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I know that Cu+ ( cuprous ) ion is less stable than Cu²+ ( cupric ) ion . There are some reasons explaining this by high hydration enthalpies and low ionization enthalpies . Even though , these reasons explain so much , I wanted to know that how do these dominate over electronic configuration. How can we define more stability in terms of energy; like I can easily see the energy released by hydration and absorbed by ionization, but how can I compare it with the potential energy of Cu+ ion which is lowered by it's stable configuration ?

I searched on internet , but was unable to find data of the potential energy of the ions . Is there any theoretical reason which can explain that why hydration enthalpy and other factors must dominate the stable configuration?

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To say that $\ce{Cu^{2+}}$ (or more accurately, $\ce{Cu^{2+}}$ plus an equimolar amount of metallic copper, which conserves mass and charge) is more stable than $\ce{Cu^+}$ is something of a misstatement. Among the fourth period metals every $2+$ ion plus an equimolar amount of metal is more stable than the $1+$ ion when solvated by water, except obviously potassium. As described here, the extra electrostatic energy from water solvation of an ion with one more charge balances about $3000$ kJ/mol ionization energy, and among the $3d$ transition elements the second ionization energy always comes in under that. (So does the third in some of these elements.)

The real question is actually the reverse: why is $\ce{Cu^+}$ relatively stable so that we can ever see it at all in aqueous chemistry, unlike all other fourth-period metals besides potassium? The second ionization energy, which is the main energy cost to forming the $\ce{Cu^{2+}}$ ion, is raised somewhat by ionizing from a full $3d$ subshell, but beyond that the $\ce{Cu^+}$ ion is relatively good at forming bonds having covalent character with soft, polarizable bases.

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