define conductivity and molar conductivity

Many students get  confused about the terms 'Conductance' and 'Conductivity'. The inverse of resistance is called Conductance(C or G) and the inverse of resistivity, ρ(Greek, rho) is called Conductivity(κ) ( or specific conductance), κ = 1/ρ. Thus, conductivity of a solution is the conductance of 1 cm3(or 1 m3) of the solution of the electrolyte. One should use the term 'Molar conductivity' rather than 'Molar conductance'.

Conductivity: The reciprocal of resistance of an electrolyte in aqueous solution is known as its conductivity. It is equal to 
Molar Conductivity: Molar conductivity of a solution is defined as the conductance of all ions present in one mole of electrolyte in the solution. If M is the molar concentration in mol L^–1, then.


Fig: Molar conductivity versus C^1/2 for acetic acid (week electrolyte) and potassium chloride (strong electrolyte in aqueous solutions)
The curve shown below gives the change in conductance against square root of concentrations. We observe that for strong electrolytes like KCl, the conductance does not change much with decrease in  whereas in the case of weak electrolyte like acetic acid (CH₃COOH) it increases much with decrease in