How does the concentration, varied between 1 and 5 mol dm^-3, of ZnSO₄⋅7H₂O in the aqueous state in a Cu–Zn voltaic cell affect the electrode potential across the voltaic cell and how does this compare to theoretical values calculated by the Nernst equation?

I chose this experiment because in my IB Chemistry and Physics courses, I have explored the different types of cell; I was in particular interested in the lead-acid accumulator, because I was not expecting that simple chemicals could also act to create a voltage and a current, since I was only used to creating currents using “standard” electrical components. Indeed, due to my keen interest in electrical engineering, I have looked into several types of cell which can be created using chemicals and concluded that a voltaic cell could provide me with a very good method for this experiment to extend my knowledge on voltaic cells.

 

This experiment involves setting up a voltaic cell using two half-cells; one half-cell will consist of a  Copper electrode (inside a CuSO₄⋅5H₂O solution), which will act as a cathode, while the other half-cell will be a Zinc electrode (inside a ZnSO₄⋅7H₂O solution), which will act as an anode. This experimental apparatus will allow me to measure a current through a salt bridge filled with KCl, which will act as a path of exchange of ions for this redox reaction.

 

For the purposes of this exploration, I will modify the classical experiment and look at the relationship between the electrode potential (voltage) measured across the battery using a voltmeter when the concentration of ZnSO₄⋅7H₂O is changed from 1 mol dm^-3 in steps of 1 mol dm^-₃ until a concentration of 5 mol dm^-3 is reached. The electrode potential for each different concentration will be calculated and subsequently compared with the theoretical values obtained via the Nernst Equation. Moreover, the Nernst equation will be used to extend my set of data for small concentrations of ZnSO₄⋅7H₂O, where experimental data cannot be collected.

Electrode potential is defined by IUPAC as the electromotive force of a cell made up of two half-cells. Specifically, the Standard Cell Potential (E ^ꝋ_cell) is the difference of the two electrodes-

 

E ^ꝋ_cell = E ^ꝋ_{Red, cathode} - E ^ꝋ_{Oxi, anode}

 

If E ^ꝋ_cell > 0, then electrons flow from the anode (Zinc) to the cathode (Copper).

 

The redox reaction for a voltaic cell with Zinc and Copper is-

 

Zn(s) + Cu²⁺(aq)  → Zn²⁺(aq) + Cu(s)

 

The half-equations involved are-

 

Zn(s) → Zn²⁺(aq) + 2e^- Oxidation

 

Cu²⁺(aq) + 2e^- → Cu(s) Reduction

 

The Standard Electrode Potential for the reaction of Zinc is-

 

Zn²⁺(aq)+2e^- → Zn(s) = - 0.76 V

 

The Standard Electrode Potential for the reaction of Copper is-

 

Cu²⁺(aq)+2e^-→Cu(s) = 0.34 V

 

The most negative potential has to be reversed because they are reduction potentials, therefore

the Standard Electrode Potential for this reaction is E^ꝋ = 1.10 V 

 

In cell-diagram conventional notation, the voltaic cell can be written as-

 

Zn(s)_oxidation | Zn²⁺(aq) ‖ Cu²⁺ (aq)_reduction | Cu(s)

 

The half-equations show that the Zinc Sulphate loses electrons, which are transferred to the Zinc electrode placed inside it, which becomes negatively charged. The Copper electrode instead is positively charged since the Copper Sulphate solutions is electron-deficient. When a salt bridge (which acts as an electrically conducting path) is connecting the two electrodes, the electrons flow from the negative electrode to the positive electrode, creating an electric current. The final effect is that Zinc Sulphate loses electrons and Copper Sulphate gains electrons.

 

An experiment such as this one requires the use of a glass salt bridge, which is made from a U-Tube. It serves many functions, in particular that of completing the circuit by connecting the anode and the cathode. The choice of the chemical to be put inside of it is important. Potassium Chloride (KCl) is chosen because it is an inert electronic conductor, meaning it does not react with either the Copper Sulphate or the Zinc Sulphate, thus it does not introduce a new redox reaction into the experiment; it is also chosen because it keeps the overall charge of the cell neutral, because it provides enough negative ions to equal the positive ions being created at the anode (during oxidation) and it provides positive ions to replace the metal ions being used up at the cathode (during reduction).

