Galvanic Cell Assignment PDF

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This is a year 12 assignment on redox reactions and galvanic cells...

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IA2, Student Experiment                         How does the reduction of concentration in the anodic solution affect the voltage produced by a Galvanic cell?  Matthew Naicker Miss Baldwin 20/03/20    ~ Words: 1998

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Rationale  Galvanic cells are defined as electrochemical cells in which spontaneous oxidation-reduction reactions produce electrical energy (Rice University, n.d). In order to convert chemical energy into electricity, two cells are created with separate electrodes. Oxidation occurs at the negative electrode (anode), and reduction occurs at the positive electrode (cathode) (Singh, 2017). The flow of electrons from the anode to the cathode species develops a current, which creates voltage according to Ohms Law (AAC, n.d). Hence, the difference in cell potential generates electricity; this is known as the electromotive force (EMF) (Kuipers et al., 2019).  Various factors can affect the functionality of a galvanic cell, including temperature, the concentration of electrolytes, and surface area (Luu, 2018). As time progresses, most batteries decrease in effectivity as a result of electrolytes drying out, specifically, the anodic solution (Ather, 2020). Standard reduction potential is usually conducted under standard conditions: 25°C, electrolyte concentration of 1.000 mol/L and one atmospheric pressure (101 kPa) (Johnson, 2016). For this experiment, using the standard potential formula is impractical as the conditions did not match the ‘standard conditions’. Therefore, the Nernst Equation can be employed to determine the cell potential under non-standard conditions (Atkins, 2020). Hence, investigating the effect of reducing the concentration of the anodic electrolyte on voltage produced in order to emulate adying battery.   Al in an AlSO2-4 solution will be the anodic cell and Cu in a CuSO4 2- will be the cathodic cell. Thus the   half equations are:  E˚(V) = -1.68 V˚oxidation = Al3+(aq) + 3e– ⇌ Al(s) E˚(V) = +0.52 V˚reduction = Cu2+ (aq) + 2e− ⇌ Cu(s)             Figure 1.1: galvanic cell  Original Experiment  ractical, a galvanic cell was utilised As outlined by the Oxford Chemistry for Queensland Units 3 & 4 p to deduce the order of metals on the electrochemical series. Subsequently, a variety of phase boundaries or metal and metal ion half cells were utilised, resulting in different amounts of voltage produced (Shaik, 2020). This created the basis for the construction of the research question.  Research Question How does the concentration of the anodic solution (AlSO4 2-) in a galvanic cell affect the overall voltage produced by an aluminium-copper galvanic cell?  

  Modifications In order to complete this experiment and collect relevant and sufficient data, the original experiment was refined by: a) Focusing on the two electrodes and their respective electrolytes. This way the effect of the anodic solution concentration could more accurately be monitored. Thus, increasing the precision and validity of the data. b) Each trial was the same duration ( 5 ± 0.01 minutes), in order to mitigate any unreliability between trials. Consequently, this increases the reliability of the data. c) An ammeter was employed to obtain quantitative data, by measuring the standard electrode potential produced by the cell. Thus, calculations can be conducted from the data. i) Beakers used had an uncertainty of ±0.10 ml. Extended By: a) 5x5 modification was utilised. Five different conditions were tested, where conditions = different concentrations for the AlSO2- 4 solution: 1.000M , 0.750M , 0.500M , 0.250M ,  0.125M. (CuSO4 2- = 1M for all trials). Each condition was trialled 5 times, to ensure sufficient data collection and more precision and accuracy. b) Deducing the theoretical standard potential through the Nernst Equation. This results in a way to reduce percentage error and compare actual vs predicted data. Management of Risks a) AlSO2-4 is regarded as a strong irritant and CuSO4 2- is considered a ‘nontoxic’ solution (Meister, 2020). Therefore, proper lab safety procedures were followed, e.g - wearing protective eyewear and clothing. b) Disposal of solutions adhered to the Waste and Chemical Disposa l Rules  outlined by the Queensland Government - https://www.qld.gov.au/environment/pollution/management/waste/disposal  Qualitative Observation The voltage produced varied slightly between initial trials, depending on the depth of submersions for the cathode. A ruler was therefore used to have equal submersion of each electrode.  Raw Data  Table 1.1 - Raw Tabulated Data, the voltage produced per concentration of A  lSO42- Concentration   (M/L)



