Does this problem require knowing the density of water?

[JeweliaHeart]

Homework Statement

What is the molality of an aqueous solution of a compound with a molar mass of 120. g/mol that has a density of 1.56 g/mL and a molarity of 5.78 M?

(A) 6.67 m
(B) 5.78 m
(C) 120. m
(D) 1.56 m
(E) None of the Above

Homework Equations

Molality= moles solute/kilograms solvent

The Attempt at a Solution

I assumed a volume of 1 L of solution, leaving me with 5.78 moles solute.

5.78 moles solute x 120 g/mole solute = 693.6 g solute

693.6 g solute x 1 mL/ 1.56 g solute =444.615 mL (the space taken up by the solute)

1000 ml(b/c I assumed 1 L solution)- 444.615= 555.385 ml (volume of solvent, water)

I don't know where to go from here b/c I don't know what the density of water is at whatever temperature the solution is at.

 

[Borek]

I believe you are misreading the question. 1.56 g/mL is density of the solution, not of the solute. If so, what is mass of the 1L of the solution? How much of this mass is water?

If 1.56 g/mL is intended to be density of the solute, there is not enough information to solve the problem.

 

[JeweliaHeart]

Thanks so much Borek.

Yes, I was misreading the problem. I tried solving it again using 1.56 g/mL as the density of the entire solution and I got the right answer, which is a) 6.67 molality.

I got to start reading these problems more carefully.

 

[Borek]

I am not surprised you misread the problem, it is lousy worded and confusing. For me it was obvious as I have seen zillions of such questions.

 

[DeeNos]

Yes, this problem does require knowing the density of water. In order to calculate the molality of the solution, we need to know the mass of the solvent (water) in kilograms. This requires knowing the volume of water, which can be calculated using the density of water. Without this information, we cannot accurately calculate the molality of the solution. Therefore, the correct answer to this problem is (E) None of the Above.