You need to know the identity of the compound.

The only way to go from milligrams, a unit of mass, to moles is by using the molar mass of the given compound.

As you know, the molar mass of a compound tells you the mass of one mole of that compound. Let’s say that your compound has a molar mass of ##M_M## grams per mol.

This tells you that one mole of this compound has a mass of ##M_M## grams.

Now, notice that before going from grams to moles you must go from milligrams to grams.

The conversion factor that you come in handy here is

##”1 g” = 10^3″mg”##

Moreover, you need to go from milliliters to liters, so a similar conversion factor is needed

##”1 L” = 10^3″mL”##

Now you’re ready to convert between milligrams per milliliter to moles per liter

##0.01(color(red)(cancel(color(black)(“mg”))))/(color(red)(cancel(color(black)(“mL”)))) * (10^3color(red)(cancel(color(black)(“mL”))))/”1 L” * (1color(red)(cancel(color(black)(“g”))))/(10^3color(red)(cancel(color(black)(“mg”)))) * “1 mole”/(M_Mcolor(red)(cancel(color(black)(“g”)))) = (0.01/M_M) color(white)(a)”mol/L”##

So, for a compound that has a molar mass equal to ##M_M##, you have

##color(green)(“0.01 mg/mL” = (0.01/M_M) color(white)(a)”mol/L”)##