Electrochemistry

Thrilled you’re here. If you haven’t already, I would recommend checking out some of my previous crash courses on Chemistry, such as Chemical Equilibrium from last week.

Electrochemistry is the study of redox reactions in the production of (1) electrical currents from spontaneous chemical reactions, and (2) non-spontaneous chemical changes by the use of electrical currents.

There are so many applications to electrochemistry! Think batteries, fuel cells, electrodes, electroplating, etc.


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Okayy, but what are redox reactions again?

Oh, all right. Redox reactions involve the transfer of electrons. Reduction is the gain of electrons, and oxidation is the loss of electrons. As you can see, one can’t happen without the other – you can’t give electrons away without there being another species to accept them, and vice versa.

Good oxidizing agents are reduced easily, and good reducing agents are oxidized easily.

Oxidation number is a bookkeeping method, which is the charge a bonded atom would have if the electron in each bond were given to the more electronegative element, so it’s not the real charge.

Like formal charge (applied to ionic bonds, of course), there are some rules for assigning oxidation numbers in polyatomic molecules.

  1. The oxidation state of all free elements is zero regardless of formula (P4, S8)
  2. The oxidation state of a monoatomic ion is equal to the charge on the ion.
  3. Because F is the most electronegative element, the oxidation number of F in its compounds is always -1.
  4. The oxidation number of O is -2 except when it is bonded to F or itself.
  5. The oxidation number of H is +1, except in metal hydrides, where it is -1.
  6. Group 1A alkali metals: +1
    Group 2A alkaline earth metals: +2
    Group 7A halogens: -1 except when bonded to oxygen or to a more electronegative halogen
  7. The algebraic sum of the oxidation states is equal to the net charge on the molecule or ion.

Balancing Redox Reactions

Our game plan is the half-reaction method:

  • Divide the overall reaction into two half-reactions, one for oxidation and one for reduction.
  • Balance the two half-reactions separately.
    In an acidic media – to the side deficient in O, add one water molecule for each missing O atom and add twice as many H+ ions to the other side.
    In a basic media – to the side with excess O, add one water molecule per extra O atom, and add twice as many OH- ions to the other side.
    Now balance with respect to charge by adding electrons to the more positive side.
  • Add the two half-reactions to give the balanced equation.
    Multiply the half reactions by appropriate factors to ensure that equal numbers of electrons are lost and gained in the half-reactions.
    After adding, you will have the balanced net ionic equation (the electrons will cancel).
    Now check to see that atoms and charges are balanced!

Concepts of Electricity (Review)

There is one more quick thing we need to review before we can talk about electrochemistry and all that good stuff, which is electricity itself!

Current (I), is the amount of charge (Q) flowing per unit time (t).

So 1 Ampere = 1 Coulomb/second.

The Faraday constant is the charge of one mole of electrons. It can be found by multiplying to charge of a single electron (1.6×10^-19) by Avogadro’s number (6.02×10^23).


Electrochemical Cells

Great. Now. There are two types of electrochemical cells: galvanic (aka voltaic) cells and electrolytic cells.

Galvanic cells produce spontaneous chemical reactions (ΔG>0) to create electrical energy (e.g. a battery).

Electrolytic cells use external electrical energy to produce a chemical change that would not occur spontaneously (ΔG<0).

Both types of cells have: (a) two half-cells containing electrolytic solutions, (b) electrical contact between cells by means of a salt bridge, (c) two electrodes, one in contact with each solution, and (d) external electrical connection between the two electrodes to complete the circuit.

For both galvanic and electrolytic cells, the cell in which oxidation occurs is the anode; the cell in which reduction occurs is the cathode.

The Galvanic (Voltaic) Cell

The Daniell cell has the overall reaction:

Zn + Cu2+ → Cu + Zn2+

with half reactions

Zn → Zn2+ + 2e- (oxidation)
Cu2+ + 2e- → Cu (reduction)

In shorthand, we represent this by:

Zn(s)|Zn2+(aq)||Cu2+(aq)|Cu(s)

By convention, the anode is on the left, | denotes a phase boundary, the || represents the salt bridge, and the cathode is on the right.

