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A mixture of CaCO(3) and MgCO(3) weighin...

A mixture of `CaCO_(3)` and `MgCO_(3)` weighing `1.84 g` on heating left a residue weighing `0.96 g`. Calculate the percentage of each in the mixture.

Text Solution

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Calcium carbonate and magnesium carbonate on heating give CaO and MgO as residues:
`CaCO_(3) overset("heat") to CaO + CO_(2)`
`underset(84 g)(MgCO_(3)) overset("heat") to underset(40 g)(MgO + CO_(2))`
Let `CaCO_(3)` present in the mixture = x g.
Wt. of `MgCO_(3)` in the mixture = (1.84 -x)g
Now, 100 g of `CaCO_(3)` gives CaO = 56 g
x g of `CaCO_(3)` give CO `=56/100 xx x g`
Similarly, 84 g of `MgCO_(3)` gives MgO = 40 g
`(1.84-x) g` of `MgCO_(3)` give `MgO = 40/84 xx (1.84-x)`
Total residue obtained.
`(56 x)/100 + 40/84 (1.84 -x) = 0.96`
4704x + 7360 - 4000 x = 8064
704 x = 704
`x=704/704 = 1 g`
Weight of `CaCO_(3)` in the mixture = 1g
Weight of `MgCO_(3)` in the mixture = 1.84 -1 = 0.84 g
% of `CaCO_(3) =1/(1.84) xx 100 = 54.35%`
% of `MgCO_(3) = (0.84)/(1.84) xx 100 = 45.65%`
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