Voltaic Cells

As we know, a redox reaction involves the transfer of electrons, both formally and physically. However, you know what other physical phenomenon involves the transfer of electrons? If you're scratching your head, the answer is circuits. Circuits are supplied voltage by batteries and inside batteries, redox reactions occur to generate current. However, the redox reactions occur in devices known as electrochemical cells. One type of electrochemical cell is a voltaic cell, in which a spontaneous redox reaction occurs.

So, the diagram above shows a voltaic cell. It seems like a lot, but let's break it down.

On the left is an anode and on the right is a cathode, and both of these are connected to an external circuit. Both the anode and cathode are collectively known as electrodes.

At the anode is where oxidation occurs, which is the Cu in this case. The Cu loses electrons due to oxidation. Those electrons go into the wire and get transferred due to the external circuit to the cathode. Once the electrons leave, what's left is Cu²⁺ in solution with NO₃^- spectator ions.

At the cathode is where reduction occurs, which is the Ag in this case. Once the electrons lost from the Cu anode come over to the cathode, the electrons interact with the Ag²⁺ ions in solution to form Ag on the cathode.

The salt bridge in the middle allows for the cell's charges to be balanced with a spectator electrolyte solution. The anions in the bridge go to the anode and the cations go to the cathode.

Cells in Standard Conditions

To proceed with this sub-topic, you'll want to understand the concepts of Gibbs Free Energy, Equilibrium, and Cell Potential.

Recall that the change in Gibbs Free energy is the maximum work that can be performed by a system. Since galvanic cells are by nature ideal and under standard conditions(298 K, 1 atm pressure, 1 M concentration), we can assume that the maximum work performed by the system is done in transferring electrons between species. Equation 4 on the Science Reference Chemistry Equation Sheet takes the product nF, which is equal to coulombs, and multiplies it with cell potential, giving electrical work.

F is known as Faraday's constant, and is equal to 96485 C/mol e-. This is a conversion factor that is essentially equal to the charge of 1 mole of electrons. Electrons have a charge of 1.60*10^-19 C so take that and multiply it across 1 mole of, or 6.022*10²³/ mole. The result you get is Faraday's Constant.

Recall that Gibbs free energy is related to the equilibrium constant of a reaction through Equation 5 on the Science Reference Chemistry Equation Sheet. We can form a relationship triangle with these 3 quantities and also derive an equation relating cell potential and the equilibrium constant through Equation 4 and Equation 5. This gives us Equation 6.

Since Equation 5 is explained in depth here and Equation 4 is explained above, let's explain Equation 6. Equation 6 is derived from Equation 4 and 5. However, the spirit of the equation(6) and what it physically means is most important here. This equation is telling us that cells with larger, positive cell potentials are more spontaneous and will proceed towards equilibrium on their own. This is important because this means that voltaic cells can start at standard conditions but as they operate for longer periods of time, slowly more products will form at the cathode and the anode will lose mass while the cathode gains it. Eventually, there won't be any anode left to oxidize and the reaction will reach equilibrium, with the charges on each end being balanced out.

Additionally, if cell potentials are higher, then so are equilibrium constants because a higher cell potential means the cathode is a very strong reducer. This means far more products will form and you'll get a cell equilibrium with way more product than reactant.

Cells in Nonstandard Conditions

So, we've talked a whole deal on how cells' cell potentials indicate their spontaneity and equilibrium. What happens when we have a cell under nonstandard conditions? Well, now we got to take a step away from equilibrium and look at reaction quotients instead. Let's look at Equation 8 on the Science Reference Chemistry Equation Sheet. This is the good-old equation for the change in Gibbs free energy based on the standard free energy difference plus the factor including the reaction quotient. The similar equation for this with cell potential is shown with Equation 9, known as the Nernst Equation. If you increase the value of Q, ln(Q) increases so cell potential decreases. This can be explained by Le Chatelier's Principle. If you increase the number of products relative to reactants, the cell system will want to decrease the concentration of products and increase the concentration of reactants. Notice that this is a non-spontaneous direction of the reaction as the cell reaction would be spontaneous if it tried making more products. Since this reverse reaction is less spontaneous, the cell potential decreases so the driving force on the electrons isn't as strong.

If we take the following cell reaction,

Cu²⁺(aq) + Zn(s) → Cu(s) + Zn²⁺(aq)

and take the reaction quotient for this reaction(given below), we can see what happens if we start messing around with the aqueous ions in solution.

If we increase the number of Zn ions in solution, Q increases which makes cell potential decrease. This means the cell reaction is headed in the non-spontaneous direction because we added more product to the reaction, causing the system to shift the equilibrium towards the reactants.

Citations/Attributions

Chemistry 2e. Provided by: Openstax. Located at: https://openstax.org/books/chemistry-2e/pages/1-introduction. License: CC BY 4.0

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