In chemistry, concentration is defined as “the quantity of a solute that is contained in a particular quantity of solvent or solution”.

 

The most common unit of measurement of concentration is molarity (M), defined as the number of moles of solute present in exactly 1 dm3 of solution-

 

\(Molarity=\frac{\text{moles of solute}}{dm^3 \text{of solution}}\)         (Equation 1)

 

From the formula, it is clear that one way of changing the molarity of a solution and hence its concentration is by varying the moles of solute, which is the change that will be performed in this experiment.

 

The Nernst is used under non-standard conditions (i.e. when the cell potentials are not standard) and is an equation relating the measured cell potential E^⊝ in a voltaic cell to the reaction quotient, Q, measured as

 

\(Q=\frac{[Zn^{2+}(aq)]}{[Cu^{2+}(aq)]}\)          (Equation 2)

 

because the concentrations of solids are taken as 1.

 

This allows for the determination of the cell potential (voltage) under non-standard conditions, i.e. when the concentrations of the reactants are changing, such as in this experiment, where the concentration of Zinc was varied from 1 mol dm^-3 to 5  mol dm^-3 in progressive changes in concentration of 1 mol dm^-3.

 

The Nernst equation can be derived from the Gibbs Free Energy under standard conditions-

 

E^⊝ = E^⊝_reduction - E^⊝_oxidation      (Equation 3)

 

and

 

∆G = -nFE           (Equation 4) ,

 

which under standard conditions is

 

∆G^⊝ = - nFE^⊝          (Equation 5)

 

where n is the number of electrons transferred during the reaction, F is Faraday’s constant, 96 500 C mol^-1, and E is the electrode potential difference.

 

The change in Gibbs energy under non-standard conditions is related to the Gibbs energy change under standard via the equation

 

∆G = ∆G^⊝ + RT ln  Q          (Equation 6),

 

which is equivalent to

 

–nFE = - nFE^⊝+RTln Q          (Equation 7)

 

Finally, the Nernst equation can be obtained by dividing both sides by –nF, yielding

 

\(E = E⊝ - (\frac{RT}{nF})ln Q\)           (Equation 8) ,

I think that as the concentration of the Zinc Sulphate increases, and hence the value for Q also increases, the voltage measured across the cell will decrease.

 

Theoretically, I think this is because the Nernst equation predicts that the voltage E is proportional to ln Q, not to Q; that is-

 

E ∝ ln (Q)

 

This can be restated mathematically as E = k ln (Q) , where k is a constant. Comparing this formula to equation (6), we see that

 

\(k≡ - (\frac{RT}{nF})\).

 

As Q increases, so does the quantity ln Q . Since R, n, F and T are positive, the graph of E_cell vs. ln Q  is in the form y = mx + c with m, the gradient of the straight line, being negative.

 

I predict that the reason for why the Ecell is not indirectly proportional to ln Q  is because the standard electrode potential E^⊝ must be taken into account, which should roughly equal 1.10 V. This is the equivalent of saying that E^⊝ = 1.10 V. So, since the literature value is E^⊝ = 1.10 V, the value obtained from the experiment can then be compared with this value.

Independent variable

I am going to change the concentration of the solution around the anode (Zinc Sulphate), measuring it in mol dm^-3. I will initially start with 1 mol dm^-3, but then I will combine the Zinc Sulphate with water to progressively decrease its concentration (as less water is added, the concentration of Zinc Sulphate increases). I am aiming to have at least 5 different concentrations: 1 mol dm^-3, 2 mol dm^-3, 3 mol dm^-3, 4 mol dm^-3, 5 mol dm^-3. The mixing will be performed by calculating the Mr of the Zinc Sulphate – this is the Mr for 1 dm³, however, so I divided this value by 10 because I used 100 cm³ per trial. Then this value is measured using a weighing scale, and for other trials, for example when doubling the concentration, double the initial mass of the substance will be diluted with that same mass of water. The absolute uncertainty on the mass of the Zinc is ± 0.01 g.

