why 0.05M HCL has a higher concentration of hydrogen ions than 0.5M CH3COOH?

Answer 1

HCl is a strong acid. That means it ionizes completely when in water. Acetic acid is a weak acid. It ionizes a small amount when in water. Most of the acetic acid remains in the molecular form in the water so very few H+ ions are present to form the acid.

Answer 2

Yes, the answer has to do with the degree of dissociation of molecules to form H+ ions.
HX <--> X- + H+
HCl dissociates almostly completely, forming a high concentration of H+ ions, and thus is regarded as a strong acid.
CH3COOH (which is organic) dissociates to a small extent, forming very little H+ ions, and thus is regarded as a weak acid.

So now I suppose the question is why does HCl release so much more H+ ions...
Picture H-Cl, with H being a very small positively charged ball, and Cl being a very very large negatively charged ball.
The charge of Cl is so much higher than H that it starts to distort the electron cloud of H+ to such an extent it robs the single electron that H has, therefore forming H+!

Answer 3

HCl is a stronger acid than CH3COOH.
it is able to dissociate into ions(H+ + Cl-) completely since it is a strong electrolyte.
0.05M HCl gives 0.05M H+
since CH3COOH is an organic acid it dissociates feebly due to the presence of +I effect ( electron pushing effect) of the -CH3 groups
thus increasing electron density around the oxygen hence it has more affinity towards the H+ .