7  Electrochemistry

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7.6 Standard Potential

7.9 Batteries

7.10 Battery Facts

# Standard Potential

When we write out our balanced redox reactions and identify the two half-reactions, we can think about creating those half-reactions by getting all the needed compounds (both reactants AND products) and using them under "standard" conditions. Let's nail down "standard conditions" for electrochemistry (same as pretty much all of chemistry)

#### Standard Conditions

• temperature is 25 °C (298.15 K)
• pressure is 1 atm*
• all solids and liquids are pure
• all aqueous species have a concentration of 1 mol/L or 1 M
• all gas species have partial pressures of 1 atm*
• a "standard" half-reaction is written as a reduction and has a standard potential (E°) given in volts

* or if you are really forward thinking you'll switch to the newer standard of 1 bar

By using all standard conditions we are matching what we put in tables for the potential (volts) of all those half-reactions out in the real world. For instance, that Daniell cell reaction... the Cu2+/Cu reduction is +0.34 volts under standard conditions, and the Zn/Zn2+ oxidation is +0.76 volts. So they combine to give a +1.10 volt cell potential. We call that the standard cell potential and it is symbolized as E°.

#### You take the DIFFERENCE of the Standard Potentials

Because all standard potentials are written as reductions (electrons on the left side of the equation), all the values given in a table are for reductions (the cathode), so to get the oxidation version you have to "flip" the reaction (write it backwards) so that the electrons are on the right side of the equation (an oxidation at the anode). Flipping the reaction changes the sign on the potential - same number, just opposite sign. So this just means you are always subtracting the reaction that is running as an oxidation (anode). So the simple formula for the standard potential of any electrochemical cell (both voltaic and electrolytic) is

E°cell = E°cathodeE°anode

Please note that the minus sign IS the flip of the reaction for the anode. Don't change the sign twice.

A Table of Standard Potentials is available to you right here in this Chembook in the appendix (chapter 10 section 5). Here's a link to this table of Standard Potentials which you'll need for working any standard potential problems. We will provide a shorter version that has all you need on any exams.

#### Proceed with Caution

Now, IF and only IF you fully understand the above formula with the cathode and anode, can you move on to use the following "push/pull" formula for standard potential. The fully realized standard potential for any overall reaction is a combination of the "push" of electrons from the anode and the "pull" on electrons from the cathode. The pull is the reduction reaction at the cathode (electrons are reactants and on the left of the reaction) and is known as the reduction potential (E°red). The push is the oxidation at the anode (electrons are on the left side of the half reaction) and is known as the oxidizing potential (E°ox). The overall potential is then:

E°cell = E°red + E°ox

You just have to remember that the oxidizing potential is the opposite in sign as that shown on the standard table of potentials. You are "flipping" the reaction to be an oxidation, and therefore you also "flip" then sign. Specifically...

E°ox = –E°at the anode = –E°from the table

This is more in keeping with how we balance redox reactions in the first place. One half reaction is a reduction and the other is an oxidation. Mathematically, we are just changing the sign and adding instead of just subtracting. Got it? Use whatever works for you, but know that an oxidizing potential is different from a reducing potential.

#### Agents of Fortune

Yes, this is the name of a classic Blue Öyster Cult album with the iconic song "Don't Fear the Reaper"... but I disgress. In our electrochemical context, I want you to know how to use a standard potential table and know where the best oxidizing agents are and the best reducing agents are. Below is a diagram of a "mini" standard potential table and it showes how the best oxidizing agents are the reactants of reductions with the most positive potentials. They are at the top and on the left of a table of standar potentials. The best reducing agents are at the other end (the bottom) and on the right side of the reaction. Those reactions will want to run backwards (reverse) and produce electrons. The diagram shows these relationships. ### Standard Hydrogen Electrode (aka: SHE)

Long long ago we had to pick some half reaction that would be our universal reference point. That half reaction ended up being the standard hydrogen electrode which corresponds to this reaction:

2H+   +   2e   ⇌   H2 (g)

So it is assigned zero volts exactly and that number is infinitely precise because it is a defined standard. Just make sure you have 1 M [H+] and 1 atm H2 and you're good to go. Another thing great about standards is that you can say it is still zero volts at all temperatures. So it can still be a reference point at other non-standard temperatures.

It is a bit of a pain in the ass to deal with though. Strong acid with hydrogen gas bubbling through it. Make sure you place your platinum electrode in the bubble stream. The shorthand notation for this cell is

Pt(s) | H2(g) | H+(aq)

That is if it is "on the left" as an anode. Just flip it if you want a cathode on the right side. Also, we sometimes save space by dropping off the states that are in parenthesis.