Looks like the problem is the factor of n in your expression of the exponent. You must be consistent in using either molar heat capacities or total heat capacities in both numerator and denominator. You can't use nR/cm.
The exponent is (Cp/Cv - 1), which in total heat capacities is nR/Cv, or in molar heat capacities is R/Cv,m.
I think just using γ-1 as the exponent is simpler and avoids this possible confusion.

Hello,

I have to solve the following problem: 2 moles of argon are expanded reversibly and adiabatically. Before expansion, the gas has a temperature of 30 ◦C (303,15 K) with a volume of 2 L. After expansion, the volume is 15 L. The
Molar heat capacity of argon is cm = 12.4 J/mol K. What is the temperature of the gas after
of expansion ? to solve that problem I use the adiabatic equation : T2= T1 * (V1/V2)^(nR/cv)   My question is if cm is the same as cv? When I use cm as cv, I get  20 K for T2 which seems wrong. Thanks in advance

I am not an organiker, so take my answer with a grain of salt.

Regioselectivity in aromatic compounds is in a large part related to deviations in the electron density - which is to some extent related to the presence of resonance structures. In general, the more resonance structures possible, the lower their individual effect (ie the deviations from the equal distribution become smaller). The larger the molecule, the more atoms involved, the more the resonance structures possible - and the less prominent effects.

So if the selectivity of the reaction on a single ring is such that you get a 90:10 mixture of products, you can speak about the reaction being selective. When you get to several rings and you get mixture of 5:6:7:5:5:4:... it is hard to speak about "selectivity" as such.

This is not to say there are no specific examples when the reaction can be selective, it is just that the general trend seems to be working against.

Why do cations with greater oxidation number form stronger metallic bonds with itself?

Do they? Metallic bonds exist in metals between neutral atoms, no cations/oxidized atoms there.

and protons have the same charge as electrons

This is wrong the charges are in opposit. Protons are positiv and electrons are negativ.
In a metal the oxidation number is Zero.

What do you mean with

Why do cations with greater oxidation number form stronger metallic bonds with itself?

.
In compounds of metal and nonmetals we have ionic bonds, where also a oxidationnumber is existing. But normally no metalic bonds.