AP Chemistry: Electrochem
What if a voltaic cell is not at standard conditions?
When a cell is at standard conditions, solution concentrations are equal (1.0 M) so...
Ecell = Ecell
G = G + RT lnQ
And now we know G = ­nFE cell and G = ­nFE cell
From thermo, we know
so...
­nFE cell = ­nFE cell + RT lnQ
Rearranging this equation will allow us to relate a cell's potential to its standard cell potential and its reaction quotient, Q...
The Nernst Equation
E cell = E cell
RT lnQ
nF
Rearranging this equation and plugging in constants and switching to the common log gives us:
E cell = E cell
.0592 n log Q
This is why, at standard conditions, Ecell = Ecell because Q = 1
So how does Ecell change compared to Ecell when the cell is not at standard conditions?
Non­standard Voltaic Cells
AP Chemistry: Electrochem
As a voltaic cell reaction proceeds, Ecell decreases until equilibrium is reached because the difference between half­cell potentials is decreasing.
When equilibrium is reached...
Ecell = 0
Why?
Q = K
and
E cell = E cell
.0592 n log Q
E cell = 0.0592
log K
n
In summary...
When Q > 1
reaction heading towards equilibrium, more products than reactants
Ecell < Ecell
When Q < 1
reaction farther away from equilibrium, more reactants than products
Non­standard Voltaic Cells
Ecell > Ecell
AP Chemistry: Electrochem
What is the cell potential of the following voltaic cell at 25 C? Ecell = 1.62 V Al (s) Al+3 (.10 M) Fe+3 (.000010 M) Fe (s)
Al + Fe+3 Al+3 + Fe
n = 3
Q = [Al+3] (.10) = 10000 = [Fe ] (.000010) +3
E cell = E cell
E cell = 1.62
E cell = 1.62
.0592 n log Q
.0592 log 10000
3
0.079 = 1.54
Cell potential depends on the concentrations of ions and/or gas pressures
In essence, cell potentials can also allow us to measure ion concentrations
How a pH meter works!
Non­standard Voltaic Cells
AP Chemistry: Electrochem
What is the [Ni+2] in the following voltaic cell
at 25 C? Ecell = 0.53 V, Ecell = 0.34 V Zn (s) Zn+2 (1.0 M) Ni+2 (aq) Ni (s)
.0592 n log Q
[Zn+2] 1.0 = Q = [Ni+2] [Ni+2] .0592 0.34 = 0.53
2 log Q
0.34 = 0.53 .0296 log Q
E cell = E cell
­0.19 = ­.0296 log Q
6.42 = log Q
1.0 106.42 = [Ni+2] [Ni+2] =
Non­standard Voltaic Cells
3.8 x 10­7 M