Question

When carbon is burned in air, it reacts with oxygen to form carbon dioxide. When 12.0 g of carbon were burned in the presence of 46.1 g of oxygen, 14.1 g of oxygen remained unreacted. What mass of carbon dioxide was produced?

Answer 1

The balanced equation of the reaction described is:

$C+O_2\rightarrow CO_2$

Now, to find the mass of CO2 produced, we will follow these steps:

1. We are told that after the reaction there are 14.1 g of oxygen left unreacted, that is, the grams of oxygen that react will be 46.1g - 14.1g =32 g O2. We calculate the moles that react using the molar mass of oxygen. Molar mass oxygen= 31.998gO2

2. We find the moles of CO2 by stoichiometry

3. We find the mass of CO2, using the molar mass of CO2. Molar mass CO2=44.01g/mol

Let's proceed with the calculations.

1. Moles of O2 that react

$\begin{gathered} molO_2=givengO_2\times\frac{1molO_2}{MolarMass,gO_2} \\ molO_2=32gO_2\times\frac{1molO_2}{31.998gO_2}=1molO_2 \end{gathered}$

2. Moles of CO2 produced

By stoichiometry, the ratio CO2 to O2 is 1/1. So, the moles of CO2 produced is:

$\begin{gathered} molCO_2=GivenmolO_2\times\frac{1molCO_2}{1molO_2} \\ molCO_2=1molO_2\times\frac{1molCO_2}{1molO_2}=1molCO_2 \end{gathered}$

3. Grams of CO2 produced

$\begin{gathered} gCO_2=givenmolCO_2\times\frac{MolarMass,gCO_2}{1molCO_2} \\ gCO_2=1molCO_2\times\frac{44.01gCO_2}{1molCO_2}=44.0gCO_2 \end{gathered}$

Answer: The mass of carbon dioxide produced was 44.0g