Mass %, Molality, Volume

[blayne]

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There are 4 aqueous salt solutions that are each 4% by mass.
A. 4% by mass of KBr in water
B. 4% by mass of KCl in water
C. 4% by mass of NaBr in water
D. 4% by mass of NaCl in water

Will 1 L of each solution have the same mass of solvent (i.e. water)? I don't think so. Won't the solution with the lowest density salt, have the smallest volume (and thus mass) of water? The explanation provided for TBR GChem question I.34 suggests that the mass of solvent would be identical.

Am I just being stupid.

 

[sciencebooks]

There are 4 aqueous salt solutions that are each 4% by mass.
A. 4% by mass of KBr in water
B. 4% by mass of KCl in water
C. 4% by mass of NaBr in water
D. 4% by mass of NaCl in water

Will 1 L of each solution have the same mass of solvent (i.e. water)? I don't think so. Won't the solution with the lowest density salt, have the smallest volume (and thus mass) of water? The explanation provided for TBR GChem question I.34 suggests that the mass of solvent would be identical.

Am I just being stupid.

If all of the solutes account for 4% of mass of the total solvent, I don't see how the solvent could possibly have the same mass since those solutes definitely don't...

Or is it saying there's always 1 L of water which is then always 1 kg? :-/

 

[blayne]

The solutes account for 4% of the mass of the total SOLUTION, NOT THE SOLVENT. It is 1L of solution. So doesn't that imply different volumes of solvent/water?

 

[MangoPlant]

Lets think about it in terms of %Mass Solvent. Each of the solutions will be 96% water by mass. Now here is the tricky part: 1L of each solution does NOT weigh the same because the dissolved solutes change the density. Since all of these solutions are 1L, and since 96% MASS of each solution is water, the solution with the highest density (which results in highest weight since all solutions have the same volume) will have the most amount of water.

In short, the solution that is most dense will have the most water. At least I think..

 

[V5RED]

You are right that this question is not very good. It should have asked for molality, not molarity. If it had asked for molality, it would be very simple. We could assume we have 1000g of solution. At 4% we end up with 40g of solute and 960g of solvent. We would then divide moles solute by kg solvent and get our answer.

Instead we were asked for molarity but not given densities, so the best guess is to guess that molarity follows molality trends. I looked up the densities and did the math, and it does appear that their answer is correct although, as mentioned, I don't agree with the presentation of the question or their reasoning.

40g NaCl=.69moles
40g NaBr=.39 moles
40g KCl= .54 moles
40g KBr= .34 moles


40g NaCl= 18.5mL--->.9785L solution--->.71M
40g NaBr= 18.3mL--->.9783L solution--->.40M
40g KCl= 20.2mL--->.9802L solution--->.55M
40g KBr= 14.6mL--->.9746L solution--->.35M