Work so far:
Molality = mol solute/kg solvent
Molarity = mol solute/L solution

So for molarity to exceed molality in the same solution, the numerical value of
kg of solvent > L of solution

From my experience this never happens. However by applying this to a very dense solvent, could the mass of solvent actually exceed the combined volume of solvent and solute. I am aware that volumes are not additive, and so if the density of a solvent is 10 g/mL the density 10 times of water and 0.5 M 2 L of HCl is added to 4 L of solvent, mass of solvent would be 40 kg solvent could the volume actually be greater then 40 L? Is there an example of a physical system where molality is lower then molarity?

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    $\begingroup$ Try thinking of very dilute solutions in a solvent denser than water, as you can make some very helpful simplifications. What is the relationship between molarity and molality then? $\endgroup$ – Nicolau Saker Neto Dec 6 '15 at 4:47

There is one possibility with glycerol With density 1.261 g/cm 3.Here the exact numerical value of mass is greater than that of volume of glycerol in kg and litres respectively.Moreover glycerol is soluble in water and vice versa.


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