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Redox reactions like all others can reach an equilibrium state. Since we have
a relationship between E0
and DG0 as well as one between DG0 and K, we can derive a relationship
between the cell voltage and the equilibrium constant. Since we have
- DG0 = -nFE0
- DG0 = -RTln(K)
we can combine
the two equations into one:
- E0 = (RT/nF)*ln(K)
At 25oC, the term RT/F has the value of 0.0257 V, so we can
simplify the above equation at 25oC
- E0 = (0.0257/n)*ln(K)
With the above equations, we can
derive the value of the cell voltage from the equilibrium constant and vice
versa
Example: The copper-zinc redox reaction shown below has an
E0 value of 1.101 V. What is the equilibrium constant for this
reaction at 25oC?
- Zn(s) + Cu+2(aq) -> Cu(s) + Zn+2(aq)
Solution: Use the above equation to determine K. Two electrons are
exchanged in the reaction, so n=2
- E0 = (0.0257/n)*ln(K)
- 1.101 V = (0.0257 V/2)*ln(K)
- ln(K) = 85.6
- K = 1.62*1037
Note that the value is huge: the
reaction goes to completion. |