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QUESTION

# How to convert 0.01 mg/ml to mol/L? Thanks

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")