For these two metals, the standard reduction potentials are: $$ \ce{2e-} + \ce{Cd^{2+}} \rightarrow \ce{Cd}:\mbox{ } E^0 = -0.403 V\\ \ce{2e-} + \ce{Ni^{2+}} \rightarrow \ce{Ni}:\mbox{ } E^0 = -0.25 V $$

But the simple ionization energies are:

$$ \ce{Ni} \rightarrow \ce{Ni^{2+}} \mbox{ } \Delta H=\Delta H_{i_{1}} + \Delta H_{i_{2}} = 2490 \ce{kJ. mol^{-1}}$$ $$ \ce{Cd} \rightarrow \ce{Cd^{2+}} \mbox{ } \Delta H=\Delta H_{i_{1}} + \Delta H_{i_{2}} = 2500\ce{kJ. mol^{-1}}$$ The difference in $E^\theta$ is greater than the difference in ionization energy of both elements.
How can this be explained?

  • $\begingroup$ Can you be more specific regarding your query? Why shouldn't they be different? $\endgroup$ – Nicolau Saker Neto Dec 11 '13 at 19:39
  • $\begingroup$ If I get asked, for which of these two equations, the normal potential will be higher, how should I go about answering that? $\endgroup$ – TMOTTM Dec 11 '13 at 20:27
  • $\begingroup$ Without looking at result, it's not obviously for me which one will be higher. I have a guess based on [this post][1]. There is a choice of filling electron from d$^8$ to d$^{10}$ vs s$^0$ to s$^2$. The prior one will cause much more electrostatic repulsion (like why 3d$^3$ is not the electronic configuration of Sc). However, this argument will predict Ni$^{2+}$ higher than Zn$^{2+}$. [1]: chemistry.stackexchange.com/questions/6921/… $\endgroup$ – user26143 Dec 12 '13 at 0:34
  • $\begingroup$ If I go down one period, the smaller $Z/r$ of Cd$^{2+}$ will also make the $E^0$ more positive, which is an opposite trend. It's hard to say how large this effect. From the experimental $E^0$, the downing period expected to be a smaller contribution. Anyway, all these are hand-waving argument, quantitative calculations are needed to justify this "explanation". $\endgroup$ – user26143 Dec 12 '13 at 0:37
  • 1
    $\begingroup$ I now found a theoretical workaround. The standard potential can in principle be calculated from a thermodynamic cycle in which an electron is transfered from a metal to $\frac{1}{2}H_2(g)$. In principle, I believe, all properties along the cycle should be calculable. $\endgroup$ – TMOTTM Dec 13 '13 at 14:27

You are acting under two false assumptions

  1. Electrode potentials are measured relative to real zero. They are not, there is no practical procedure to measure absolute electron potential. All standard potentials are measured relative to standard hydrogen electrode (well, actually some more pragmatic standard electrode, but recalculated to be against standard hydrogen electrode)

  2. That values got for gas has anything to do with values for condensed matter. Hydration energy can and does shift electrode potentials greatly, as well as energy of crystal lattice.

  • $\begingroup$ +1. I'd make one slight amendment to your answer here. You want "Solvation energy," since often electrochemistry is not in water. $\endgroup$ – Geoff Hutchison Sep 22 '14 at 19:00

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