 

Dependent variable

I will measure the electrode potential across the circuit after changing the concentration (which can be thought of as being the flow of electrons through the salt bridge from the Zinc to the Copper). The range of the electrode potential should be around 1.00 V < E < 1.15 V. The electrode potential is measured using a voltmeter and in Volts, with an absolute uncertainty of ± 0.001 V. I will determine this change using the Nernst equation because since I am changing the concentration, these values will not be for standard conditions.

 

Control Variables

• The surface area of the Zn and Cu electrodes. This has to be kept the same throughout the experiment, and both substances must have the same surface area because the experiment would otherwise be unfair since unequal amounts of electrons would be transferred from one metal to the other. The dimensions of both sheets were width 2 cm and length 8 cm, which were measured with a ruler and obtained by cutting with scissors through larger pieces of both samples of material. This was kept the same by using the same sheets of Zn and Cu electrodes throughout the experiment. The uncertainty in the length and width of both sheets is \(\Delta l=\Delta w=\pm0.5mm\) -
• The beaker size of the beakers containing solutions of ZnSO₄. 7H₂O and CuSO₄5H₂O. The height of the beakers is h_b = 6.4 cm and the width of the beakers is wb = 9 cm. This must be controlled because otherwise there could be different levels of solutions in the beakers– this would lead to an imbalance in the number of electrons transferred if one electrode is immersed in one solution more than the other– this means that the height of the solution inside the beakers must also be controlled-
• The volume of ZnSO₄.7H₂O and CuSO₄.5H₂O used has to be constant because there would be an imbalance in electron transferral otherwise. This will be kept constant at 100 cm³ and will be measured using volumetric flasks. The uncertainty in the volume is \(\Delta v=\pm0.10cm^3\)-
• The voltmeter used must be the same throughout the experiment because different voltmeters may have different absolute uncertainties and thus the experiment would be inconsistent. The uncertainty in the voltage is ∆V = ± 0.001 V, one of the systematic errors of this experiment-
• The chemical filling the salt bridge must always be the KCl and never another chemical. This is because KCl has the property that it is inert, hence it doesn’t introduce new redox reactions into the experiment; furthermore, the concentration of KCl must be kept constant because otherwise the salt bridge will not allow for an equal movement of ions from one half-cell to the other-
• The material of the plugs used to block the flow of KCl should always be the same (cotton) since different materials may allow for more of the KCl to leak into the solutions.

The temperature of the room around us will be monitored using a thermometer, and it should remain constant at around 25℃ by not changing the room in which the experiment is carried out. The uncertainty in the temperature is \(\Delta T=\pm0.05K\)

 

The pressure of the room around us will be monitored using a barometer and it should remain near constant by not changing room. The pressure was measured at 1.02 atm.

 

The humidity in the laboratory will be monitored using a hygrometer.

 

The Relative Humidity of the laboratory was around 45%, which is a suitable value.

 

Apparatus

• Salt bridge made from glass (a U-Tube) through which there will be a movement of ions
• Two cotton plugs which will be placed at the bottom of the opening in the salt bridge to stop the KCl inside from leaking into the ZnSO₄⋅7H2O and CuSO₄⋅5H₂O solutions
• Voltmeter connected in parallel to the whole of the battery (the battery is made from the salt bridge and the anode and cathode). The absolute uncertainty on the voltage is ∆V = ± 0.001V
• Zinc electrode– a thin sheet of zinc of width 2 cm and length 8 cm ±0.5 mm.
• Copper electrode– a think sheet of copper of width 2 cm and length 8 cm ±0.5 mm.
• Two glass beakers of a maximum capacity of 0.2 dm³ in which the ZnSO₄ and CuSO₄ will be placed. It is not important to know their uncertainty as they are only used to hold the solutions which have already been prepared and measured.
• Two glass volumetric flasks of maximum capacity 0.25 dm³, used to hold the solutions of Zinc Sulphate and Copper Sulphate. The absolute uncertainty on this capacity of liquid is ∆C = ± 0.015 dm³.
• Two wires to connect the voltmeter to the electrodes
• Pipette to fill the salt tube with KCl
• Two crocodile clips to connect the voltmeter to the wires in contact with the electrodes
• Weighing scale used to measure the mass of the chemicals used. The absolute uncertainty on the mass of the chemicals as measured by the weighing scale is ∆m = ± 0.01 g.

