Multiple choice

A sample containing only $CaCO_{3}$ and $MgCO_{3}$ is ignited to $CaO$ and $MgO$. The mixture of oxides produced weight exactly half as much as the original sample. The mass percentages of $CaCO_{3}$ and $MgCO_{3}$ in the sample are respectively :

  1. $28.4$%, $71.6$%
  2. $71.6$%, $28.4$%
  3. $56.7$%, $43.3$%
  4. $78.5$%, $21.5$%
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AI explanation

Let the mass of CaCO3 be x and the mass of MgCO3 be y; the total mass is x + y. Upon heating, the mass of the oxides is (56/100)x + (40/84)y, which equals 0.5(x + y). Solving the equation 7x/25 + 10y/21 = (x + y)/2 gives 44x = 111y. Substituting y = 44x/111 into the total mass expression yields a CaCO3 mass percentage of 28.4% and a MgCO3 percentage of 71.6%.

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