Electrochemistry
Nernst Equation
The cell potential calculated under standard condition considering the concentration of the species involved in the electrode reaction as unity. But, in practically a real voltaic cell differ from the standard condition, so it becomes necessary to adjust the calculated cell potential to account for the differences.
Walther H. Nernst, a German scientist established the relationship between cell potential of half cell in standard condition with cell potential in practical condition. This relationship is called Nernst Equation.
Nernst showed that for an electrode reaction
Mn+(aq) + ne– → M(s)
The electrode potential (cell potential) at any concentration measured with respect to standard hydrogen electrode can be represented by
`E_((M^(n+)//M))` `= E_((M^(n+)//M))^(⊖)-(RT)/(nF) ln\ [M]/([M^(n+)])`
Since, concentration of solid M is taken as unity, thus above equation can be written as
`E_((M^(n+)//M))` `= E_((M^(n+)//M))^(⊖)-(RT)/(nF) ln\ 1/([M^(n+)])`
Where, ` E_((M^(n+)//M))` is the electrode potential of a cell at any concentration
` E_((M^(n+)//M))^(⊖)` is the electrode potential of a cell at standard condition measured with respect to standard hydrogen electrode.
R is the gas constant which is equal to 8.314 JK–1mol–1
F is Faraday constant which is equal to 96487 C mol–
T is the temperature in Kelvin
[Mn+] is the concentration of the species Mn+
n = number of moles of electrons transferred in the balanced equation
Nernst Equation considering a Daniel Cell
A typical Daniel cell consists of copper and zinc as electrodes. Thus, electrode potential for any given concentration of Cu2+ and Zn2+ ions can be written as:
At cathode
`E_((Cu^(2+)//Cu))` `= E_((Cu^(2+)//Cu))^(⊖)-(RT)/(2F) ln\ 1/([Cu^(2+)(aq)])`
At Anode
`E_((Zn^(2+)//Zn))` `= E_((Zn^(2+)//Zn))^(⊖)-(RT)/(2F) ln\ 1/([Zn^(2+)(aq)])`
Thus, The cell potential,
`E_(cell) = E_(Cu^(2+)//Cu) - E_(Zn^(2+)//Zn)`
`=E_((Cu^(2+)//Cu))^(⊖)-(RT)/(2F) ln\ 1/([Cu^(2+)(aq)])` `-E_((Zn^(2+)//Zn))^(⊖)-(RT)/(2F) ln\ 1/([Zn^(2+)(aq)])`
`=E_((Cu^(2+)//Cu))^(⊖)-E_((Zn^(2+)//Zn))^(⊖)` `-(RT)/(2F)[ln\ 1/([Cu^(2+)(aq)])` `+ ln\ 1/([Zn^(2+)(aq)])]`
`=>E_(cell)=E_(cell)^(⊖)-(RT)/(2F)ln\ ([Zn^(2+)])/([Cu^(2+)])`
Reference: