# Can the rate of reaction of a Voltaic/Galvanic cell be determined theoretically?

I am conducting a chemistry practical in which I measure the voltage of a Zn-Cu Voltaic cell over time.

Assuming that the surface area of the electrodes are known, concentration of reactants are known, wire resistance is known (Could assume negligible for simplicity). Is it possible to determine the rate of the reaction for this setup? Could I then determine respective concentration of reactants? This would enable the use of the nernst equation to determine theoretical voltage.

Many thanks,

• You deal with 2 independent things, thermodynamics, determining the Nernst equation, and kinetics, determining the electrode uquivslnce establishing and response to the load. The latter involves diffusion in free solution, diffusion in dielectric layer and kinetic rate of electrode reactions – Poutnik Oct 10 at 16:28

Since battery scientists got Nobel this week, this question is worth pondering. It is not a trivial question. However consider this question:

A car battery has 12 V, whereas 9 V cells are also common. If we connect two 1.5 V cells and one 9 V cell on series, one can generate 1.5+1.5+9 =12 V, yet this arrangement cannot start a car despite producing the same voltage.

What is so magical about the lead-acid car battery and this series arrangement? All this shows is that voltage and current produced by battery (which is the rate, hence kinetics and hence the rate of reaction) are two separate things. The main problem in batteries, the rate of electron transfer, is always a limiting factor as to how much current can be drawn from them. So far the lead acid battery is still one of the best because it has a very fast electron transfer rate unparalleled by other batteries. I do remember there was another Nobel Prize winner (Marcus?) who did a lot of work on electron transfer kinetics on the electrodes.

The Nernst potential you see for batteries is the potential when a very very small amount of current is drawn (ideally none) from the battery. This way of measurement of the potential is called null point potentiometry. Under those conditions, the rate of reaction is nearly zero because no current is being drawn from the battery.

In short one cannot measure the rate of the electrochemical reaction just from the Nernst potential because it heavily depends on the amount of current being drawn from the battery. Indeed a non-trivial problem worth someone's PhD.

• The rate of the chemical reaction perfectly correlates to the current drawn. Not sure if Farady got a doctorate for that, but they named the proportionality constant after him. ;) – Karl Oct 11 at 19:36
• Faraday never got a doctorate, masters or bachelors, but his experimental hand, ingenuity and original thinking was far better than hundreds of PhDs churned out by universities today. If you read Nature, time and again mention that enough PhDs please :-) If someone can figure out how to control, actually speed up, electron transfer kinetics battery science will make great progress. – M. Farooq Oct 12 at 0:00

You can very easily determine the rate of the reaction, its the current flowing in your wire, divided by Faradays constant.

If you want to ask what the maximum current of your battery is: That depends on which is the rate determining step in these:

• electron transport in wire (sure not)
• reaction at cathode
• reaction at anode
• transport of anion in electrolyte
• transport of cation

Chances are that it is one of the latter, i.e. the maximum reaction rate depends (in first approximation) simply on the diffusivity of the slower of your two ions and its charge.

Then you have to wrap that, together with the voltage and dimensions (electrode size and distance), into an equation, and I would guess you wont come out too far from reality.

If your electrodes are large and closely spaced or your electrolyte more concentrated, then the last nanometers at the electrodes become important. Thats more complicated, large books have been written about it.

• Ok, so we are supposed to estimate the limiting factor of the reaction and work from there? – NoBullshit Oct 11 at 7:30
• Obviously. The steps can only work together, so the slowest one determines the speed. – Karl Oct 11 at 19:29
• For short, the limit on the battery is either external resistance in the circuit, in which case the battery will have its nominal voltage. Or interval resistance, in which case the voltage of the battery will drop accordingly. – Stian Yttervik Oct 13 at 7:56
• @StianYttervik Each battery consist of two potential differences, connected by your external load (light bulb or whatever) and the electrolyte. If the resistance of the load is not much larger than that of the electrolyte, then you need to take that internal resistance into account. – Karl Oct 13 at 18:47