Electrochemistry
E-chem Definitions
reduction is the gain of electrons and occurs at the cathode.
this means that electrons always flow into the cathode from the external circuitry
oxidation is the loss of electrons and occurs at the anode.
this means that electrons always flow out of the anode into the external circuitry
Standard Cell Potential, E°cell
The BEST way to think about getting E°cell
If you really "think like a chemist" then you should be thinking about the push/pull nature of the electrochemical cell. The anode is pushing electrons out while the cathode is pulling electrons in. The standard potential is really the addition of two standard potentials, one is the driving force of the reduction (\(E^\circ_{\rm red}\), the pull) and the other is the driving force of the oxidation (\(E^\circ_{\rm ox}\), the push). Put these together and you get:
\[{\cal E}^\circ_{\rm cell} = {\cal E}^\circ_{\rm red} + {\cal E}^\circ_{\rm ox} \]
You must "flip" a reaction from the table of standard potentials in order to get an oxidation potential. Also remember, when you flip a reaction, you change the sign on the state function, which in this case is \(E^\circ\). Realize that you have to flip the oxidation reaction anyway when you write out the balanced equation. So this is the best way to do it.
Shortcut method Unfortunately, we tend to teach you the shortcut first and it leads to misconceptions. None-the-less, the fact is that the standard potential for any electrochemical cell is simply the difference in the standard potentials of the two half cells.
\[{\cal E}^\circ_{\rm cell} = {\cal E}^\circ_{\rm cathode} - {\cal E}^\circ_{\rm anode} \]
Realize that the standard cell potential (or reaction potential) can be positive (+) or negative (–). Also realize that the \(-E^\circ_{\rm anode}\) term IS the oxidation potential which is the push of \(E^\circ_{\rm ox}\) shown in the first equation.
Shorthand Cell Notation
We "tell" you which 1/2 cell is the anode by writing it on the left side in the shorthand notation:
anode \(\bigl|\) anodic solution \(\bigl| \bigr|\) cathodic solution \(\bigr|\) cathode
Cell Potential and Free Energy
standard conditions: \(\Delta G^\circ = -n F {\cal E}^\circ \)
non-standard conditions: \(\Delta G = -n F {\cal E} \)
The "Triforce" of CH302
\(-n F {\cal E}^\circ = \Delta G^\circ = -RT\ln K\)
Non-standand Cell Potentials
Non-standard cell potentials are calculated via the Nernst Equation:
\[{\cal E}_{\rm cell} = {\cal E}^\circ_{\rm cell} - {RT\over nF}\ln(Q) \]
The temperature (T) is usually 298.15 K for most of our problems. The faraday is always 96485 C/mol of e-, and R is always 8.314 J/mol K. Therefore you can use either of the following versions of the Nernst equation to save yourself from punching in all those long numbers into your calculator.
\[{\cal E}_{\rm cell} = {\cal E}^\circ_{\rm cell} - {0.0257\over n}\ln(Q) \]
\[{\cal E}_{\rm cell} = {\cal E}^\circ_{\rm cell} - {0.05916\over n}\log(Q) \]
FYI... calculate \(RT/F\) and you'll use (8.314)(298.15)/96485 to get 0.02569 which is where that 0.0257 came from up above. You have to use natural log for that number though. If you want to use log base 10 (log), then you'll need to multiply the log 10 version of Q by ln(e) which is 2.303 and that is why the 0.05916 number is there.
Algebra, logarithms, and the Nernst equation
Know your basic logarithm algebra laws
\(x = 10^{\log(x)}\hskip36pt x = e^{\ln(x)}\)
\(\log(xy) = \log(x) + \log(y)\)
\(\log(x/y) = \log(x) - \log(y)\)
\(\log(x)^y = y\log(x)\)
Now lets combine two of the above relations to get our "formula" for natural log using base10 log.
\(x = 10^{\log(x)}\) Now take the natural log (ln) of both sides.
\(\ln(x) = \ln(10)^{\log(x)}\) which will solve to
\(\ln(x) = \log(x)\ln(10) = \log(x)\cdot 2.302585...\)
So, natural log of any number is the same as the log base10 number times 2.303 (4 sig figs). So that is why the Nernst equation can be rewritten as
\({\cal E}_{\rm cell} = {\cal E}^\circ_{\rm cell} - {2.303RT\over nF}\log(Q) \)
\({\cal E}_{\rm cell} = {\cal E}^\circ_{\rm cell} - {0.05916\over n}\log(Q) \)
"Electric World"
Potential is given the symbol \({\cal E}\) in equations and is measured in volts.
Volts (or voltage) is a unit of measure and is abbreviated with just V.
Electric current is given the symbol I in equations and is measured in amps.
Amps is a unit of measure and is abbreviated with an A.
An amp (A) is also just a rate of charge transfer which is coulombs/second or C/s.
Time is given the symbol t (lowercase!) and is measured on many different scales.
Those scales of time are typically seconds, minutes, hours, days, or years. The SI unit of time is the second (s).
Reminder, temperature is given the symbol T (uppercase!) and has 3 different scales that can be used (°F, °C, or K).
Power is given the symbol P in equations and is measured in watts.
Watts (or wattage) is a unit of measure of power and is abbreviated with just W.
Power is defined as a rate of energy use or energy/time. A watt is really just a joule/second or J/s. One common equation for calculating power is: \(P = I \cdot {\cal E}\). Yes, it spells "pie" but is really power = current × potential.
Charge is given the symbol q in equations and is measured in coulombs.
Charge is calculated via current × time or: \(q = I\cdot t\)
Energy (joules, J) is calculated via charge × potential or: Energy = \(q\cdot {\cal E}\)
Don't confuse energy and potential, they are typically both symbolized with an E. Sometimes (not always) a script looking \({\cal E}\) is used for potential to be different from the E used for energy. The unicode script E looks like this, ℰ. Just note the context in which it is used - it is usually obvious which one we mean (blatantly obvious once you LEARN the concepts).
The main conversion factor to know in order to convert from "electricity world" to "chemistry world" is the faraday constant, F. It tells us the number of coulombs in a mole of ionic unary charge - to be even more specific, for our needs, the faraday is 96485 coulombs which is the total absolute charge on 1 mole of electrons. The faraday doesn't care about being positive or negative, it only cares about the magnitude of the charge. YOU need to remember the signs for charge... but no matter where the charge is coming from... 1 F = 96485 C/mol of electron charge.
Electricity World ⇄ Chemistry World (Big Picture)
So the flow of conversions is the following:
current → charge → moles of e– → moles of reaction
So taking all the conversions needed and putting them all into one big equation we get
\[{I\cdot t\over n\cdot F} = {\rm moles\;of \;reaction}\]
(that is moles of reaction that uses n moles of electrons for the way you balanced it)