You are given two aqueous solutions with different ionic solutes (Solution A and Solution B). What if you are told that Solution A has a greater concentration than Solution B by mass percent, but Solution B has a greater concentration than Solution A in terms of molality? Is this possible? If not, explain why not. If it is possible, provide example solutes for A and B and justify your answer with calculations.

Yes, it is possible. Let us consider an example of two solutions, that is, solution A having 20 percent mass RbCl (rubidium chloride) and solution B is having 15 percent by mass NaCl or sodium chloride.  

It is found that solution A is having more concentration in comparison to solution B in terms of mass percent. The formula for mass percent is,  

% by mass = mass of solute/mass of solution * 100

Now the formula for molality is,  

Molality = weight of solute/molecular weight of solute * 1000/ weight of solvent in grams

Now molality of solution A is,  

m = 20/121 * 1000/80 (molecular weight of RbCl is 121 grams per mole)

m = 2.07

Now the molality of solution B is,  

m = 15/58.5 * 1000/85

m = 3.02

Therefore, in terms of molality, the solution B is having greater concentration (3.02) in comparison to solution A (2.07).