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

  1. Oct 6, 2013 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant 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

    3. 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.
     
  2. jcsd
  3. Oct 6, 2013 #2

    Borek

    User Avatar

    Staff: Mentor

    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?
     
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