Chemicals

• 1 dm³ of 1 mol dm^-3 KCl used inside the salt bridge to fill it up
• 1 dm³ of 1 mol dm^-3 ZnSO₄ in the aqueous state; 0.1 dm³ of this will be inside a beaker
• 1 dm³ of 1 mol dm-3 CuSO₄ in the aqueous state; 0.1 dm³ of this will be inside the other beaker

1. The goal is to set up the materials as shown in the diagram below
2. Cut out one piece of Zinc and one piece of Copper from larger samples. Ensure that their dimensions are the same (as specified above) by measuring them with a ruler. This will further ensure that the same surface area of both electrodes is submerged in solution.
3. Place 100 cm³ of Copper Sulphate in one of the beakers and 100 cm³ of Zinc Sulphate in the other beaker. This will be measured by comparing the level of both solutions to the measurements shown on the beakers. Hence, by ensuring the levels stays the same, the electrodes should stay both equally immersed
4. Connect the wires to the voltmeter
5. Connect one of the crocodile clips to the Zinc sheet
6. Connect the other crocodile clip to the Copper sheet
7. Place the salt bridge outside both beakers, in such a way that it does not spill inside the solutions. The salt bridge should be filled with KCl and blocked at its openings solely using cotton plugs throughout the experiment.
8. Fill the salt tube with KCl using a pipette
9. Turn on the voltmeter and record the measurement
10. Repeat the experiment (steps 7-9) using a different concentration for Zinc Sulphate- this can only be done for positive values of ln (Q)
11. Calculate the electrode potential of the cell for negative values of ln (Q) using the Nernst Equation, solving for E.

Copper sulphate and Zinc sulphate are toxic solutions which can damage the natural environment, particularly the wildlife and water-based ecosystems in the vicinity of them. Therefore, they must be disposed of with care not by pouring them down the sink but instead by pouring them in the heavy metal and metal salts container. Subsequently, they will be disposed of following local regulations.

Anomalies have been highlighted and have not been considered for subsequent data analysis. The values for concentrations and for ln (Q) have not been quoted with uncertainties because they are variable.

The data from this table was collected using the formula E = E^⊝ - \((\frac{RT}{nF})\) ln Q  (Equation 8). The values of Q were selected such that the values of ln Q  extended onto the negative numbers. The values are quoted to three decimal places to match the experimental results.

When the KCl was being added, it was continuously leaking through the cotton barriers designed to stop it, hence I had to always add some more solution to the salt bridge in order for the reaction to occur. Moreover, the Copper Sulphate solution lost, over time, its blue colour and became more and more similar to a very light blue; this happened because of a movement of ions from the Copper half-cell to the Zinc half-cell. The problems with the salt bridge caused the voltmeter to record a voltage only when a lot of KCl was added; the voltage reading would shoot instantaneously from 0V to some reading between 1.040 V and 1.100 V, and then, when the salt bridge contained too little KCl, the voltage immediately returned down to 0 V. This is because, at insufficient levels of KCl, anions and cations stopped being exchanged by the half-cells.

The absolute uncertainty on the voltage was found by considering the number of decimal places with which the voltmeter delivered recordings for the voltage across the voltaic cell, which was three.

 

The uncertainty lies on the last digit, therefore ∆V = ± 0.001 V.

