A sample of CaCO _ 3 and MgCO _ 3 weighed 2 .21 g is ignited to...

$CaC{O}_{3}\left(s\right)\overset{\Delta}{\to}CaO\left(s\right) + C{O}_{2}\left(g\right)$

$MgC{O}_{3}\left(s\right)\overset{\Delta}{\to}MgO\left(s\right) + C{O}_{2}\left(g\right)$

Let the weight of $CaC{O}_{3}$ be $xgm$

$∴$ weight of $MgC{O}_{3} = \left(2 .21 - x\right)gm$

Moles of $CaC{O}_{3}$ decomposed = moles of $CaO$ formed

$\dfrac{x}{100} =$ moles of $CaO$ formed

$∴$ weight of $CaO$ formed $= \dfrac{x}{100} \times 56$
Moles of $MgC{O}_{3}$ decomposed = moles of $MgO$ formed

$\dfrac{\left(2 .21 - x\right)}{84} =$ moles of $MgO$ formed

$∴$  weight of $MgO$ formed $= \dfrac{2 .21 - x}{84} \times 40$ $⇒ \dfrac{2 .21 - x}{84} \times 40 + \dfrac{x}{100} \times 56 = 1 .152$

$∴ x = 1 .187 g =$ weight of $CaC{O}_{3}$ and weight of $MgC{O}_{3} = 1 .023 g$