the measured cell voltages are supposed to be smaller than the theoretical cell voltages, but when I'm calculating the theoretical cell voltages they are smaller. And I don't know why I'm getting these. Can you please check if I'm doing it right. Thank you.
Measured Cell voltages
1) Zn|Zn^+2 (1M)| Cu|Cu^+2 (1M): 0.947
2) Cu|Cu^+2 (1M)| Zn|Zn^+2 (1M):-0.947
3) Fe|Fe^+2 (1M)| Cu|Cu^+2 (1M):0.703
4) Zn|Zn^+2 (1M)| Cu|Cu^+2 (0.1M):0.906
5) Cu|Cu^+2 (1M)| Cu|Cu^+2 (0.1 M):-0.0143
Theoretical Cell Voltage( my calculataions)
1) 0.42
2) -0.42
3)-0.11
4)-0.450
5)0.31
#5 you did it but the rest I'm not sure.
I don't know what you are using for Eo. Texts vary so the voltage calculated will vary. Here is how to do the first one using my values. You should substitute values from your text.
Zn ==> Zn^+2 + 2e Eo = 0.762 as written.
Cu^+2 + 2e ==> Cu Eo = 0.345 as written.
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Zn + Cu^2+ ==> Cu + Zn^2+ Eocell = 0.762 + 0.345 = 1.107 v calculated. Since the concns are 1 M we know Ecell is the same as Eocell; therefore, Ecell = 1.107
Note that I added an oxidn half rxn to a redn half rxn to arrive at the cell rxn; therefore, I added the oxidn half potential to the redn half potential to arrive at the cell potential.
#2 is -1.107v.
#3.
Fe^2+ ==> Fe^3+ + e Eo = -.771
Cu^2+ + 2e ==> Cu Eo = 0.345
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2Fe^2+ + Cu^2+ ==> 2Fe^3+ + Cu Eocell = -0.771 + 0.345 = -1.533 v and this cell is not spontaneous. As in #1 and #2, this is also at 1M concn for both; therefore, Ecell = Eocell.
By the way, I wonder why you have written the cell notation as you have. For example, I would have written #1 as
Zn|Zn^+(1M)||Cu^2+|Cu.
#4 is not 1M so I will do it as I described before.
Zn ==> Zn^2+ + 2e Eo = 0.762 as written
Cu^2+ + 2e ==> Cu Eo= -0.345 as written
----------------------------
Zn + Cu^2+ ==> Zn ^2+ + Cu Eocell = 1.107v. Then we correct for the fact that Cu^2+ is 0.1M and not 1 M.
Ecell = Eocell -(0.0592/2)log Q
log Q = (Zn^2+)(Cu)/(Zn)(Cu^2+)
Substitute Zn^2+ = 1M
(Cu)(s) = 1--that's the standard state for SOLID copper and it is 1 by definition.
(Cu^2+) = 0.1M
(Zn)(s) = 1 by definition.
log Q then is log (1*1/1*0.1 = log10 = 1
Ecell = 1.107 - 0.0296(1) = 1.077 v.
To troubleshoot the issue, let's first understand the concept behind calculating theoretical cell voltages.
The theoretical cell voltage is the difference in the standard electrode potentials of the two half-cells involved in the cell. It is calculated using the Nernst equation:
E°cell = E°cathode - E°anode
where E°cell is the theoretical cell voltage, E°cathode is the standard electrode potential of the cathode half-cell, and E°anode is the standard electrode potential of the anode half-cell.
Now, let's go through the calculations for each cell and compare them to the measured cell voltages:
1) Zn|Zn^+2 (1M)| Cu|Cu^+2 (1M):
The standard electrode potential of zinc (Zn^2+|Zn) is -0.76 V, and for copper (Cu^2+|Cu) it is +0.34 V. Therefore, the theoretical cell voltage would be:
E°cell = E°cathode - E°anode
E°cell = 0.34 - (-0.76) = 1.1 V (positive value)
The measured cell voltage is 0.947 V, which is smaller than the theoretical value.
2) Cu|Cu^+2 (1M)| Zn|Zn^+2 (1M):
Using the same standard electrode potentials as above, the theoretical cell voltage would be:
E°cell = E°cathode - E°anode
E°cell = 0.34 - (-0.76) = 1.1 V (positive value)
The measured cell voltage is -0.947 V, which is smaller than the theoretical value. However, the negative sign indicates that the current is flowing in the opposite direction, so it is possible that the measured value is correct.
3) Fe|Fe^+2 (1M)| Cu|Cu^+2 (1M):
The standard electrode potential of iron (Fe^2+|Fe) is -0.44 V. Using the standard electrode potential of copper (Cu^2+|Cu) as 0.34 V, the theoretical cell voltage would be:
E°cell = E°cathode - E°anode
E°cell = 0.34 - (-0.44) = 0.78 V (positive value)
The measured cell voltage is 0.703 V, which is smaller but close to the theoretical value.
4) Zn|Zn^+2 (1M)| Cu|Cu^+2 (0.1M):
The standard electrode potentials remain the same for zinc and copper. The theoretical cell voltage would be:
E°cell = E°cathode - E°anode
E°cell = 0.34 - (-0.76) = 1.1 V (positive value)
The measured cell voltage is 0.906 V, which is smaller than the theoretical value.
5) Cu|Cu^+2 (1M)| Cu|Cu^+2 (0.1 M):
In this case, both half-cells contain copper, so no net reaction occurs. Therefore, the theoretical cell voltage should be zero, which matches the measured value of -0.0143 V.
Based on the calculations, it seems like you have made an error in the calculation for cell 1 and 2. The correct theoretical cell voltages should be as follows:
1) Zn|Zn^+2 (1M)| Cu|Cu^+2 (1M):
Theoretical cell voltage = 1.1 V
2) Cu|Cu^+2 (1M)| Zn|Zn^+2 (1M):
Theoretical cell voltage = -1.1 V
I hope this helps clarify the discrepancy between the measured and theoretical cell voltages. Let me know if you have any further questions.