Voltage in a Cell: Factors

[justadream]

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I read somewhere that voltage is independent of the amount of stuff you have in your battery (assuming the concentration of reactants is the same).

But then why does linking up multiple batteries in series allow you to increase the voltage (by summing up the voltages of the individual cells)?

Aren't some batteries themselves made up of multiple small cells connected together? \

I know there must be some critical difference I am missing.

 

[The Brown Knight]

I think it's important to differentiate between the AMOUNT OF ELECTRODE MATERIAL and the NUMBER OF ELECTROCHEMICAL CELLS.

For a electrochemical apparatus, changing the amount of the metal in the electrodes won't affect voltage, as long as the metals don't run out (I'm not saying it doesn't matter AT ALL). Voltage provided by a single electrochemical apparatus depends on metal ion concentrations according to Nernst Equation.

Now when you have multiple electrochemical apparatuses providing voltage in the same direction and connected in series (as you mentioned), voltages provided add up. Here's a better mathematical explanation:
Nernst Equation: E = E0 - (RT/nF)ln Q
For two electrochemical cells you will be adding the voltages together: Etotal = E(cell 1) + E(cell 2) = E1 + E2 - (RT/nF)ln Q1Q2
For a single electrochemical cell you will be able to work with only one standard potential: Etotal = E1 - (RT/nF)ln Q1
Hence, even if the overall weight of both was the same, clearly it's better to have two cells in series (assuming you don't run out of electrode material and the Q's allow spontaneous reaction).

For the double cell above, even if you varied the electrode material (by which I mean the solid metal that doesn't appear in Q of Nernst Equation), you won't have a difference in voltage.

 

[justadream]

@The Brown Knight

Right I can see it in the formulas you presented but intuitively why is this?

Like if you have a certain amount of material for the anode and a certain amount of material for the cathode, why is it that if you separate that material into different cells it makes voltage higher?

Theoretically then, if you made more and more cells, you could have infinite voltage by just making more cells (and having less material in each one)?

 

[Teleologist]

@The Brown Knight

Right I can see it in the formulas you presented but intuitively why is this?

Like if you have a certain amount of material for the anode and a certain amount of material for the cathode, why is it that if you separate that material into different cells it makes voltage higher?

Theoretically then, if you made more and more cells, you could have infinite voltage by just making more cells (and having less material in each one)?

Voltage is potential difference. Another way to look at it is the "pressure" that electrons exert. Stringing together cells in series increases pressure (voltage). Two water pumps acting with each other have double the pressure of just one water pump.

 

[The Brown Knight]

I have a similar intuitive analogy as Teleologist:

Think of a battery as a pump pushing a bucket of water atop a slope; once it reaches top of the slope another pump does the same and pushes the water further up a second slope, so now it's even higher. In other words, the second pump will treat the water it receives as if it was on the ground and will push it with whatever ability it has. This can continue further with more batteries. One battery can push up only ONE slope, regardless of how thick your electrodes are.

It's true you can just make a battery with several cells in series; but if you compare a battery(1) with one cell and one battery(2) with several cells in series and if you keep the OVERALL MASS THE SAME for both, battery(2) will provide greater voltage but will run out MUCH sooner than battery(1). Ideally, of course, you'd want to use a battery with infinite cells in series with each cell containing infinite material. But realistically, you want to find a good compromise between voltage provided (number in series) and size of electrodes (electrode material).