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Homework Statement
"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."
Homework Equations
Decomposition equations.
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.