Understanding Density vs. Molality & Molarity (TBR Problem)

[ilovemcat]

I'm having trouble understanding this problem. The explanation for the answer doesn't really help either.

44. Given that a solute is denser than the solvent into which it dissolves, what is TRUE of the concentration measurements of different solutions made up solely of the two components?

A. The solution with the greatest density also has the greatest molarity and molality.
B. The solution with the greatest density also has the greatest molarity, but the molality is the same for all of the solutions.
C. The solution with the greatest density also has the lowest molarity and molality.
D. The solution with the greatest density also has the lowest molarity, but the molality is the same for all of the solutions.

The Correct answer is A.

Can someone explain the unit conversion behind obtaining the answer (had there been numbers involved) or atleast explain this so that I can better understand what the heck is going on here, lol.

Thanks.

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[ilovemcat]

I guess everyone else is just as confused as I am, haha.

 

[MediCynical]

I'm having trouble understanding this problem. The explanation for the answer doesn't really help either.

44. Given that a solute is denser than the solvent into which it dissolves, what is TRUE of the concentration measurements of different solutions made up solely of the two components?

A. The solution with the greatest density also has the greatest molarity and molality.
B. The solution with the greatest density also has the greatest molarity, but the molality is the same for all of the solutions.
C. The solution with the greatest density also has the lowest molarity and molality.
D. The solution with the greatest density also has the lowest molarity, but the molality is the same for all of the solutions.

The Correct answer is A.

Can someone explain the unit conversion behind obtaining the answer (had there been numbers involved) or atleast explain this so that I can better understand what the heck is going on here, lol.

Thanks.

I didn't use any unit conversion, but think of it this way.
You have 3 solutions, each with 1L of solvent and increasing amounts of solute.
Regardless of the density of the solute, increasing amounts of it will make the overall solution more dense because there will be more weight per unit volume.
The most dense solution will therefore have the most amount of solute in it = most moles of solute = greatest molarity.
Finally, since molality is just moles solute/kg solvent, and since all solutions will have the same amount of solvent, the solution with the most solute will also have the greatest molality.

 

[PiBond]

I didn't use any unit conversion, but think of it this way.
You have 3 solutions, each with 1L of solvent and increasing amounts of solute.
Regardless of the density of the solute, increasing amounts of it will make the overall solution more dense because there will be more weight per unit volume.
The most dense solution will therefore have the most amount of solute in it = most moles of solute = greatest molarity.
Finally, since molality is just moles solute/kg solvent, and since all solutions will have the same amount of solvent, the solution with the most solute will also have the greatest molality.

this is sorta how I thought about it as well. seek to understand the concept rather than unit conversion. i probably wouldn't use numbers if this was on my actual MCAT test

they tell us that the solute is denser than the solvent. thus, a solution with the greatest density must have the most amount of the denser particles in it relative to the amount of the less dense solvent. the more particles it has, the more moles it has. molality is just moles/kg solvent...therefore, the more moles we have the higher the molality, so therefore it must also have the highest molarity as well (moles/L solution)

hope that helps

 

[ilovemcat]

Yeah, I looked at this problem and was like ... whaaat. I probably re-read it like 3 times. I never really considered density with molality or molarity but I'm glad they did because I wasn't aware of the unit conversion there.

It might look a little like this:

[(Density) x Volume Solution/ Molar Mass ] = moles
--------------------------------------------------------
Volume Solution (Molarity) or Kilogram Solvent (Molality)


When thinking of density, I always considered it to be "mass over volume" and not really "mass of solute over volume solution." I guess that's why I got confused. Anyways, thanks fellas!

 

[Silverfalcon]

Yeah, I looked at this problem and was like ... whaaat. I probably re-read it like 3 times. I never really considered density with molality or molarity but I'm glad they did because I wasn't aware of the unit conversion there.

It might look a little like this:

[(Density) x Volume Solution/ Molar Mass ] = moles
--------------------------------------------------------
Volume Solution (Molarity) or Kilogram Solvent (Molality)


When thinking of density, I always considered it to be "mass over volume" and not really "mass of solute over volume solution." I guess that's why I got confused. Anyways, thanks fellas!

If you don't get the solution, then read it again. I recall this problem. It's one of tougher ones in that chapter, so you will have to read it and write the solution out until you understand.