# Does the relationship equation between standard cell potential and equilibrium constant violate potential's intensive properties?

The equation:

$$E^{。}_{cell}= \frac{RT}{nF}\ln K_{eq}$$

We all know cell potential is intensive, not affected by the amount, Because: $volt=\frac{joule}{coulomb}$. Both joule and coulomb will be doubled altogether.

But as seen from the equation, cell potential is affected by the number of electrons transferred.

No, there is no violation of "intensivity". The reason is that $K_{eq}$ depends on $n$, and changes in one cancel the other out.

For example, consider the electrolysis of water:

1. $$\ce{2H2O_{(l)} -> 2H2_{(g)} + O2_{(g)}}$$

The equilibrium constant for this reaction is $K_{1}=\frac{[\ce{H2}]^2 [\ce{O2}]}{1}$ and if you wrote out each electrochemical half reaction separately, $n$ would be 4.

Now consider this reaction:

1. $$\ce{4H2O_{(l)} -> 4H2_{(g)} + 2O2_{(g)}}$$

The equilibrium constant is now $K_{2}=\frac{[\ce{H2}]^4 [\ce{O2}]^2}{1}=(K_1)^2$. If you wrote out the half-reactions for this reaction, $n$ would be 8, twice as big. But the $\ln K_{eq}$ term would also be twice as big, since $\ln K_2 = \ln{(K_1)^2} = 2 \ln K_1$.

• Wow, I should have spent sometime playing around with it first. But I was too lazy. Apr 18 '15 at 22:55
• No worries. Electrochemistry is confusing, mainly because physicists and engineers refuse to get rid of silly units like "volt", "coulomb", and "ampere". Ever since Milliken's experiment, sensible folks have been wishing for those to be replaced by "J/mol", "mol", and "mol/s". Apr 18 '15 at 23:00
• Is it more accurate to say standard cell potential is an intensive property? Apr 20 '15 at 17:13
• Hello!! ^Last comment. Apr 30 '15 at 10:32
• No, all cell potentials, standard or not, are intensive properties. Apr 30 '15 at 16:12