Conductivity of a solution at any given concentration is the conductance of 1 unit volume of solution kept between 2 electrodes which are unit length apart and have unit area of crossection. It is the conducting power of all ions confined in 1m3 of volume. Mathematically, it is the reciprocal of resistivity.
Molar conductivity is defined as conducting power of all ions produced by 1 mole of an electrolyte kept between the electrodes of a conductivity cell at unit distance but having area of crossection large enough to accommodate sufficient volume of the solution that contains 1 mole of electrolyte.
Conductivity of solution decreases with dilution because on dilution no. of ions in 1 unit volume decreases. As the no. of ions decreases the conductivity also decreases.
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