Answer :
Certainly! Let's work through the problem of finding out how many grams of CO₂ are produced when 30 liters of O₂ are reacted at Standard Temperature and Pressure (STP).
### Step-by-Step Solution:
1. Understanding the Reaction:
The chemical reaction given is:
[tex]\[
C_5H_{12} + 8O_2 \rightarrow 5CO_2 + 6H_2O
\][/tex]
This tells us that 8 moles of O₂ produce 5 moles of CO₂.
2. Molar Volume at STP:
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters.
3. Calculate Moles of O₂:
Given the volume of O₂ is 30 liters. To find out how many moles of O₂ this volume represents, use the molar volume:
[tex]\[
\text{Moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar Volume at STP}} = \frac{30}{22.4} \approx 1.34 \text{ moles}
\][/tex]
4. Use Stoichiometry to Find Moles of CO₂:
According to the reaction, 8 moles of O₂ yield 5 moles of CO₂. Therefore, we can set up a ratio to find the moles of CO₂ produced:
[tex]\[
\text{Moles of } CO_2 = \left(\frac{5}{8}\right) \times \text{Moles of } O_2 \approx \left(\frac{5}{8}\right) \times 1.34 \approx 0.84 \text{ moles}
\][/tex]
5. Calculate Mass of CO₂ Produced:
The molar mass of CO₂ is calculated by adding the atomic masses of carbon (C) and oxygen (O):
- Carbon: 12 g/mol
- Oxygen: 16 g/mol (each, thus 32 for O₂)
- CO₂ = 12 + 32 = 44 g/mol
Now, calculate the mass of CO₂ produced:
[tex]\[
\text{Mass of } CO_2 = \text{Moles of } CO_2 \times \text{Molar Mass of } CO_2 = 0.84 \times 44 \approx 36.83 \text{ grams}
\][/tex]
### Conclusion:
The mass of CO₂ produced when 30 liters of O₂ are reacted at STP is approximately 36.83 grams.
Therefore, the correct answer, considering the given options, is:
- Option f (40) is closest to the calculated 36.83 grams.
So, the answer is f (40) grams of CO₂.
### Step-by-Step Solution:
1. Understanding the Reaction:
The chemical reaction given is:
[tex]\[
C_5H_{12} + 8O_2 \rightarrow 5CO_2 + 6H_2O
\][/tex]
This tells us that 8 moles of O₂ produce 5 moles of CO₂.
2. Molar Volume at STP:
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters.
3. Calculate Moles of O₂:
Given the volume of O₂ is 30 liters. To find out how many moles of O₂ this volume represents, use the molar volume:
[tex]\[
\text{Moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar Volume at STP}} = \frac{30}{22.4} \approx 1.34 \text{ moles}
\][/tex]
4. Use Stoichiometry to Find Moles of CO₂:
According to the reaction, 8 moles of O₂ yield 5 moles of CO₂. Therefore, we can set up a ratio to find the moles of CO₂ produced:
[tex]\[
\text{Moles of } CO_2 = \left(\frac{5}{8}\right) \times \text{Moles of } O_2 \approx \left(\frac{5}{8}\right) \times 1.34 \approx 0.84 \text{ moles}
\][/tex]
5. Calculate Mass of CO₂ Produced:
The molar mass of CO₂ is calculated by adding the atomic masses of carbon (C) and oxygen (O):
- Carbon: 12 g/mol
- Oxygen: 16 g/mol (each, thus 32 for O₂)
- CO₂ = 12 + 32 = 44 g/mol
Now, calculate the mass of CO₂ produced:
[tex]\[
\text{Mass of } CO_2 = \text{Moles of } CO_2 \times \text{Molar Mass of } CO_2 = 0.84 \times 44 \approx 36.83 \text{ grams}
\][/tex]
### Conclusion:
The mass of CO₂ produced when 30 liters of O₂ are reacted at STP is approximately 36.83 grams.
Therefore, the correct answer, considering the given options, is:
- Option f (40) is closest to the calculated 36.83 grams.
So, the answer is f (40) grams of CO₂.
