# Unit conversion of Molar Conductivity

I know this might be a silly question but I am confused with different answers of internet. My question is:

Molar conductivity is given as:

Molar conductivity = $k÷M$.

SI unit of : k is S/m &

M is in mol/$m^3$.

Thus Molar conductivity in SI is S$m^2$/$mol$ ......(1)

When I substitute 1m=100cm in (1). I got new unit as [S$cm^2$/$mol$]×$10^4$. But in a book It was given as [S$cm^2$/$mol$]×$10^3$ ........(2), where they have taken S in S/cm and molarity in mol/Litre. But where I was wrong.

If you feel the question too confusing just explain me How I can convert that SI unit given in (1) into unit given in (2).

• If M is molarity then yes it is taken in mol/litre and you have taken it mol/${m^3}$ which you can't do because it is defined that way. – Raghav Feb 1 '17 at 17:44
• But SI unit of M is actually moles/m3. And hence for SI unit of molar conductivity it must include M in moles/m3 & k must be in S/m. Then only we get SI unit of molar conductivity as Sm^2/mol. – Avi Feb 2 '17 at 3:35

You were actually right about the $\mathrm{10^4\ S\ cm^2/mol =S\ m^2 /mol}$. Check if the $\mathrm{10^3}$ you are referring to has molarity included in its equation because molarity is given as moles per litre.