How Do You Calculate the Percentage Composition of a Heated Mixture?

[FeDeX_LaTeX]

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;

CaCO_{3} \rightarrow{} CaO + CO_{2}
MgCO_{3} \rightarrow{} MgO + CO_{2}

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

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

100.1A + 84.3B = 10

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.

 

[Borek]

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

Compare:

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