Standard electrode potential vs ionization energy

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Here is the Wikipedia page on electrode potentials. Here's how I'm reading it, which makes no sense:

If a singly ionized atom of strontium donates an electron to the hydrogen in the standard hydrogen electrode, this will emit 4.101 eV of heat (395.68 kJ/mol). If cesium is used, there will be 3.026 eV (291.96 kJ/mol).

Now, what I thought this involves is, you take an electron from strontium (549.5 kJ/mol) and give it to hydrogen (1312 kJ/mol) for a net gain of 762.5 kJ/mol. With cesium, the ionization energy is 375.7, so you should gain 936.3 kJ/mol.

Where is the rest of it, and why is strontium higher?

I understand these are half-reactions, but I don't understand what a half-reaction is.
 

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TeethWhitener
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Reduction potentials are generally measured in aqueous solutions, while ionization energies are measured in the gas phase.
 
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Charles Link
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Reduction potentials are generally measured in aqueous solutions, while ionization energies are measured in the gas phase.
To add to what @TeethWhitener said, there will be an energy change for the atom on the electrode as it becomes an ion in the solution=the binding energy of the atom to the electrode needs to be overcome. On the receiving end, the hydrogen (ion) comes out of solution and usually results in the diatomic form of hydrogen gas.
 
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I thought the electrolyte probably plays a role, but I wasn't sure what that role is. And also had a hard time picturing what is going on.

So the electron isn't simply moved from one atom to another. The metal goes from M (s) to M+ (aq), so it would break the bonds it had in the crystal, but also form new bonds with water. And the hydrogen does its own version of that. Is that about right?

But how do you get strontium to be +1? As far as I know, it always goes to +2 in water.

Also, when they write H+, do they really mean H3O+?
 
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Charles Link
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I thought the electrolyte probably plays a role, but I wasn't sure what that role is. And also had a hard time picturing what is going on.

So the electron isn't simply moved from one atom to another. The metal goes from M (s) to M+ (aq), so it would break the bonds it had in the crystal, but also form new bonds with water. And the hydrogen does its own version of that. Is that about right?

But how do you get strontium to be +1? As far as I know, it always goes to +2 in water.

Also, when they write H+, do they really mean H3O+?
The valence of +2 is something I didn't consider, but if it is +2, the energy for the reaction would need to be specified as per mole of electrons or per mole of strontium. The table has two entries for Sr. One for ## Sr^{+1} ## and one for ## Sr^{+2} ##. The ## Sr^{+2} ## has a potential of -2.899.
 
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Borek
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I thought the electrolyte probably plays a role
Beware: not electrolyte (although it can be of importance as well) but a solvent is what is the first thing to consider here.

Also, when they write H+, do they really mean H3O+?
Yes, they are sometimes used interchangeably. Note, that H3O+ is actually not correct - in reality proton is surrounded by several water molecules, so the real formula is something like H(H2O)n+. This is actually a series of compounds in equilibrium with each other, from what I remember n takes values up to 5 or 6.

Now, take into account energy released by each water molecule attracted by the proton, and imagine the same thing happening to the metal ions (we say they are solvated, or hydrated). These energies can be quite large (think how concentrated sulfuric acid gets hot on dilution, think how anhydrous CaCl2 gets hot when dissolved) - do you see why it is not enough to speak just about the ionization energies?
 
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