Chemistry Forum

xmaybexmemoriesx wrote: ↑Wed Oct 27, 2021 7:57 pm I think it's just a minor oversight. You seem to have left your reaction at the "midway" point, because most equations that contain negative coefficients result in some kind of mistake or incorrect answer due to the initial reaction not being properly or fully balanced.

The first equation can be balanced:

2 Fe₃+ + -1 e = 3 Fe₂+
2 Fe₃⁺ + -1 ^-1e = 3 Fe₂⁺

But because there is a negative coefficient [-1 e] in this equation, it needs to be reorganized further, this time to move the corresponding compound over to the opposite side of the reaction:

2 Fe₃⁺ = ^-1e + 3 Fe₂⁺
where e = 0.77

The second equation can also be balanced:

H₂O₂ = O₂ + 2 H+1 + 2 e-
H₂O₂ = O₂ + 2 H
where e = 0.68

Now, plug in your value for your Nernst equation electrochemical equation, which is used to determine cell potentials at non-standard conditions. There's a relationship between E∘cell and the thermodynamics quantities such as ΔG°(Gibbs free energy) and K (the equilibrium constant). In order to accurately calculate everything, we need to know if this is under "standard conditions" (i.e. 298.15 K), because this directly affects our values we plug into our formulas and how we calculate them. If the conditions under which we are calculating is not mentioned, we are to assume that it is under "standard conditions".
We can verify the signs are correct when we realize that n and F are positive constants and that galvanic cells, which have positive cell potentials, involve spontaneous reactions. Thus, spontaneous reactions, which have ΔG < 0, must have Ecell > 0.

ΔG∘ = −nFE∘cell 📖

This provides a way to relate standard cell potentials to equilibrium constants, since:

ΔG∘ = −RT ln K
−nFE∘cell = −RT ln K
OR
E∘cell = RT/nF ln K

The negative signs for the work indicate that the electrical work is done by the system (the galvanic cell) on the surroundings versus the idea of free energy, which is defined as the energy that was available to do the work.
It's worth recalling that the charge on 1 mole of electrons (n = 1) is given by Faraday’s constant (F).

Most of the time, the electrochemical reactions are run at standard temperature (298.15 K). Collecting terms at this temperature yields:

E∘cell = RT/nF ln K = (8.314J/K⋅mol)(298.15K)/n × 96,485C/V⋅mol ln K = 0.0257V/n In K
Where n is the number of moles of electrons.

Back to the Nernst equation - for historical reasons, the logarithm in equations involving cell potentials is usually expressed using base 10 logarithms (log), which changes the constant by a factor of 2.303"

E∘cell = 0 .0592V/n[*]logK[/color][/b] 📖, where n = 3 [due to the total number of electrons (e) in the two original equations we balanced at the very top]
E∘cell = 0.0592V/n [*] logK
= 0.0592/3 [*] log10^3
= 996.621 (it equals approximately 1000 with all the proper rounding throughout every step)
Therefore: K = 10^3 [or K = 1000]

You were originally using:

K = 10 [*]nE°(fem)/0,0592[/b] 📖 - I believe that is more for stable, standardized conditions; whereas the above equations appeared to be non-standardized with no specifics and were unstable as we had to reorganize and balance them out into equilibrium prior to being able to apply any constants/formulae.

Hopefully you arrive at the answer of 1 x 10^3 = 1000, which you mentioned is the answer in your textbook.

ChenBeier wrote: ↑Wed Oct 27, 2021 10:21 pm 996.6 is also similar as 1097,84 also not accurate to 1000.

anto007 wrote: ↑Thu Oct 28, 2021 3:06 am

xmaybexmemoriesx wrote: ↑Wed Oct 27, 2021 7:57 pm I think it's just a minor oversight. You seem to have left your reaction at the "midway" point, because most equations that contain negative coefficients result in some kind of mistake or incorrect answer due to the initial reaction not being properly or fully balanced.

The first equation can be balanced:

2 Fe₃+ + -1 e = 3 Fe₂+
2 Fe₃⁺ + -1 ^-1e = 3 Fe₂⁺

But because there is a negative coefficient [-1 e] in this equation, it needs to be reorganized further, this time to move the corresponding compound over to the opposite side of the reaction:

2 Fe₃⁺ = ^-1e + 3 Fe₂⁺
where e = 0.77

The second equation can also be balanced:

H₂O₂ = O₂ + 2 H+1 + 2 e-
H₂O₂ = O₂ + 2 H
where e = 0.68

Now, plug in your value for your Nernst equation electrochemical equation, which is used to determine cell potentials at non-standard conditions. There's a relationship between E∘cell and the thermodynamics quantities such as ΔG°(Gibbs free energy) and K (the equilibrium constant). In order to accurately calculate everything, we need to know if this is under "standard conditions" (i.e. 298.15 K), because this directly affects our values we plug into our formulas and how we calculate them. If the conditions under which we are calculating is not mentioned, we are to assume that it is under "standard conditions".
We can verify the signs are correct when we realize that n and F are positive constants and that galvanic cells, which have positive cell potentials, involve spontaneous reactions. Thus, spontaneous reactions, which have ΔG < 0, must have Ecell > 0.

ΔG∘ = −nFE∘cell 📖

This provides a way to relate standard cell potentials to equilibrium constants, since:

ΔG∘ = −RT ln K
−nFE∘cell = −RT ln K
OR
E∘cell = RT/nF ln K

The negative signs for the work indicate that the electrical work is done by the system (the galvanic cell) on the surroundings versus the idea of free energy, which is defined as the energy that was available to do the work.
It's worth recalling that the charge on 1 mole of electrons (n = 1) is given by Faraday’s constant (F).

Most of the time, the electrochemical reactions are run at standard temperature (298.15 K). Collecting terms at this temperature yields:

E∘cell = RT/nF ln K = (8.314J/K⋅mol)(298.15K)/n × 96,485C/V⋅mol ln K = 0.0257V/n In K
Where n is the number of moles of electrons.

Back to the Nernst equation - for historical reasons, the logarithm in equations involving cell potentials is usually expressed using base 10 logarithms (log), which changes the constant by a factor of 2.303"

E∘cell = 0 .0592V/n[*]logK[/color][/b] 📖, where n = 3 [due to the total number of electrons (e) in the two original equations we balanced at the very top]
E∘cell = 0.0592V/n [*] logK
= 0.0592/3 [*] log10^3
= 996.621 (it equals approximately 1000 with all the proper rounding throughout every step)
Therefore: K = 10^3 [or K = 1000]

You were originally using:

K = 10 [*]nE°(fem)/0,0592[/b] 📖 - I believe that is more for stable, standardized conditions; whereas the above equations appeared to be non-standardized with no specifics and were unstable as we had to reorganize and balance them out into equilibrium prior to being able to apply any constants/formulae.

Hopefully you arrive at the answer of 1 x 10^3 = 1000, which you mentioned is the answer in your textbook.

Thank you very much for your explanation, but some passages are obscure to me, perhaps I do not understand the meaning of the symbols you have used. What do you mean by this writing: [*]?