Question

calcium carbonate, caco₃, decomposes when heated to calcium oxide (cao) and carbon dioxide (co₂). if 100 g of calcium carbonate is allowed to decompose, 56 g of calcium oxide is produced. what mass of carbon dioxide is produced by the decomposition?
your answer should be rounded to the nearest whole number. do not include units in your answer.
enter the answer

Explanation:

Step1: Write the decomposition equation

The decomposition of calcium carbonate ($CaCO_3$) is $CaCO_3(s)\xrightarrow{\Delta}CaO(s)+CO_2(g)$.

Step2: Determine molar masses

The molar mass of $CaCO_3$ is $M_{CaCO_3}=40 + 12+3\times16=100\ g/mol$, the molar mass of $CaO$ is $M_{CaO}=40 + 16 = 56\ g/mol$, and the molar mass of $CO_2$ is $M_{CO_2}=12+2\times16 = 44\ g/mol$.

Step3: Use the stoichiometry

From the balanced - equation, the mole - ratio of $CaCO_3$ to $CO_2$ is $1:1$. Given $100\ g$ of $CaCO_3$ (which is $n_{CaCO_3}=\frac{100\ g}{100\ g/mol}=1\ mol$), and $56\ g$ of $CaO$ (which is $n_{CaO}=\frac{56\ g}{56\ g/mol}=1\ mol$). According to the stoichiometry of the reaction, when $1\ mol$ of $CaCO_3$ decomposes, $1\ mol$ of $CO_2$ is produced.

Step4: Calculate the mass of $CO_2$

Since $n_{CO_2}=1\ mol$ (from the stoichiometry), and $m = nM$, so $m_{CO_2}=n_{CO_2}\times M_{CO_2}=1\ mol\times44\ g/mol = 44\ g$.

Answer:

44