[PoetryInMotion]

Problem. In which of the following media is MeMgBr stable?
a) Water
b) Ammonia
c) Ether

My thoughts. The reaction with the solvent is more or less a simple acid-base reaction:

Me:^- + HA MeH + A-

with ⁺MgBr more or less acting as a spectator ion.

pKa for MeH is approximately 60 whereas it is 16 for water and 35 for ammonia, so in these cases it is quite obvious that the Gringard reagent will react with the solvent.

As for the ether, however, I have not found any pKa values in my literature, but as far as I have learned, the electronegative oxygen atom should inductively make the α carbons more acidic than alkanes. But at the same time I know from practice that ether is a common solvent for Grindgard reagents, so somehow I must do something wrong in my reasoning. Can anyone explain to me what?

[discodermolide]

Using pK_a values for the various components is OK. You won't find these values for ether as is is a neutral molecule. But pK_a is only part of the story. Gringards react with carbonyl groups, what is the pK_a of the C=O carbon in acetone? I don't think you will find that either. Gringards react with carbonyl groups.
Ether forms a solvate with these compounds which helps to stabilise them, same for methyl lithium.
So you also need to include the functionality of the solvent in your analysis, that is what other groups than NH or OH will react with organometallic compounds of this type?

In terms of this question the proposal you put forward are OK.