# 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 = $$\frac{\kappa}{M}$$.

S.I. unit of : $$\kappa$$ is $$\pu{Sm}^{-1}$$ &

$$M$$ is in $$\mathrm{mol \, m^{-3}}$$.

Thus, Molar conductivity in S.I. is $$\mathrm{S \, m^2 \, mol^{-1}} \tag{1}$$

When I substitute 1 m = 100 cm in (1). I got new unit as $$[\mathrm{S \, cm^2 \, mol^{-1}}] \times10^4$$. But in a book It was given as

$$[\mathrm{S \, cm^2 \, mol^{-1}}] \times 10^3 \tag{2}$$

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. Feb 1, 2017 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, 2017 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.