:
Mass change = final mass – initial mass
Due note however that this formula can only be used for calculating the mass change taking place at the cathode (copper electrode where reduction takes place). This is because copper 2+ is being converted to copper metal and is being deposited at the cathode. Obviously this would result in a mass gain at the cathode. Therefore, it would be better for us to use the formula ‘Mass change = final mass – initial mass’ so that it gives us a positive value for the mass change taking place at the cathode.
Example 1
Mass change = final mass – initial mass
=> 32.08 – 32.05
=> 0.03g
Example 2
Now to calculate the mass change taking place at the anode (zinc electrode), we use the following formula, Mass change = initial mass- final mass. In this case we use this formula because we know that the zinc is being oxidized to zinc 2+ leading the zinc electrode to corrode. This therefore results in a decrease in mass of the anode (zinc electrode). Thus, it would be better for us to use the formula ‘Mass change = initial mass - final mass’ so that it gives us a positive value for the mass change taking place at the anode.
Mass change = initial mass - final mass
= > 31.29 – 31.27
= > 0.02
Table 2 –Mass changes of anode and cathode for each time interval
Graph 1:-
Graph 2:-
To derive the equation for the two separate reactions, the number of electrons gained or lost during the process has to be deduced.
The mass change per minute can be deduced from the gradient. Therefore we first calculate the gradient of graph 1 (mass changes for zinc electrode). For calculating the gradient, find two points which perfectly fits in the grid. In this case, the points (0.04. 100) and (0.08, 200)
Gradient= (Y2 – Y1) ÷ (X2 – X1)
= (0.08- 0.04) ÷ (200 – 100)
= (0.04) ÷ (100)
= 0.0004
Therefore, the gradient of the first graph is 0.0002. So the mass change per minute for the anode is 0.0004.
Next, we calculate the gradient of graph 2 (mass changes for copper electrode). To find the gradient, we work with the points (0.20. 500) and (0.24, 700)
Gradient= (Y2 – Y1) ÷ (X2 – X1)
= (700 – 500) ÷ (0.24- 0.20)
= (200) ÷ (0.04)
= 0.0002
Therefore, the gradient of the first graph is 0.0002. So the mass change per minute for the cathode is 0.0002.
The uncertainties also need to be propagated through the summation of the fractional uncertainties.
Uncertainties regarding zinc electrode:-
Fractional uncertainty of mass = absolute uncertainty ÷ actual value
= 0.01 ÷ 0.02
= 0.500
Fractional uncertainty of time = absolute uncertainty ÷ actual value
= 0.21 ÷ 300
= > 0.0007 = 0.001
Total uncertainty = 0.001 + 0.500 = 0.501 to 3 decimal places
Therefore the rate of change is 0.004 ± 0.501 g/s
Table 3 – Rate of change for each time interval for anode (zinc electrode)
To calculate the number of electrons in zinc electrode, the following equation may be used:-
Number of electrons = molar mass ÷ mass of electrode (mass of one of the samples)
= 65.37 ÷ 31.27
= 2.09
Therefore, this would be the half-equation which would occur at the cathode:
Zn→ Zn2.09+ + 2.09e-
Due to the loss in a bit more electrons compared to the theoretical formula, it would be a stronger reducing agent therefore the electrode potential would be lower (more negative) than that of the original value. Nevertheless, the electrode potential cannot be determined.
Uncertainties regarding copper electrode:-
Fractional uncertainty of mass = absolute uncertainty ÷ actual value
= 0.01 ÷ 0.03
= 0.333
Fractional uncertainty of time = absolute uncertainty ÷ actual value
= 0.21 ÷ 300
= > 0.0007 = 0.001
Total uncertainty = 0.001 + 0.333= 0.334 to 3 decimal places
Therefore the rate of change is 0.002 ± 0.334 g/s
Table 3 – Rate of change for each time interval for cathode (copper electrode)
To calculate the number of electrons in copper electrode, the following equation may be used:-
Number of electrons = molar mass ÷ mass of electrode (mass of one of the samples)
= 65.50 ÷ 32.08
= 2.04
Therefore, this would be the half-equation which would occur at the cathode:
Cu2.04+ + 2.04e- → Cu
Due to the gain of a bit more electrons compared to the theoretical formula, it would be a slightly weaker oxidizing agent therefore the electrode potential would be slightly lower than that of the original value. Nevertheless, the electrode potential cannot be determined.
Conclusion
My results show that as the duration/ time intervals increase, the mass of the anode (zinc electrode) decreases and the mass of the cathode (copper electrode) increases. We can see that there is a strong positive correlation between the time it takes for both electrodes to change in masses. If the duration is longer, then more electrons flow from the zinc electrode to the copper electrode (anode to cathode) through the electrical wires, while ions flow through the salt bridge to complete. As we know, in a voltaic cell/ galvanic cell, oxidation occurs at the anode (negative electrode) where as reduction occurs at the cathode (positive electrode). Primarily, zinc is oxidized at the anode and converted to zinc 2+. This causes corrosion at the zinc electrode due to the metal being converted to ions thus the mass of the zinc electrode (anode) decreases. On the other hand, copper undergoes reduction at the cathode and the copper 2+ ions get converted to copper metal. This causes the copper metal to be deposited at the cathode thus leading to the copper electrode (cathode) to increase in mass as the duration is increased. The following anodic reaction takes place at the zinc electrode (this is the theoretical equation):-
Zn (s) → Zn2+ (aq) + 2e-
However the equation we found experimentally is:-
Zn→ Zn2.09+ + 2.09e-
Hence, this suggests that since the former zinc sample has more electrons to lose, it is an even stronger oxidizing agent compared to the theoretical equation and is slightly higher in the electrochemical series than the latter zinc samples.
According to the results that have been gathered, there is a positive correlation between the time it takes to electrolyse an aqueous solution and the rate of electrolysis. The rate of electrolysis was measured using the mass of cathode. If the duration of electrolysis is longer, then more electrons will flow through the circuit and more ions will flow from the anode to the cathode. Oxidation occurs at the anode whereas reduction occurs at the cathode. The cathode gains electrons therefore the mass decreases. The following reaction has taken place (although this is the theoretical equation):
Cu2+ (aq) + 2e- → Cu (s)
However, the experimental equation is:
Cu1.75+ + 1.75e- → Cu
Therefore this implies that since the former copper sample has more electrons to gain, it is a stronger oxidizing agent and it is lower in the electrochemical series than the latter copper sample.
The value of the electrode potential hasn’t been calculated, however, the number of electrons is 25% off there that shows that there is a great difference between the literature value and the experimental value. According to the graph in the previous page, there is a very strong positive correlation between the mass change and duration of electrolysis as can be deduced from the high R squared value. The change in mass over a certain period of time is very gradual because of the size of the electrons. Although a lot of electrons are able to flow through the electrolyte, there is not such a drastic change. By looking at the graph, almost all the error bars for the points touch the line of best fit which means the data is fairly accurate.
The theoretical mass of a copper electrode would be 31.75g. From the results that have been tabulated, the mass of a copper electrode is 36.21g.
The percentage error can be calculated using the following formula:
Percentage error = difference x 100
theoretical value
= 4.46 x 100
31.75
= 14.04%
This shows that although there is not such a big difference between the theoretical value and the experimental value.
Evaluation