Voltage Produced (±0.01 V) 

AlSO4 2-

 Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

0.125M

 0.83

0.83 

0.83 

0.83 

0.83 

0.25M

 0.83

0.81 

0.81 

0.82 

0.82 

0.5M

 0.81

0.8 

0.8 

0.8 

0.8 

0.75M

 0.76

0.76 

0.76 

0.77 

0.76 

1.00M

 0.74

0.74 

0.74 

0.74 

0.74 

Ambient Temperature = 298.15 K Pressure = 101 kPa

 



  Processed Data The data was analysed to determine the relationship between decreasing concentration of the anodic solution and the voltage produced. Calculations of the data assist in answering the research question and determine the validity and reliability of the data (see table 1.2).  The absolute error of the measuring devices can be used to find percentage uncertainty. This represents the precision and reliability of the results produced. The Nernst equation can be used to determine the percentage error of the data, which exhibits the validity and accuracy of the data.    ample Calculations Table 1.2 - S Calculation

Example

Standard Electrode Potential 

V˚cell= V˚red− V˚oxid

Mean

μ = μ =

 0.52 - (-1.68) = 2.2 V˚cell.

Σ xi , where Σ = sum off, Xi all scores present, n = sample size  n 0.83 + 0.83 + 0.83 + 0.83 + 0.83  5

 = 0.83 Percentage uncertainty (Voltage)

absolute uncertainty ) * 100 measured value 0.01 (1M) → %uncertainty = ( 0.83) * 100 

%uncertainty =

(



= ± 1.20% uncertainty (V) Nernst Equation   

E˚(V) = + 1.68 Oxidation Reaction (flipped) = Al(s) ⇌ Al3+(aq) + 3e–   − E˚(V) = + 0.34 Reduction Reaction = Cu2+ (aq) +  2e ⇌ Cu(s)   (aq) + 3e– + Cu(s)  E˚(V) = + 2.20 Net Reaction = Cu2+(aq) + 2e−+Al(s) ⇌ Al3+  Balance for moles of electrons: E˚(V) = +1.68 = x2 → 2Al(s) ⇌ 2Al3+  (aq) + 6e–     E˚(V) = +0.34 = x3 → 3Cu2+  (aq) + 6e− ⇌ 3Cu(s)    (aq)+ Reduced Redox Reaction = 2Al(s) + 3Cu2+  (aq) ⇌ 2Al3+  3Cu(s)  By manipulating the standard free energy equation (under standard state) - ΔG = ΔG˚ + RT ln(Q), the Nernst Equation may be derived:  Veq = V˚cell −

RT zF

* ln(Q)

 Where:  Veq = Theoretical voltage for cell V˚ cell = V˚red−V˚oxid  = 2.2  R = universal gas constant = 8.314 J.K-1.mol-1 

T = temperature, nb. in Kelvin = 298.15 K  n = transfer of valence electrons = 6  F = Faraday's constant = 96485 C.mol-1   [C ]c *[D]d Q = reaction quotient → a b  [A ] *[B ] 

RT zF * ln(Q), in this form this infers a theoretical  proportional logarithmic relationship where Veq ∝ln(Q)  By manipulating the above equation, it can be derived: Veq = V˚ - 0.0257 * log(Q) 

Note, while Veq = V˚cell −

z

 [C ]c *[D]d Q= a b [A] *[B ]

2

Al3+ ] [  → 2+ 3 [Cu ]



∵Q  =

[1]2 3 [ 1]

= 1

 ∴ Veq = 2.2 = 2.2 range  2 0.83−0.83 = 2

Mean Uncertainty

−

0.0257 6

* log(1)



= μ ± 0.00

| actual − predicted | * 100  predicted | 0.83 − 2.2| = * 100  2.2 = 62.27%

Percentage error

Note, all sample calculations use data → 1M AlSO2 4    Table 1.3 - Display of Sample Calculations AlSO 4 2- 













Concentration (M)



1

0.75

0.5

0.25

0.125

Q



1

0.563

0.250

0.063

0.016

2.200

2.201

2.203

2.205

2.208

Theoretical (Nernst) % Error



66.364

65.380

63.588

62.905

62.405

Mean (V ± 0.01)



