Electrochemical Potential

The last piece to understand about galvanic cells is exactly WHY they work and how cells differ from each other. 

Why cells work

To understand how cells really work, we need to remember that nothing gives away electrons. No positive nucleus has ever given away negative electrons.

What we really mean when we say that something gives away an electron is that it doesn’t fight very hard when something else tries to take an electron. In other words, sodium atoms do NOT give away electrons, but they also don’t hold their electrons very strongly, so they are likely to lose any time another element pulls on its electron.

Comparing what we commonly say and the truth side-by-side will give you a pretty clear picture of why we commonly (and intentionally) misspeak.

However, if we are going to understand galvanic cells in a meaningful way we need to consider the truth. For this we’ll consider these two half-reactions:

\(Zn^{+2} + 2~e^{-1} \rightarrow Zn\)

\(Cu^{+2} + 2~e^{-1} \rightarrow Cu\)

These two reactions are nearly identical. Both involve a +2 ion, pulling in two electrons to make a neutral atom.

If these two reactions are placed in the two beakers of a galvanic cell they will be pitted against each other - the copper trying to take electrons from the zinc and the zinc trying to take electrons from the copper. In simple terms, we will have created a chemical tug-of-war between the two elements for electrons.

Since different atoms are different, we can expect that one of these elements will pull more strongly than the other and will “win” the tug-of-war.

In this particular case, the copper pulls more strongly on the electrons and therefore it wins. That means that the zinc loses.

\(Zn^{+2} + 2~e^{-1} \rightarrow Zn\) -- Loser

\(Cu^{+2} + 2~e^{-1} \rightarrow Cu\) -- Winner

More specifically, instead of \(Zn^{+2}\) ions taking in electrons and making Zn atoms, the reaction will occur the other direction - Zn atoms will lose electrons and create \(Zn^{+2}\) ions. So, the two half-reactions that will actually occur are these:

\( Zn \rightarrow Zn^{+2} + 2~e^{-1}\)

\(Cu^{+2} + 2~e^{-1} \rightarrow Cu\)

Determining Who Wins

The question that may have occurred to you is “How do I know which reaction ‘wins’?”

The answer is actually pretty simple. Chemists, a long time ago, ran a massive tug-of-war tournament between LOTS of half-reactions and ranked them. This ranked list is called a Standard Reduction Potential Table.

To fully understand the table, we need to understand the title. We’ll do that in reverse order.

Table - this is simply an organized list. In this case the organization is based on strength (rather than the alphabet or some other feature). That can make it more difficult to find the half-reaction you are looking for, but the utility of having them in order outweighs those considerations.

Potential - This is the electrical measurement commonly called voltage. The physics definition for potential (amount of work needed to move a unit charge from a reference point to a specific point against an electric field - Britannica.com) is not terribly helpful for our understanding, so let’s come up with our own.

Potential can be thought of as the force with which electrons are moved through a wire. That’s not a perfect definition, and it probably causes pain in your physics teacher’s brain, but it will help us to understand that this is all about.

In a galvanic cell, each half-reaction is pulling on electrons. The potential recorded on the table is a measure of how hard the half-reaction is pulling. The reaction with the more positive potential will “win” and the reaction with the less positive potential will lose. The difference between the two numbers is the potential (or voltage) that will be measured in the wire.

Reduction - All half-reactions on the table are written as a reduction, that is all of them are taking in electrons. Just as in a tug-of-war, each is trying to take the electrons from the other. Even the losers are trying, just not as effectively.

Standard - All of the measurements on the table were made under “normal” or standard conditions. That means that all of the measurements were taken at 298 K (\(25^oC\)). In addition, all ions are present at a concentration of 1.00 M, gases are present at 1.00 atm, and elements and compounds are in their standard states.

This matters, because if you have a huge number of positive ions, even relatively weak ions, they will end up pulling harder than a tiny number of other ions, even if they are stronger. In simple terms 10,000 kindergarten students will pull harder than one professional football player.

Recording all of these values at standard conditions makes the comparison fair and meaningful.

So, the Standard Reduction Potential Table is simply a list of half-reactions showing how strongly they pull on electrons listed from weakest to strongest.

Going back to the reactions from the top of the page, now listed with their potentials:

\(Zn^{+2} + 2~e^{-1} \rightarrow Zn~~~~~~~E^{o} = -0.76V\)

\(Cu^{+2} + 2~e^{-1} \rightarrow Cu~~~~~~~E^{o} =+0.34V\)

From this we can determine two things: 1) copper wins, since it has the more positive potential, and 2) the potential on the galvanic cell that these two half-reactions would make is 1.10 V (the difference between the two values).

Let’s try one other example. Let’s match our zinc reaction to another “competitor.”

\(Zn^{+2} + 2~e^{-1} \rightarrow Zn~~~~~~~E^{o} = -0.76V\)

\(Sr^{+2} + 2~e^{-1} \rightarrow Sr~~~~~~~E^{o} = -2.89V\)

In this case, the zinc is the winner with the more positive potential and the potential on the cell would be 2.13V, with the reactions being:

\(Zn^{+2} + 2~e^{-1} \rightarrow Zn\)

\(Sr\rightarrow Sr^{+2} + 2~e^{-1}\)