For strong electrolytes, according to Kohlrausch, molar conductivity decreases as the concentration increases.
( i don't know why I'm not allowed to attach a photo here in order to show you the diagram ), but however I'm trying to explain how the diagram looks.
In the diagram we have strong electrolytes like HCl, H2SO4, KCl, LaCl3, Na2SO4$\ce{HCl,\, H2SO4,\, KCl,\, LaCl3,\, Na2SO4}$ whose molar conductivity decreases as the concentration increases. But, what I don't understand is that in the diagram we have also CH3COOH$\ce{CH3COOH}$ which is a weak electrolyte, and his molar conductivity also is decreasing and even far more rapidly, as the concentration increases.
Can somebody explain this ?