Very hard chemistry challenge!?

[yanglovescuticles]

What's the molarity of 0.5 molal solution of calcium nitrate that has density of 1.045g/mL?

After you tried, read the details please
I keep getting
The molality is 0.5 molal, so I assumed there's 0.5 mol of Ca(NO3)2 to start with and 1 kg of water.
molar mass of Ca(NO3)2 is 164.08 g/mol
so
0.5 mol Ca(NO3)2 X (164.08g/mol) X (1mL/1.045g) = 78.507 mL
So the solid Ca(NO3)2 alone would take up 78.507 mL of the solution.
Since 1 kg of water is 1 L, 1.079 would be the volume of the solution. Since we started with 0.5mol, the molarity I figured should be 0.5mol/1.079L = 0.463M BUT IT'S NOT!!! AHHHHHHHHHHHHH!!! The answer is 0.483M.
Chinmaya, molality is moles over kg of SOLVENT.
No, the answer is 0.483M. Do you think I lied?
And for all your nerds, the rule of thum is, your molarity is always smaller than molality in this kind of problem (with water being solvent and with solute taking up significant volume)
I can't type today ^_^
m w, you seem to be getting it! yay finally! I think my mistake was, I thought the density referred to the density of the solid rather than the whole solution.
Oh nice! Charu, I think you got it.
Wait actuallly you didn't...
wait now you did lol sorry
How did you guys know the density was referring to the solution rather than the solute Ca(NO3)2?