Calculate Jones Reductor Equilibrium Constants @ 298.15 K

[Big-Daddy]

Homework Statement

Give the reactions that take place when the following solutions are passed through a Jones-redactor (amalgamated zinc), and calculate the equilibrium constant at 298.15 K for each.
0.01 mol/dm3 CuCl2
0.01 mol/dm3 CrCl3
0.01 mol/dm3 NH4VO3 (pH =1)

Data:
Couple, E° value
Cu²⁺/Cu 0.34
Cr³⁺/Cr –0.74
Cu2+/Cu+ 0.16
Cr2+/Cr –0.90
VO₂⁺/VO²⁺ 1.00
Zn2+/Zn –0.76
VO²⁺/V³⁺ 0.36
TiO²⁺/Ti³⁺ 0.10
V3+/V2+ –0.255
Ag+/Ag 0.80
V2+/V –1.13
Fe3+/Fe2+ 0.77

Homework Equations

The usual equations - ΔG=-nFE, ΔG°=-nFE°, ΔG=-RTln(K).

The Attempt at a Solution

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So one redox equation going on for all cases is the Zn2+/Zn couple, E°=–0.76, Zn²⁺ + 2e^- ::equil:: Zn. The forward reaction will occur if E°[Zn²⁺/Zn]>E°[Couple j], where j is the couple which represents the redox equation occurring on the other side.

But how do I know which equation j will be, from all the different choices we get for each case? For example, in the first case, is it Cu²⁺ + e- -> Cu⁺, Cu⁺ + e- -> Cu, or Cu²⁺ + 2e- -> Cu which we need to consider as couple j against E°[Zn²⁺/Zn]? And how do we determine which equation we need to take for all three cases. I have seen the solutions but this question, of which one to choose of the possible equations, is not properly explained.

 

[nate808]

it is important to carefully consider the data given and use it to make informed decisions about which equations to use. In this case, the data includes the E° values for several redox couples, which can help us determine which reactions are likely to occur.

To start, we can look at the E° values for the Cu2+/Cu and Cr3+/Cr couples, which are 0.34 and -0.74, respectively. These values tell us that the Cu2+/Cu reaction is more likely to occur than the Cr3+/Cr reaction, as the E° value for Cu2+/Cu is more positive. Therefore, we can assume that the reaction occurring in the first case is Cu2+ + 2e- ↔ Cu, since this is the only reaction involving Cu2+ that has a positive E° value.

Similarly, for the second case, the E° value for the Cr3+/Cr couple is more negative than the E° value for the V3+/V2+ couple, which is -0.255. This means that the V3+/V2+ reaction is more likely to occur. Again, we can use this information to determine that the reaction occurring in this case is V3+ + e- ↔ V2+.

Finally, for the third case, the E° value for the V3+/V2+ couple is more positive than the E° value for the VO2+/VO2+ couple, which is 1.00. This means that the VO2+/VO2+ reaction is more likely to occur. Therefore, the reaction occurring in this case is VO2+ + e- ↔ VO2+.

Now that we have determined which reactions are occurring, we can use the Nernst equation to calculate the equilibrium constant (K) for each reaction at 298.15 K. This can be done using the E° values given for each couple and the equation ΔG° = -RTln(K). We can then use the equilibrium constant to calculate the standard free energy change (ΔG°) for each reaction, which can be used to determine the equilibrium constant at 298.15 K.

In summary, as a scientist, it is important to carefully analyze the data given and use it to make informed decisions about which equations to use in order to solve a problem. In this case, we used the E° values for each redox couple to determine which reactions