# Standard electrode potential of a galvanic half cell is zero at equilibrium at standard conditions?

At standard conditions(at 1atm pressure and unit activity(1molal or 1molar concentration)of all dissolved compounds),the electrode potential is equal to the standard electrode potential by the Nernst equation. $$\Delta E = \Delta E^0$$ At the same time,while the electrochemical reaction is at equilibrium,the electrode potential of the cell, $$\Delta E =0$$

So this must mean,that when ANY reaction is at equilibrium under the standard conditions, $$\Delta E = \Delta E^0 = 0$$ Which is quite surprising.Is this correct?please explain.

• Why would you expect the standard electrode potential of a reaction in equilibrium not to be 0? – Jerry Apr 1 '13 at 8:15
• given that the standard electrode potential determines the tendency of the system to follow the forward reaction,does the value of $$E^0$$ change as the reaction proceeds towards equilibrium? – scienceauror Apr 1 '13 at 8:46

There is a difference in the meaning of $\Delta E^\circ$ and $E^\circ$. $\Delta E^\circ$ actually denotes the change in standard electrode potential while $E^\circ$ denotes standard electrode potential.

$E^\circ$ is always constant for a given redox couple (eg. $\ce{Zn^2+|Zn}$). So no matter what concentration of $\ce{Zn^2+}$ you take in a certain electrode, the standard electrode potential of $\ce{Zn^2+|Zn}$ is always $-0.76\ \mathrm{V}$.

Since $E^\circ$ is always constant, it never changes. So the value of $\Delta E^\circ$ (change in $E^\circ$) would always be zero and so it is quite a useless quantity to consider.

For $\Delta E$ however, consider the Nernst equation, $$E = E^\circ - (RT/nF)\ln Q$$ Change in $E$ $$\Delta E = \Delta E^\circ - \Delta(RT/nF)\ln Q$$ therefore $$\Delta E = -(RT/nF)\Delta\ln Q$$

At equilibrium $\Delta E$ is zero because there is no change in the reaction quotient $Q$ of the reaction (therefore $\Delta \ln Q$ is zero).

• But then we do have a list of standard electrode potentials of different half cells with respect to the standard hydrogen electrode,right?how can $$\Delta E^0$$ be zero? – scienceauror Apr 1 '13 at 18:40
• That is quite different... $E^o$ itself is the standard electrode potential of the electrode with respect to the Standard Hydrogen Electrode. So the value of $E^o$ for a given redox couple would never change unless you changed the reference electrode (you find the electrode potential of the electrode with respect to some other electrode instead of the SHE). – kaliaden Apr 2 '13 at 3:06
• I am confused.I have solved some problems,where I had to calculate $\Delta E^0$ for calculating emf of the cell,or $\Delta G^0$ where I simply put the Nernst equation at equilibrium.All questions consider the state of equilibrium,standard conditions,and given half cell connected to SHE.is it correct to get non zero $\Delta E^0$ ? – scienceauror Apr 2 '13 at 11:07