The Concentration Dependence of Cell Emf - The Nernst Equation
The
Concentration Dependence of Cell Emf - The Nernst Equation
Consider an electrochemical equilibrium
whose overall cell reaction is represented by the scheme -
aA+bB cC+dD (3)
where a, b, c and d are the number of
moles of the reagents taking part in the reaction The reagent or reagents could
be gases, ions or molecules in solution. Solids may also be involved but they
are treated as constants.
For 1mole of species A, the free energy is
given by
GA=GA°+RT
in aA (4)
where GA is the
electrochemical free energy, and GA° is the standard free energy and
aA is the activity of reagent A.
For a moles of reagent A,
aGA =
aGA + aRT ln aA
aGA +
RT in (aA)a
Similar-expressions can be written for
the other three reagents.
The overall free energy change is the
free energy of the products minus free energy of the reactants:
G =Gproducts - Greactants
G = G0 + RT In
Recall
G =-nEF and G° = -nE°F
Hence
E=E0 - (5)
Equation (5) is known as the Nernst
equation and gives the dependence of the electrode or cell potential in terms
of activities or concentrations of the reactants and products. E° is known as
the standard e.m.f of the cell and it is the cell potential when the activities
are all unity.
At 25°C equation (5) reduces to
E=E0 –
E=E0 – (6)
Also by definition,
G° = -RT In K = -nE0F,
therefore
E0 =
(7)
where K is the equilibrium constant for
the electrode or the cell reaction and hence equation (6) can also be written
as:
E= (8)
Exercise 1
For the following cell at 298K,
Zn(s)/Zn(aq)2+
(a = I )//Pb(aq)2+ (a = 1 )/Pb(s)
(i) Write individual electrode reactions
and the overall cell reaction.
(ii) Calculate E°cell.
(iii) Calculate G° of the cell reaction.
(iv) In which direction is the cell
reaction spontaneous?
Given E0Zn2+/Zn
= 0.762V and E0Pb2+/Pb =-0.126V
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