EK nerst equation Problem 993 almost to the end!

[GRod18]

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993. A concentration cell is created using silver electrodes and aqueous silver solution. The reduction half reaction for silver is

Ag + (aq) + e- -> Ag (s) E (naught) = 0.80

If the silver ion concentration at the cathode is 1 M, which of the following could be the silver ion concentration at the anode in a galvanic cell?

Answer is 0.1 M


Note: Nerst equation was given for this problem.
E = E(naught) -0.06 log (Q)

EK solution says

Electrons flow from the anode to the cathode in a galvanic cell. A concentration cell, which is a galvanic cell tries to even out the concentrations. therefore, the cation concentration in a concentration cell will always be greater at the cathode. The concentration cell will move electrons to the cathode to reduce the concentration in an attempt to even the concentrations in the half cells.. This can also be seen from the Nernst equation, where Q must be less than one for a positive potential.


I don't get how Nernst equation relate to this. For Q to be less than one it would mean that electromotive force is greater than standard electromotive force? this dosen't make sense to me.

this is what I take from this let me know if this is right, so in a galvanic cell electrons move anode to cathode, this in turn attracts Ag+ ions, and in order to balance out the changes, even more electrons will be attracted to the cathode, this goes in a cycle until both the silver ion in solution and the silver anode electrode is depleted??


Thanks in advance!

 

[Rabolisk]

OK, a concentration cell is a galvanic cell in which the two half-reactions are equal, just opposite. The cathode is the reduction of Ag+, and the anode is the oxidation of Ag. That is, the overall equation is Ag+ + Ag -> Ag + Ag+. This means that the standard reaction potential for this and any concentration cell is 0, because the two sides (cathode and anode) cancel out.

Now, if that's the case, how does one get any reaction? Remember that E(naught) describes standard concentrations, (everything 1M and 1 atm). We know that E changes as concentration (Q) changes through the Nernst eq. A spontaneous reaction has to have a positive E, which means that log Q has to be negative, which leads to Q being less than 1. Thus the concentration at cathode > concentration at anode.

Another way of thinking about this is that concentration cells work because of the unequal concentration at cathode and anode. Silver ion is being reduced at the cathode, and solid silver is being oxidized at the anode. The reaction stops when the concentrations are equal. In order for the reaction to occur, the ion concentration at the cathode had to be initially greater than that at the anode. Hope that helped!

There's no reason why electromotive force at any given condition cannot be greater than the standard electromotive force (E naught) per the Nernst equation. In fact, if you want a battery to go for longer, you would start out with greater concentration at cathode to provide an E that is greater than E naught.

 

[GRod18]

OK, a concentration cell is a galvanic cell in which the two half-reactions are equal, just opposite. The cathode is the reduction of Ag+, and the anode is the oxidation of Ag. That is, the overall equation is Ag+ + Ag -> Ag + Ag+. This means that the standard reaction potential for this and any concentration cell is 0, because the two sides (cathode and anode) cancel out.

Now, if that's the case, how does one get any reaction? Remember that E(naught) describes standard concentrations, (everything 1M and 1 atm). We know that E changes as concentration (Q) changes through the Nernst eq. A spontaneous reaction has to have a positive E, which means that log Q has to be negative, which leads to Q being less than 1. Thus the concentration at cathode > concentration at anode.

Another way of thinking about this is that concentration cells work because of the unequal concentration at cathode and anode. Silver ion is being reduced at the cathode, and solid silver is being oxidized at the anode. The reaction stops when the concentrations are equal. In order for the reaction to occur, the ion concentration at the cathode had to be initially greater than that at the anode. Hope that helped!

There's no reason why electromotive force at any given condition cannot be greater than the standard electromotive force (E naught) per the Nernst equation. In fact, if you want a battery to go for longer, you would start out with greater concentration at cathode to provide an E that is greater than E naught.

Thanks a ton!