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Percentage Composition of Mixture

  1. Sep 25, 2011 #1

    FeDeX_LaTeX

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    Gold Member

    1. The problem statement, all variables and given/known data
    "A mixture of calcium carbonate and magnesium carbonate with a mass of 10.000g was heated to constant mass, with the final mass being 5.096g. Calculate the percentage composition of the mixture, by mass."

    2. Relevant equations
    Decomposition equations.

    3. The attempt at a solution

    Here's my method, but it's not getting the supposed correct answer.

    Decomposition of both substances;

    [tex]CaCO_{3} \rightarrow{} CaO + CO_{2}[/tex]
    [tex]MgCO_{3} \rightarrow{} MgO + CO_{2}[/tex]

    Let the number of moles of CaCO3 = A
    Let the number of moles of MgCO3 = B

    Since [itex]n = \frac{m}{M_{r}}[/itex], then, using the fact that the total initial mass of the mixture is 10g;

    [tex]100.1A + 84.3B = 10[/tex]

    100.1 is the Mr of CaCO3, 84.3 is the Mr of MgCO3.

    Since the final mass is 5.096g (not including the CO2 formed), then;

    56.1A + 40.3B = 5.096

    We can do this because the ratios of moles in these reactions is 1:1:1 for both decompositions, as shown above. So we have a system of equations to solve. Solving, you get;

    A = 0.038252013(...)
    B = 0.073202531(...)

    Mass of CaCO3 = n*Mr = 100.1A = 3.83g (3 s.f.)
    Mass of MgCO3 = n*Mr = 84.3B = 6.17g (3 s.f.)

    Therefore, the percentage compositions of the mixture by mass are 38.3% CaCO3 and 61.7% MgCO3.

    Yet, my answer is supposedly wrong, since it's supposed to be 43.8% CaCO3 and 56.2% MgCO3...

    I can't see anything wrong with my method; can anyone point me in the right direction?

    Thanks.
     
  2. jcsd
  3. Sep 29, 2011 #2

    Borek

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    Staff: Mentor

    Looks to me like your method and your result are correct.

    Compare:

    CaCO3MgCO3.png

    Check if mass of the solid left agrees with the data for the answer given.
     
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