Q3.144CP - Chemistry: Molecular Nature Of Matter And Change

Question

When carbon-containing compounds are burned in a limited amount of air, some CO(g)as well as CO₂(g)is produced. A gaseous product mixture is 35.0 mass % COand 65.0 mass % CO₂ What is the mass % in the mixture?

 

Step-by-Step Solution

Answer

The mass % of C in the mixture is 32.75%.

Step 1: Write the combustion equation of the carbon-containing compound

Whenthe  carbon-containing compound is heated in presence of a limited amount of oxygen, it gives carbon dioxide and carbon monoxide. The combustion equation of carbon-containing compound is:

$Compound\left(s\right)+O_2\left(g\right)\to C{O}_2\left(g\right)+CO\left(g\right)$

Step 2: Relation between mass and number of moles

The number of moles is calculated by the mass and Molar mass. The relationship between the number of moles, mass, and molar mass is given below.

$Number of moles=\frac{mass}{Molar mass}$

Step 3: Determine the mass of CO and CO2:

Consider 100 g of carbon-containing compound is burned and forms 35 mass % $CO$ and 65 mass % $C{O}_2.$ This states that 100 g of carbon-containing compound produces 35 g of CO and 65 g of CO₂

Step 4: Calculate the number of moles of CO

The mass of CO = 35 g

The molar mass of CO = 28.01 g/mol

The number of moles of CO is calculated as

$\begin{array}{rcl}moles of CO& =& \frac{mass of CO}{Molar mass of CO}\\ & =& \frac{35 g}{28.01 g/mol}\\ & =& 1.2496 mol\end{array}$

Step 5: Calculate the number of moles of C

Since 1 mol of the C atom is present in 1 mol of CO

So, the number of moles of C is:

$\begin{array}{rcl}1 mol of CO& =& 1 mol of C\\ 1.2496 mol of CO& =& 1.2496 mol of C\end{array}$

Step 6: Calculate the mass of Carbon

The molar mass of Carbon = 12.01 g/mol

Thus, the mass of Carbon is:

$\begin{array}{rcl}mass of C& =& moles of C\times molar mass of C\\ & =& 1.2496 mol\times 12.01 g/mol\\ & =& 15.01 g\end{array}$

Step 7: Calculate the number of moles of CO2

The mass of CO₂ = 65 g

The molar mass of CO₂ = 44.01 g/mol

The number of moles CO₂  is calculated as

$\begin{array}{rcl}Moles of C{O}_2& =& \frac{mass of C{O}_2}{Molar mass of C{O}_2}\\ & =& \frac{65 g}{44.01 g/mol}\\ & =& 1.4769 mol\end{array}$

Step 8: Calculate the number of moles of carbon

Since 1 mol of the carbon atom is present in 1 mol of $C{O}_2.$

So, the number of moles of  C is:

$$\begin{gathered} \text{1} \text{mol} \text{of} {\text{CO}}_{\text{2}}\text{=1} \text{mol} \text{of} \text{C} \\ \text{1.4769} \text{mol} \text{of} {\text{CO}}_{\text{2}}\text{=1.4769} \text{mol} \text{of} \text{C} \end{gathered}$$

Step 9: Calculate the mass of carbon

The molar mass of carbon = 12.01 g/mol

Thus, the mass of carbon is:

$\begin{array}{rcl}Mass of C& =& moles of C\times molar mass of C\\ & =& 1.4769 mol\times 12.01 g/mol\\ & =& 17.74 g\\ & & \\ & & \end{array}$

Step 10: Determine the total mass of C from CO and CO 2

The total mass of C is the sum of the mass of C present in CO and CO₂Therefore, 

$\begin{array}{rcl}mass of C& =& 15.01 g+17.74 g\\ & =& 32.75 g\end{array}$

Step 11: Calculate the mass % of the in the mixture

The mass % of the Carbon is calculated as

$\begin{array}{rcl}mass \% of C& =& \frac{mass of C}{mass of carbon containing compound}\times 100\%\\ & =& \frac{32.75 g}{100 g}\times 100\%\\ & =& 32.75\%\end{array}$