The net reaction in a voltaic cell with Eºcell= +.726V
2Fe^3+(aq) + 3Zn(s) --> 2Fe(s) + 3Zn^2+(aq)
What is the delta Gº for this reaction at 25ºC
I tries using this equation:
delta G = -nFEºcell
= -n(90485)(.726)
However, I don't know how to calculate n in this. I understand that n= # of electrons tranfered but how do you calculate that?
One way is to write the two half reactions.
Fe^+3 + 3e ==> Fe(s)
Zn(s) ==> Zn^+ + 2e
======================
The first reaction was multiplied by 2 and the second by 3 for a total of 6 electrons.
So you just multiply by the coefficients of the 2 half reactions?
then let's say if you had:
Cu^2+ + Zn ==> Cu + Zn^2+
this would give you 1 electron?
or if you had
Mg + 2AgNO3 ==> 2Ag + Mg(NO3)2
this would give you 2 electrons? because one of the reactions is multplied by 2 and the other by 1?
this would give you
Yes and no. It's ther total number of electrons in the reactions. For the reaction in question, you had a total of 6e gained for Fe (after multiplying by 2) and a total of 6e lost by Zn after multiplying by 3. To complete this perhaps I should have just added the two equations together to show you. Here they are again.
2*(Fe^+3 + 3e ==> Fe(s))
3*(Zn(s) ==> Zn^+2 + 2e)
============================
Now multiply and add to get this.
2Fe^+3 + 6e + 3Zn(s) ==> 2Fe(s) + 3Zn^+2 + 6e
Then the electrons cancel and we never see them again but that is the total number of electrons. You have 6e on one side and 6e on the other.
For the Cu and Zn example you gave, your conclusion is wrong because it isn't the coefficient that you use. It's the total number of electrons. The Cu(II) gains 2e and the Zn loses 2e so the total number of electrons is 2.
Cu^2+ + Zn ==> Cu + Zn^2+
The Mg/AgNO3 example you gave is correct. The total is 2 electrons.
Thank you so much! I understand now!
To calculate the value of "n" in this equation, you need to consider the balanced chemical equation of the reaction. The stoichiometric coefficients of the species participating in the reaction represent the ratio of moles of each species reacting.
In the given reaction:
2Fe^3+(aq) + 3Zn(s) --> 2Fe(s) + 3Zn^2+(aq)
You can see that 3 moles of Zn solid react with 2 moles of Fe^3+ ions. Each mole of Zn loses 2 electrons, and each mole of Fe^3+ ions gains 2 electrons.
Therefore, the number of electrons transferred (n) in this reaction would be 2, as it is the coefficient of electrons in the half-reaction.
Now, let's calculate the value of delta Gº using the correct value of "n":
delta Gº = -nFEºcell
= -(2)(96485)(0.726)
Note: The constant 96485 is the Faraday constant, representing the charge of one mole of electrons.
Calculating this expression will give you the value of delta Gº for this reaction at 25ºC.