Questions: Using the balanced equation for the combustion of acetylene (C2H2), answer the following questions. 2 H-C ≡ C-H+5 O2 → 4 CO2+2 H2O a. How many moles of O2 are needed to react completely with 1.80 mol of C2H2? b. How many moles of C2H2 are needed to form 0.26 mol of CO2?

Using the balanced equation for the combustion of acetylene (C2H2), answer the following questions. 2 H-C ≡ C-H+5 O2 → 4 CO2+2 H2O
a. How many moles of O2 are needed to react completely with 1.80 mol of C2H2?
b. How many moles of C2H2 are needed to form 0.26 mol of CO2?

Transcript text: Using the balanced equation for the combustion of acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$, answer the following questions. $2 \mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}+5 \mathrm{O}_{2} \rightarrow 4 \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ a. How many moles of $\mathrm{O}_{2}$ are needed to react completely with 1.80 mol of $\mathrm{C}_{2} \mathrm{H}_{2}$ ? b. How many moles of $\mathrm{C}_{2} \mathrm{H}_{2}$ are needed to form 0.26 mol of $\mathrm{CO}_{2}$ ?

Solution

Solution Steps

Step 1: Understand the Balanced Chemical Equation

The balanced chemical equation for the combustion of acetylene ($\mathrm{C}_{2} \mathrm{H}_{2}$) is:

\[ 2 \mathrm{C}_{2} \mathrm{H}_{2} + 5 \mathrm{O}_{2} \rightarrow 4 \mathrm{CO}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \]

This equation tells us that 2 moles of $\mathrm{C}_{2} \mathrm{H}_{2}$ react with 5 moles of $\mathrm{O}_{2}$ to produce 4 moles of $\mathrm{CO}_{2}$ and 2 moles of $\mathrm{H}_{2} \mathrm{O}$.

Step 2: Calculate Moles of $\mathrm{O}_{2}$ Needed for 1.80 mol of $\mathrm{C}_{2} \mathrm{H}_{2}$

From the balanced equation, the mole ratio of $\mathrm{C}_{2} \mathrm{H}_{2}$ to $\mathrm{O}_{2}$ is 2:5. Therefore, for every 2 moles of $\mathrm{C}_{2} \mathrm{H}_{2}$, 5 moles of $\mathrm{O}_{2}$ are required.

To find the moles of $\mathrm{O}_{2}$ needed for 1.80 moles of $\mathrm{C}_{2} \mathrm{H}_{2}$:

\[ \text{Moles of } \mathrm{O}_{2} = 1.80 \, \text{mol} \, \mathrm{C}_{2} \mathrm{H}_{2} \times \frac{5 \, \text{mol} \, \mathrm{O}_{2}}{2 \, \text{mol} \, \mathrm{C}_{2} \mathrm{H}_{2}} = 4.50 \, \text{mol} \, \mathrm{O}_{2} \]

Step 3: Calculate Moles of $\mathrm{C}_{2} \mathrm{H}_{2}$ Needed to Form 0.26 mol of $\mathrm{CO}_{2}$

From the balanced equation, the mole ratio of $\mathrm{C}_{2} \mathrm{H}_{2}$ to $\mathrm{CO}_{2}$ is 2:4, which simplifies to 1:2. Therefore, for every 1 mole of $\mathrm{C}_{2} \mathrm{H}_{2}$, 2 moles of $\mathrm{CO}_{2}$ are produced.

To find the moles of $\mathrm{C}_{2} \mathrm{H}_{2}$ needed to produce 0.26 moles of $\mathrm{CO}_{2}$:

\[ \text{Moles of } \mathrm{C}_{2} \mathrm{H}_{2} = 0.26 \, \text{mol} \, \mathrm{CO}_{2} \times \frac{1 \, \text{mol} \, \mathrm{C}_{2} \mathrm{H}_{2}}{2 \, \text{mol} \, \mathrm{CO}_{2}} = 0.13 \, \text{mol} \, \mathrm{C}_{2} \mathrm{H}_{2} \]