0.1 mole of acetic acid will have better conduction of electricity or 1mole of acetic acid???

0.1 mole of acetic acid will conduct electricity better than 1 mole of acetic acid present in the same volume of water.
Molar conductivity,Λm=specific conductancecwhere c is the concentration of the solution

Acetic acid is a weak electrolyte and is dissociated to a lower degree in concentrated solution. 
Dilute solution have a higher degree of dissociation and hence more number of ions are present to conduct electricity.

Hence, in a fixed volume of solvent, the lower number of moles will conduct electricity better.

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