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We can combine the relationships between DG and E at
non-equilibrium conditions to get a relationship between the two in much the
same way that we can relate K and E at
equilibrium. We have the relations
Combining the three relations gives the Nernst equation
- E = E0 -(RT/nF)*ln(Q)
R is the gas constant, K the
Kelvin temperature, n the number of electrons transferred between the species, F
the Faraday constant and Q the
reaction quotient. This equation allows us to compute the cell voltage at
any concentration of reactants. products and at any temperature.
We can simplify the equation slightly by combining constants. At
25oC, the term RT/F is equal to 0.0257 V, so
- E = E0 -(0.0257/n)*ln(Q)
Example: The copper-zinc cell shown below has E0 = 1.101 V.
If the reaction is done in a cell in 5.00 M Zn+2 and 0.30 M
Cu+2 at 25oC, what is the cell voltage?
- Zn(s) + Cu+2(aq) -> Cu(s) + Zn+2(aq)
Solution: First, work out the reaction quotient Q. Since zinc and
copper metals are solids, they don't show up in the reaction quotient
- Q = [Zn+2]/[Cu+2]
- Q = 5.00/0.30
- Q = 16.7
Two electrons are transferred between the zinc and
copper, so n=2. Plug everything in
- E = E0 -(0.0257/n)*ln(Q)
- E = 1.101V - (0.0257 V/2)*ln(16.7)
- E = 1.101V - 0.0362 V
- E = 1.065 V
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