Mass of water greater at lower temperature???

[aardvarkm12]

In a Berkeley Review question, it asks to compare the molality of 1.0g of compound MX with 10mL of water at 25C and at 50C.

However, according to Berkeley Review, "Because the density of water decreases as the temperature of water increases, the mass of 10 mL water is greater at the lower temperature".

So they are saying the molality of 1.0g of MX with 10mL of water at 25C is HIGHER than the molality of 1.0g of MX with 10mL of water at 50C. But...my understanding was that molality does NOT change with temperature, while molarity does.

Can anyone explain the statement " the mass of 10 mL water is greater at the lower temperature"???

Thanks!

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[Cawolf]

The volumes are stated to be equal and it is known that densities are different. Therefore the mass will differ.

There is equal solute, so the more massive (colder) solution will have a greater mass of solvent.

Molality is moles/kg, so the more massive solution will have a lower molality.

The molarity should be constant, because the units are moles/Liter, which is the same in both samples.

 

[NextStepTutor_1]

Exactly, @Cawolf nailed it.
Remember your equations.
Molality = moles of solute / mass of solvent
Molarity = moles of solute / volume of solvent

Because the volume of the water is remaining the same with increasing temperature, the molarity is remaining the same.
Because the mass of the water is changing (due to density change) with increasing temperature, the molality is changing.

 

[Czarcasm]

@NextStepTutor_1 @Cawolf Either of you willing to loan out your brain for a day? I promise I'll return in it in good condition. Seriously though, I appreciate you guys' replies, especially with physics and chemistry stuff - really helpful.

 

[Cawolf]

I wish! I am just starting my MCAT studying this week - so I doubt I can be of much aid.

But I am happy to reply to questions on topics I am comfortable with!

 

[techfan]

Cawolf and NextStep have given great explanations, but I'll chime in to see if my understanding is good. I look at it as the molecules of water at a higher temperature "bounce around" more and take up more volume (like giving kids crack {I guess candy would've worked too} and having them go into a bouncy castle), in the problem they fix the volume (size of the bouncy castle) so the amount of molecules is limited by the temperature (fit less cracked out kids {assuming you don't want injury/lawsuits} in bouncy castle than kids on Ambien).