 

The absolute uncertainty on the measure electrode potential is variable, and was obtained by considering the range of electrode potentials measured in all five trials and dividing it by two, so for example for when the concentration of Zinc Sulphate was 5 mol dm^-3-

 

\(\Delta E=\frac{1.059-1.058}{2}=\pm 0.0005V\)

 

Consequently,

 

E = (1.0590 ± 0.0005) V

 

In calculating the uncertainty in [Zn²⁺(aq)], it must be considered that the standard 1 mol dm^-3 solution was created by taking an amount in g equal to the molar mass of ZnSO₄⋅7H₂O, that is 287.55 g mol^-1. The uncertainty on the molar mass of Zn²⁺(aq) is

 

\(\Delta m=\pm0.01g\)

 

This was combined with water which was placed in a 1 dm3 volumetric flask; the capacity of the volumetric flask had an uncertainty of

 

\(\Delta c=\pm0.015dm^3\)

 

Therefore, the percentage uncertainty in the concentration of 1 mol dm^-3 Zn²⁺(aq) is found by combining these two values. The percentage uncertainty is obtained via the formula-

 

 \(percentage \, \,uncertainty =\frac{absolute \, \,uncertainty}{absolute \, \,value}×100\)

 

Therefore, substituting the values-

 

 \(\% Δm[Zn2+(aq)] =\frac{0.01}{287.55}×100 = 3 × 10-3\%\)

 

\(%\Delta\)

 

The total percentage uncertainty is thus: % Δ_total = 2% + 3 × 10^-3 % = 2%

 

The above formula can be rearranged to get that the absolute uncertainty for the concentration of [Zn²⁺(aq)] is-

 

\(absolute \, \,uncertainty=\frac{percentage \, \,uncertainty \,× \,absolute \, \,value}{100}\)

 

\(\Delta_{[Zn^{2+}(aq)]}=\frac{2×1}{100}=\pm2×10^{-2}mol \, \,dm^{-3}\)

 

Therefore,

 

Zn²⁺(aq) = (1 ± 2 × 10^-2) mol dm^-3

 

The same procedure is found for finding the uncertainty in Cu²⁺(aq); the molar mass of CuSO₄⋅5H₂O is 249.677 g mol^-1-

 

\(\Delta_{[Cu2+(aq)]}=\frac{2×1}{100}\pm2×10^{-2}mol \, \,dm^{-3}\)

 

Hence,

 

[Cu²⁺(aq)]=(1 ± 2 × 10^-2) mol dm^-3

 

The values of ln (Q)  were found by using the formula ln \((Q)=In(\frac{[Zn^{2+}(aq)]}{[Cu^{2+}(aq)]})\)

 

For example, if [Zn²⁺(aq)] = 5 mol dm^-3, then ln \((Q)=In(\frac{5}{1})=1.609\) .

 

Since Q is calculated using the formula \(Q=\frac{[Zn^{2+}(aq)]}{[Cu^{2+}(aq)]}\), the uncertainty in the values of Q is given by-

 

\(\Delta Q=Q\sqrt{(\frac{\Delta[Zn^{2+}(aq)]}{[Zn^{2+}(aq)]})^2+(\frac{\Delta[Cu^{2+}(aq)]}{[Cu^{2+}(aq)]})^2}\)

 

Considering [Zn²⁺(aq)] = [Cu²⁺(aq)] =1 mol dm^-3, then

 

\(\Delta Q=1×\sqrt{(\frac{2×10^{-2}}{1})^2+(\frac{2×10^{-2}}{1})^2}=\pm3×10^{-2}\)

 

It follows that

 

Q = 1.0 ± 3 × 10^-2

 

The uncertainty in the values of ln (Q)  was calculated using the formula:  \(​ Q ± \Delta Q) = ln​(Q)\pm\frac{\Delta Q}{Q}\)

 

As an example, considering again [Zn²⁺(aq)] = [Cu²⁺(aq)] = 1 mol dm^-3, leads to

 

\(In(1\pm3×10^{-2})=In(1)\pm\frac{3×10^{-2}}{1}=0\pm3×10^{-2}\)

 

Regarding the theoretical data, it was calculated using the formula

 

\(E=E^ꝋ-(\frac{RT}{nF})In Q\)          (Equation 6)

 

taking T = 298 K, F = 96485 C mol^-1, R = 8.31 J mol^-1 K^-1 and n = 2.

 

For example, for Q = 0.2 ln Q = -1.609 and

 

\(E=1.10-(\frac{8.31×298}{2×96485})×-1.609=1.11V\)

 

The temperature in the room was measured using an analogue thermometer. Being an analogue device, its uncertainty is found by considering its smallest division (0.1 K) and diving that by two; therefore: ΔT = ± 0.05 K.

