[INeedSerotonin]

Hello

I was given two semi-reactions for a cell:

Ag⁺ + e^- ---> Ag°       E° = + 0.80 V
Sn²⁺ + 2e^- ---> Sn°    E° = - 0.14 V

The exercise asks me to find the electromotive force. I am confused, because I was taught that I should subtract the greatest E° by the smallest E°, so that would be 0.80 - (-0.14) = 0.94 V, right?

Ok, but what confuses me is that I tried to do it another way, but I didn't get to the same result.

I tried multiplying the first semi-reaction by two (getting E° = + 1.6 V) and inverting the second semi-reaction (getting E° = + 0.14V). Adding both equations now, I would get the following:

2Ag⁺ + 2e^- ---> 2Ag°       E° = + 1.60 V
Sn° ---> Sn²⁺ + 2e^-         E° = + 0.14 V

2Ag⁺ + Sn° ---> 2Ag° + Sn²⁺    E° = + 1.74 V

Why does one way give me 0.94 V, while this other way gives me + 1.74 V? I don't understand! Shouldn't they both be the same?

Thanks

[Borek]

I tried multiplying the first semi-reaction by two (getting E° = + 1.6 V)

Why?

[INeedSerotonin]

I tried multiplying the first semi-reaction by two (getting E° = + 1.6 V)

Why?

So I could obtain the overall reaction of the cell. By multiplying the first semi-reaction by two and inverting the second semi-reaction, I can cancel both "2e^-" on both sides.

[Borek]

Balancing the reaction doesn't change the voltage.

[mjc123]

Have you come across the equation ΔG° = -nFE°?
Energy is an extensive property, electrode potential is an intensive property.
If you were working out ΔG for the reaction of Ag⁺ and Sn, you would have to balance the electrons. But to get the cell voltage you don't have to.
So if you wrote the reaction as Ag⁺ + 1/2 Sn  Ag + 1/2 Sn²⁺, E° = 0.94V and ΔG° = -0.94F (I'm not working it out) J/mole of Ag⁺
But if you wrote it as 2Ag⁺ + Sn  2Ag + Sn²⁺, E° = 0.94V and ΔG° = -2*0.94F J/mole of Sn

[INeedSerotonin]

Thank you both for your answers!

Indeed I haven't come across that equation. I didn't know the concepts of extensive and intensive properties. Thank you.

So if I wanted to have a greater voltage in my cell, how would I do it? If I brought more copper wires between Ag and Sn, I think that the current would just divide itself, and there wouldn't be more electrons flowing through it. Isn't there a way to improve a cell?

If voltage is an intensive property, does it mean that it does not matter the size of my cathode and my anode? But if I have many more grams of Ag and Sn, wouldn't more electrons flow through it? If I connect them to other piles of Ag and Sn, wouldn't the voltage be greater? 

[Borek]

So if I wanted to have a greater voltage in my cell, how would I do it?

Simple answer: no way to do it. Or rather, the only practical and viable way is to combine cells in series.

There is a bit of leeway as the voltage of the cell depends on the concentration of active species (Nernst equation). In practice it is not a way of increasing teh voltage, rather the source of a problem, as voltage changes during the battery life cycle (redox reaction changes concentrations of ions involved).

If I brought more copper wires between Ag and Sn, I think that the current would just divide itself, and there wouldn't be more electrons flowing through it. Isn't there a way to improve a cell?

If voltage is an intensive property, does it mean that it does not matter the size of my cathode and my anode? But if I have many more grams of Ag and Sn, wouldn't more electrons flow through it? If I connect them to other piles of Ag and Sn, wouldn't the voltage be greater? 

You can make a large cell which will be able to provide higher current, but not a higher voltage. Intensive vs extensive again.