I need help calculating molality, molarity and mole fraction from density.

Question

an aqueous solution is 5.50% by mass of a nonelectrolyte (MM= 134 g/mol). If the density of the solution is 1.026 g/mL, calculate the molarity, mole fraction and molarity of the solution.
I have no idea where to even begin :(

Answer 1

Each of this measures of concentration contains a different basis, so the first thing to establish is the volume of the solution and the mass of the electrolyte.

 

Let us consider 1 ml of solution.   That weights 1.026 grams, 5.5% of which is the electrolyte.

So mass of electrolyte = 0.0550 * 1.026 gm = 0.0564 gm of solute.   

The mass of the solvent is then 1.026 -0.0564 or 0.970 g or   9.7 * 10-4 kg 

Since the density of water is 1kg/liter, there are also 9.7 * 10-4 liters of water

The moles of solute are 0.0564 g / 134 g/mol or 4.21 * 10 -4 moles

Assuming that the solvent is water, then the number of moles of water is   0.970g / 18 g/mol or .0539 moles of solvent.   

 

Now we have what is needed to calculate all of the required measures.

the mole fraction is  4.21 * 10-4 /0.0539 = .00781 or 0.781%

the molarity is moles/liter = 4.21 * 10-4/9.70 * 10-4 =0.434 M

The molality is moles of solvent per kg of solution =   4.21 * 10-4 moles/1.026 * 10-3kg = 0.410 moles/kg