0.74

0.76

0.80

0.82

0.83

Mean Uncertainty



0

0.010

0.005

0.005

0

1.35

1.31

1.25

1.22

1.20

Percentage Uncertainty (%)

Note. average percentage uncertainty = ± %1.27

Graph 1.1 - Average Voltage produced per concentration

  Graph 1.2 - (Nernst Equation) Theoretical Voltage produced per concentration

  Graph 1.3 - Theoretical and Actual Data VS Concentration





Graph 1.4 - Linearising Theoretical Function to Validate Theory

  Trends, Patterns & Relationships Graph 1.1, reveals the trend that as the concentration of anode solution increases, the voltage produced decreases. Subsequently, the variation in concentration from 0.125M to 0.25M causes the most significant change in voltage as every following change has a less dramatic effect. This can be attributed to the apparent inversely proportional relationship. So, the trend seems to plateau towards an asymptote. This supports the theory, Veq ∝ln(Q).  Graph 1.2, is the theoretical standard electrical potential of the solution as determined by the Nernst Equation. It exhibits similar patterns to Graph 1.1. Furthermore, it displays a precise inversely proportional relationship (R2 1), and a trend that as the concentration of anode decreases, the voltage increases. This further represents the theory, Veq ∝ln(Q).  Graph 1.3, was created to exhibit the difference in the actual vs theoretical data. Although both  results depict the same trend with high R2 values, there is a large discrepancy in the two results. Consequently, there is a large percentage error (see limitations), which shows a lack of validity in the recorded data.  Graph 1.4 employs log linearisation to assess the theory Veq ∝ln(Q). As seen in graph 1.4, there is a linear trend with an extremely high R2 value ( 0.9936) therefore, validating the inversely proportional relationship between Veq ∝ln(Q).  Limitations - Reliability and Validity of the Experiment The limitations and reliability and validity of the results are displayed in Table 1.4. Table 1.4 - Limitations and Analysis of Reliability and Validity of Data Limitations

Reliability and Validity

Discrepancy in the actual VS theoretical data (graph 1.3)

There was a large difference between the actual vs predicted data. This is possibly attributed to extraneous variables changing as the test was being conducted. In order to quantify this, percentage error was calculated.

The average percentage error = 64.12%. This is extremely high and shows a lack of accuracy and validity in the results.

Extraneous Variables:

Galvanic cells can be affected by

The percentage error (64.12%),

Electrode crust, ambient various variables. The electrodes temperature and salt bridge. are subject to rusting or residue build-up, which can affect the standard electrical potential (BBC, 2020). The ambient temperature could have changed during the experiment, affecting the voltage produced. As temperature has a significant effect on the voltage potential (Johnson, 2016). Furthermore, the level of concentration in the salt bridge may affect the voltage produced, as the water can evaporate over time. This inhibits the experiment, as bridge acts as a stabilizer by maintaining electrical neutrality (Dr Allen,2015).

can most likely be attributed to these extraneous factors. Thus, once again, showing a lack of validity and reliability in the data retrieval process.

Measuring devices (ammeter and making solutions)

Due to systematic errors, like the effect of the external circuit affecting the voltage produced. The percentage uncertainty = ±1.27%. Furthermore, the solutions had an uncertainty of ±0.10 ml. Consequently, the experimental process lacks reliability due to systematic errors.

There was a slight variation in the voltage produced. There was an average percentage uncertainty of ±1.27% This is attributed to the ammeter being imprecise and external circuit resistance (Whitting, 2015). Creating solutions manually can lead to inaccuracies and lowered validity.

 Conclusion Overall, the results depict changing the concentration of the anodic electrolyte does affect the voltage produced by the cell. It appears as the anodic electrolyte concentration increases towards equal concentration of the cathodic electrolyte, the voltage produced decreases logarithmically. This supports the theoretical relationship between the concentration of electrolytes and voltage, as modelled by the equation Veq∝ln(Q). This equation was validated in graph 1.4, which linearised the equation. Subsequently, the data produced a linear function with a high R2 , and therefore, the relationship between the concentration and the voltage is inversely proportional. Therefore, as Q is dependent on concentration when the concentration of the anodic solution is decreased, the voltage should increase.  The relationship between concentration and voltage is expounded by research conducted by J. Chandler in Assessment of electrochemical properties of a galvanic system  (2015). When lowering the anode concentration (AlSO4 2- ) concentration, the reaction is shifted to the right and places further out of equilibrium, due to Le Châtlier's Principle (Atkins, 1994). See reaction here: 2Al(s) + 3Cu2+(aq)



⬇2Al3+ (aq)+  3Cu(s)

 Consequently, there is a larger potential difference between half cells, and so the longer the cell is being reduced, the more voltage can be produced (University of Alabama, 1959). Therefore, the relationship shown in graph 1.1, can be attributed to creating a larger EMF due to an increased difference in the concentration gradient.

  On average, the percentage uncertainty of the results were ±1.27%. This Is a systematic error, which can be attributed to the ammeter which had an uncertainty of ±0.01. Additionally, there is a mean uncertainty range of ±0.00 to ±0.01 (Table 1.2). Therefore, the low level of uncertainty shows reliability and accuracy in the data collected. However, regarding the validity, the data is quite weak, due to an average percentage error of 64.12% (random and systematic error). This indicates the collected data differs substantially from the theoretical data. Consequently, lowering the validity of the experiment. As a result, the findings are precise; however, they lack accuracy.  Ultimately, the results display the expected theoretical relationship between concentration and voltage produced in a galvanic cell. Subsequently, the research question can be answered, that the concentration of anodic (AlSO4 2-) solution in an aluminium-copper galvanic cell affects the voltage produced by an inversely proportional relationship. Therefore, as concentration increases, the voltage logarithmically decreases. However, there are limitations and lack of validity in the data, but, overall, can be considered reliable. Therefore, the experiment can be refined to increase validity.  Extensions and Improvements Table 1.5 - Extensions and Improvements  Analysis

Improvements & Extensions

Systematic Error Ammeter absolute uncertainty

To alleviate this: - run more trials until a consistent measure is achieved. Use more precise and quality measurement tools. This lowers the uncertainty and increases accuracy and reliability.

Random Error Salt Bridge moistness and electrode crusting

This can be diminished by: - cleaning the electrodes - re-moistening the salt bridge between trials. Hence, each trial has similar conditions, Consequently, validity and precision are increased.

Random error Changing Ambient Temperature

This can be mitigated by: - conducting all the trials simultaneously or at one period in time. Consequently, reducing the extraneous variable, and increasing the precision and validity of the results.

Systematic Error Concentrations of electrolytes

This can be reduced by improving the experimental process: - using pre-developed solutions of 1M, 0.75M, 0.50M 0.25M and 0.125M. Opposed to personally developing solutions. Consequently, there is a higher level of reliability and accuracy of the results.

Extension Investigate higher electrolyte concentrations

 



Testing increased anode concentrations may validate the findings, as it was deduced the difference in cell concentration effects voltage. For example, comparing 2M anodic electrolyte VS 1M cathodic.

References  Atkins, P. (2020). Nernst Equation. Retrieved 13 March 2020, from https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/El ectrochemistry/Nernst_Equation  Brady, J. (2019). Voltaic Cells. Retrieved 19 March 2020, from https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/El ectrochemistry/Voltaic_Cells  N.a, n.d, Can the concentration of the salt bridge be anything for this experiment to work?. (2020). Retrieved 21 March 2020, from https://www.enotes.com/homework-help/galvanic-cell-you-change-concentration-one-307505  Chandler, J. (2015). Assessment of electrochemical properties of a galvanic systems. Molecular Biotechnology, 3( 1), 75-75.  Hardwood, N. (2019). Batteries: Electricity though chemical reactions. Retrieved 4 March 2020, from https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/El ectrochemistry/Exemplars/Batteries%3A_Electricity_though_chemical_reactions  Johnson, J. (2016). The Effect of Temperature and Concentration on Galvanic Cells. Yr 12 EEI, 3.33(1).   Kuipers, K. (2020). Chemistry For Queensland Units 3 & 4  (1st ed.). Australia: Oxford University Press.   Luu, S. (2018). Factors Effecting Voltage of Electrochemical Cells. Retrieved 22 March 2020, from https://www.ukessays.com/essays/chem...