 

The data obtained using this method have no uncertainty, since they are all calculated assuming an exact value of Q.

It can be concluded from the raw data and the graphs that as ln (Q)  increases, E decreases, and vice versa. This is shown as follows: for E = 1.091 V, ln Q = 0; but for E = 1.0590 V, ln Q = 1.609. Furthermore, it is clear from both graphs that the two variables have an inverse relationship, as the result of both plots is a straight line with negative slope. This is because, plotting a graph of E_cell against ln Q , a straight line with r² = 0.9989 is obtained.

 

Since 0 ≤ r² ≤ 1, where 1 denotes a fit which perfectly denotes the data, it is presumable that this type of curve is a very good fit for the points obtained.

 

This is explained using ideas similar to Le Chatelier’s Principle; considering the half-equation for Zinc: Zn(s) ⇌ Zn²⁺(aq) + 2e- as an equilibrium system, it is evident that increasing the concentration of Zn²⁺ will shift equilibrium to the left, so that the forward reaction becomes less favourable. Hence, the value for the electrode potential of the cell decreases since there is less tendency for Zn to oxidise and form ions which will then conduct electricity.

 

Moreover, as the reaction goes on, [Zn²⁺(aq)] in the anode increases, because the Zinc electrode is dissolving, releasing ions, while [Cu²⁺(aq)] in the cathode steadily decreases, as the Copper is deposited on the electrode. This means that 

\(Q=\frac{[Zn^{2+}(aq)]}{[Cu^{2+}(aq)]}\) increases, therefore the cell potential decreases. During the course of the experiment, the value of

Q increases further, leading to a steady decrease in the value of E_cell.

 

However, it cannot be said that they are inversely proportional, because there is a y - intercept equal to 1.091 V. The percentage error of the experimental data compared to the accepted values can be calculated using the formula-

 

For ln Q=0:  percentage error = \(\frac{|1.091-1.100|}{|1.100|}×100=0.8%\)

 

This is not a very significant error, which suggests that the method used in this investigation was suitable in obtaining accurate values. It must also be considered, however, that the absolute uncertainty in the value E = 1.091 ± 0.001V does not make this experimental value lie within the theoretical value (they are not concordant), suggesting that the value obtained is not accurate. This error is mostly attributable to systematic uncertainty in the experiment: this is because random uncertainty was mostly contained by performing several trials for each concentration, while systematic uncertainties such as contamination of the ZnSO₄. 7H₂O and CuSO₄. 5H₂O solution by the KCl as well as the uncertainty in the voltmeter will have contributed to the experimental value not being concordant with the theoretical value.

The above analysis strongly suggests that my hypothesis was proven to be correct; I was able to correctly predict the relationship and correlation between my variables. The validity of my hypothesis is further enhanced by the fact that I had stated that the y-intercept would signify that the two variables are not inversely proportional, and this has turned out to be the case. However, to make an even stronger hypothesis I could have used a more convincing argument from the point of view of chemistry in support of the strong negative correlation between electrode potential and ln Q .

 

The procedure I followed also has its merits. First of all, having the possibility to compare my experimental values with theoretically calculated values was an advantage because it allows for comparison of the two methods and to calculate the percentage the error involved in this kind of experiment, as shown in the conclusion above. Moreover, I believe that taking five trials for each different concentration improved my method because it allowed for a lot of data to be used to produce graphs and it reduced random errors. Other strong points of the method I used include the fact that although I was using potentially dangerous chemicals, I was able to easily comply with safety measures and overall, I believe that the experiment was safe, as I didn’t find any risks for my safety throughout.

 

From the experimental data emerged several anomalous results. There are various reasons as to why these might have occurred. For example, the random error in the measurements of the mass of the solutions by the top-hand balance might have contributed. This, in turn, may have been caused by the slight variation in the amount of water added to the solutions, which is limited by the uncertainty on the volumetric flasks. These errors could have been reduced by using different equipment with smaller uncertainties, such as a measurement transducer.