What is the relation between molality, molarity and density? is this correct, 'molality = molarity / density'? I got this off the internet....

molarity = mole / volume
density = mass / volume
molality = mole / mass

molality = molarity / density
mole / mass = (mole / vol) / (mass / vol)
mole / mass = mole / mass [proved]

The molarity of a solution is written as 

Molarity =  number of moles of solute / Volume of solution (in litres)

The molality of a solution is given by 

Molality = number of moles of solute / mass of the solvent (in Kg)

So, we see that the two are different terms. While one uses the volume of solution, the other term uses the mass of the solvent. So, when you use the relation 

 molality = molarity / density

you might not get the correct answer as volume of solution and volume of solvent, are not same most of the times. Consider the expression for molality again

 Molality = number of moles of solute / mass of the solvent (in Kg)

Now let us divide and multiply the RHS of the above relation by the volume of solvent. We get 

 Molality = (number of moles of solute / Volume of solvent) X [Volume of solvent / mass of the solvent (in Kg)]

 =  (number of moles of solute / Volume of solvent) X  (1/Density)

But for molarity, we use volume of solution and not volume of solvent. Hence the above expression might not give the correct answer. 

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i no M nd density i.e. 

M = %strength * density*10 / molar mass of solute

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