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Derive equilibrium constant from Nernst ...

Derive equilibrium constant from Nernst equation.

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Consider the following cell reaction ,
`Lambda+bB hArr cC+dD`
Nernst equation for cell reaction at 298 K is
`E_(cell)=E_(cell)^(@)-(0.0591RT)/(n)"log"([C]^(c)[D]^(d))/([A]^(a)[B]^(b))`
`=E_(cell)^(@)-(0.0591RT)/(n)logQ_(c)`
where `Q_(c)` is concentration quotient.
At equilibrium, `E_(cell)=0 and Q_(c)=K_(c)`
`therefore 0=E_(cell)^(@)-(0.0591RT)/(n)logK_(c)`
or `E_(cell)^(@)=(0.0591RT)/(n)logK_(c)("at "298K)`
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