Dolomite is a mixed carbonate of calcium and magnesium that decomposes to CO2 and the metal oxides MgO and CaO upon heating. When 11.15 g of dolomite is heated, 5.70 g of MgO and CaO are produced. What is percent by mass of MgCO3 in the original sample of dolomite?

So, [tex]\frac{x}{84.314}[/tex] moles of magnesium carbonate will produce = [tex]\frac{1}{1}\times \frac{x}{84.314}=\frac{x}{84.314}mol[/tex] of magnesium oxide

Mass of magnesium oxide = [tex]\text{Moles of magnesium oxide}\times \text{Molar mass of magnesium oxide}[/tex]

Mass of magnesium oxide = [tex](\frac{x}{84.314}\times 40.304)g[/tex]

The chemical equation for the heating of calcium carbonate follows the equation:

[tex]CaCO_3\rightarrow CaO+CO_2[/tex]

By Stoichiometry of the reaction:

1 mole of calcium carbonate produces 1 mole of calcium oxide

So, [tex]\frac{(11.15-x)}{100.087}[/tex] moles of calcium carbonate will produce = [tex]\frac{1}{1}\times \frac{(11.15-x)}{100.087}=\frac{(11.15-x)}{100.087}mol[/tex] of calcium oxide

Mass of calcium oxide = [tex]\text{Moles of calcium oxide}\times \text{Molar mass of calcium oxide}[/tex]

Mass of calcium oxide = [tex](\frac{(11.15-x)}{100.087}\times 56.077)g[/tex]

We are given:

Mass of MgO and CaO produced = 5.70 g

[tex](\frac{x}{84.314}\times 40.304)+(\frac{(11.15-x)}{100.087}\times 56.077)=5.70\\\\0.478x+6.244-0.560x=5.70\\\\0.082x=0.544\\\\x=\frac{0.544}{0.082}=6.63g[/tex]

To calculate the mass percentage of magnesium carbonate in dolomite, we use the equation:

[tex]\text{Mass percent of magnesium carbonate}=\frac{\text{Mass of magnesium carbonate}}{\text{Mass of dolomite}}\times 100[/tex]

Mass of dolomite = 11.15 g

Mass of magnesium carbonate = 6.63 g

Putting values in above equation, we get:

[tex]\text{Mass percent of magnesium carbonate}=\frac{6.63g}{11.15g}\times 100=59.5\%[/tex]

Hence, the mass percent of magnesium carbonate in given amount of dolomite is 59.5 %