Hence, electrons flow from left to right through the external circuit in the case of a Galvanic cell (anode is negative, cathode is positive).

By definition, the flow direction of electric current is always opposite to the flow direction of electrons.

The salt bridge is necessary to allow ions to flow between the two half-cells and prevent the buildup of charge. The negative SO4 2- cells flow into the left half-cell to offset the removal of electrons via the anode, and the positive Na+ ions move into the right half-cell to offset the addition of electrons via the cathode.

The Galvanic cell constitutes a complete electric curcuit because there is a continuous flow of charge in a cycle.

The Electrolytic Cell

Electrical energy is used to drive a non-spontaneous chemical change in our second type of cell (note the difference from the definition of a galvanic cell).

Because we are driving electrons into the cathode in an electrolytic cell, the electrode connected to the negative terminal of the power source is the electrode at which reduction will occur.

Therefore, in contrast to the Galvanic cell, the anode is positive and the cathode is negative for an electrolytic cell.

A practical application for electrolytic cells is silver plating via the cathode. For example, pretend that the cathode is a spoon, and the anode is a bar of silver. When the silver ions go to the cathode to be reduced, they will become solid metal on the surface of the cathode, resulting in a silver-plated spoon.

For BOTH galvanic and electrolytic cells:
(1) electron flow in the external circuit is from anode to cathode, and
(2) inside the cell, anions flow toward the anode, and cations flow toward the cathode.


Standard States and Cell Voltages

The cell potential E(cell) is a quantitative measure of the tendency of a redox reaction to occur – a large positive cell potential corresponds to a very favorable redox reaction.

For an electrochemical cell, the cell potential can be found in terms of the reduction potentials:

E(cell) = E(cathode) – E(anode)

If the reaction is spontaneous, it will have a positive E(cell). So if E(cell) >0, the reaction will occur as written; if E(cell) <0, the reaction will occur spontaneously in the opposite direction.

Standard cell potential values can be calculated from tables with standard reduction potentials. The standard state of a solute in a solution is the concentration of 1 M.

A metal’s position in the activity series is determined by the free energy change associated with the loss of electrons, and the relative ease with which it forms ions.

All these reduction potential values are relative – so the reference half-cell is the standard hydrogen electrode (SHE), which is arbitrarily assigned a standard reduction potential value of 0.

The SHE consists of hydrogen gas at 1 bar pressure, bubbled into a 1M H+ acid solution at 25C containing a platinum electrode. The hydrogen molecules dissociate on the Pt electrode to form H+ ions. The Pt electrode is inert – it doesn’t undergo any change.

Because each half reaction can be reversed, any electrode can act as a cathode or an anode.


The Gibbs Free Energy and Cell Voltage

Electrical work is the product of the amount of charge (Q) times the voltage difference (E) through which it is transferred, so

w(elec) = -QE

where w is the work done on the system.

If n moles of electrons are transferred through a potential difference E, since
Q = nF, the electrical work done on ht electrochemical cell is

w(elec) = -nFE(cell)

For constant temperature, constant pressure, and for a reversible process:

w(rev,elec) = ΔG

The maximum amount of electrical work, equal to ΔG, will be done ON a system in a reversible process at constant T and P.
For a spontaneous irreversible process, when a finite amount of current is flowing, the work will be less than for the equivalent reversible change.

Hence, the change in Gibbs free energy is a measure of the maximum electrical work a chemical system can do.

Since this is true, ΔG = -nFE(cell).

So it is possible to calculate Gibbs free energy changes by measuring cell voltages.

Electrochemical cells and equilibrium constants

By combining ΔG=-RT ln K with ΔG=-nFE(cell), we get

Screenshot 2016-11-13 at 1.05.43 PM.pngThis is known as the Nernst equation. It relates the standard cell potential with the equilibrium constant.


Okay, so to sum up, we can relate the equilibrium constant,  standard Gibbs free energy change, and standard cell potential with the following diagram:

Thanks for reading! For those of you studying for finals this time of year, good luck. You can do it!

As usual, the comments section is open to anyone who wants to ask questions or leave feedback/show love!

Soon to come: a chemistry post on acid and bases!

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