Calculate Mole Fraction, Density, & %w/w given Molarity and Molality?

[kariibex]

Homework Statement

Consider the following aqueous solution at 25°C

Cr2(SO4)3, 1.26 mol/L, 1.37 mol/kg

Calculate the mole fraction, density and % w/w

Homework Equations

χ = n Cr2(SO4)3 / n Cr2(SO4)3 + n H2O
Unit conversions
ρ= g solvent / mL solution
% w/w = mass solvent / 100 g solution

The Attempt at a Solution

I attempted to solve for density first:

1.26 mol/L x 391.992g/mol x 1 L / 1000 mL = 0.493g/mL (The actual answer is 1.41g/mL)

Without density I do not know how to figure out the mole fraction. I am stuck at this part so far.

Thank you in advance.

 

[Borek]

Most general approach: try to derive the formula for conversion of molarity to molality. You will find molality is a function of molarity, density and molar mass - solve for density, all others are known.

Less general approach: imagine you have 1000 g of the solution. How many moles of chromium(III) sulfate does it contain (hint: use molality)? If so, what volume does it have (hint: use molarity)? Can you find density now, knowing volume and mass?