Calculate the volume of CO2 produced from the complete combustion of 7.50 kg of propane (C3H8).

To determine the volume of \( \text{CO}_2 \) produced from the complete combustion of 7.50 kg of propane (\( \text{C}_3\text{H}_8 \)), we can proceed with the following steps:

### Step 1: Write the Balanced Combustion Reaction
The complete combustion of propane is:
\[
\text{C}_3\text{H}_8 + 5 \text{O}_2 \rightarrow 3 \text{CO}_2 + 4 \text{H}_2\text{O}
\]

This equation tells us that 1 mole of \( \text{C}_3\text{H}_8 \) produces 3 moles of \( \text{CO}_2 \).

### Step 2: Calculate the Molar Mass of Propane
Propane (\( \text{C}_3\text{H}_8 \)) has a molar mass calculated as follows:
\[
3 \times 12.01 + 8 \times 1.008 = 44.094 \, \text{g/mol}
\]

### Step 3: Convert the Mass of Propane to Moles
Convert 7.50 kg of propane to grams, then to moles:
\[
7.50 \, \text{kg} = 7500 \, \text{g}
\]
\[
\text{Moles of } \text{C}_3\text{H}_8 = \frac{7500 \, \text{g}}{44.094 \, \text{g/mol}} \approx 170.07 \, \text{moles}
\]

### Step 4: Calculate Moles of \( \text{CO}_2 \) Produced
According to the balanced equation, 1 mole of propane produces 3 moles of \( \text{CO}_2 \):
\[
\text{Moles of } \text{CO}_2 = 170.07 \times 3 \approx 510.21 \, \text{moles}
\]

### Step 5: Convert Moles of \( \text{CO}_2 \) to Volume
Assuming ideal gas conditions (at STP: 1 mole of gas occupies 22.4 liters):
\[
\text{Volume of } \text{CO}_2 = 510.21 \, \text{moles} \times 22.4 \, \text{L/mol} \approx 11428.7 \, \text{L}
\]

### Answer
The volume of \( \text{CO}_2 \) produced is approximately:
\[
11,428.7 \, \text{L}
\]

Would you like a detailed breakdown of any step or have further questions?

Here are 5 related questions that could help further:
1. How would the volume of \( \text{CO}_2 \) change if the temperature or pressure conditions were not at STP?
2. What is the volume of oxygen required for the complete combustion of 7.50 kg of propane?
3. How would the result change if incomplete combustion occurred?
4. Can this calculation be adjusted for real gas conditions using the ideal gas law?
5. How would you determine the energy released from burning 7.50 kg of propane?

**Tip:** Always balance combustion equations carefully, as they provide essential mole ratios for calculations.

Learn how to calculate the volume of CO2 produced from the complete combustion of 7.50 kg of propane (C3H8). This solution involves stoichiometry, molar mass calculations, and the ideal gas law, showing step-by-step how to find that approximately 11,428.7 L of CO2 is generated at STP. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation