Presenting one of the most difficult to understand equations called the Nernst equation:
E = Eº – (RT/nF)ln Q
where
E = cell potential or emf at non-standard conditions
Eº = standard cell potential or standard emf
R = universal gas constant = 8.314 J/(K mol)
F = Faraday's constant = 9.65 x 104 C/mol
T = temperature in K
Q = [C]c[D]d/[A]a[B]b = reaction quotient for a reversible reaction: aA + bB <==> cC + dD
In A-level, I always tried to understand every single science concept by starting from its fundamentals. So I asked how the Nernst equation came about. I checked that its derivation is traced back to Thermodynamics (∆G = ∆H – T∆S). But this field of science is even more confusing. I saw many strange names like Gibbs free energy G and entropy S which were not in the Chemistry syllabus in my time. It was hopeless to comprehend the intimidating derivation plagued with strange math notations. My usual way of understanding, in this case, was therefore useless. But in the first place, the equation wasn't even in the syllabus. My teacher showed it out of so called “extra knowledge that's good for us”. So to think, I shouldn't be too concerned over it. Today, this equation is still not in the A Level syllabus. But the ∆G = ∆H – T∆S is.
The Nernst equation is
derived from ∆G = ∆H – T∆S...
I believe many JC teachers, like mine, would expose their students with the Nernst equation. This is done typically after describing how to use Eº of half cells to calculate the Eº of a cell. Why introduce it since questions with non-standard conditions will not be tested? It's to tell you that Eº applies to standard conditions (temperature = 25 ºC, pressure = 1 atm, concentration = 1 M). To find E for non-standard conditions, we use the Nernst equation. This equation can also be used to predict whether the forward or backward reaction will be favored under some non-standard condition.
The Nernst equation is
used to find cell potential E under non-standard conditions...
Let's look at how each term in the equation comes about without looking at its full derivation. E and Eº come from the changes in Gibbs free energy:
∆G = -nFE and
∆Gº = -nFEº
This may not ring a bell unless you're also a Physics student who has come across the definition of electric potential V = W/q.
==> W = qV
where
W = work done in bringing a charge from infinity to a point in an electric field,
q = charge = number of moles of electrons n x charge per mole F
What's G if you're still wondering? The Gibbs free energy G is the available PE of a closed system to do non-expansion work such as electrical work at constant pressure and temperature. The change in Gibbs free energy ∆G tells whether a reaction is energetically favorable or spontaneous, meaning whether they can occur without any external help.
- So long as G of the reaction decreases or ∆G is negative,
the reaction is spontaneous.
- On the other hand, if G increases or ∆G is positive, the
reaction is non-spontaneous.
- ∆G becomes 0 when the reaction reaches equilibrium.
Reaction is spontaneous
if ∆G < 0...
Because E = -∆G/nF and Eº = -∆Gº/nF, the reaction is:
- spontaneous if E is positive and
- non-spontaneous if E is negative.
Reaction is spontaneous
if E > 0...
Where does ln Q come from? It comes from this equation:
∆S = -k ln (concentration of
state 1/concentration of state 2)
It's okay if you don't get this. But the following is useful to know. As you read the following, compare to your more familiar Le Chatelier's Principle.
- If Q > equilibrium constant K ==> ln Q is more positive
==> E becomes more negative ==> reaction proceeds to the left
- If Q < equilibrium constant K ==> ln Q is more negative
==> E becomes more positive ==> reaction proceeds to the right
- If Q = equilibrium constant K ==> E = Eº – (RT/nF)ln Q
= 0 ==> Eº = (RT/nF)ln K ==> ln K = nFEº/RT
Forward reaction is
favoured if Q < K...
I don't know if my explanation of the Nernst equation is effective in clearing your doubt. Still, the best way of understanding any equation is to practice questions that use it. Here's one example of a calculation question that uses the Nernst equation.
http://chemistry.about.com/od/workedchemistryproblems/a/Nernst-Equation-Example-Problem.htm
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