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Answer :
To solve this problem, we'll calculate the pressure of carbon dioxide (CO₂) gas using the ideal gas law equation, which is:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in atm.
- [tex]\( V \)[/tex] is the volume in liters.
- [tex]\( n \)[/tex] is the number of moles of gas.
- [tex]\( R \)[/tex] is the ideal gas constant (0.0821 L·atm/mol·K).
- [tex]\( T \)[/tex] is the temperature in Kelvin.
Let's break down the steps:
1. Convert the temperature to Kelvin:
Given: Temperature in Celsius = [tex]\( 35^\circ C \)[/tex]
[tex]\[ T = 35 + 273.15 = 308.15 \, K \][/tex]
2. Calculate the number of moles of CO₂:
Given:
- Mass of CO₂ = 33.0 g
- Molar mass of CO₂ = 44.01 g/mol
[tex]\[ n = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} = \frac{33.0}{44.01} = 0.7498 \, \text{moles (approximately)} \][/tex]
3. Use the ideal gas law to find the pressure:
Given:
- Volume [tex]\( V \)[/tex] = 50.0 L
- Gas constant [tex]\( R \)[/tex] = 0.0821 L·atm/mol·K
Using the formula:
[tex]\[ P = \frac{nRT}{V} = \frac{0.7498 \times 0.0821 \times 308.15}{50.0} \][/tex]
Calculating the pressure:
[tex]\[ P = 0.379 \, \text{atm (approximately)} \][/tex]
Based on these calculations, the pressure of the CO₂ gas in the container is approximately 0.379 atm. Therefore, the correct answer is option C: 0.379 atm.
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in atm.
- [tex]\( V \)[/tex] is the volume in liters.
- [tex]\( n \)[/tex] is the number of moles of gas.
- [tex]\( R \)[/tex] is the ideal gas constant (0.0821 L·atm/mol·K).
- [tex]\( T \)[/tex] is the temperature in Kelvin.
Let's break down the steps:
1. Convert the temperature to Kelvin:
Given: Temperature in Celsius = [tex]\( 35^\circ C \)[/tex]
[tex]\[ T = 35 + 273.15 = 308.15 \, K \][/tex]
2. Calculate the number of moles of CO₂:
Given:
- Mass of CO₂ = 33.0 g
- Molar mass of CO₂ = 44.01 g/mol
[tex]\[ n = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} = \frac{33.0}{44.01} = 0.7498 \, \text{moles (approximately)} \][/tex]
3. Use the ideal gas law to find the pressure:
Given:
- Volume [tex]\( V \)[/tex] = 50.0 L
- Gas constant [tex]\( R \)[/tex] = 0.0821 L·atm/mol·K
Using the formula:
[tex]\[ P = \frac{nRT}{V} = \frac{0.7498 \times 0.0821 \times 308.15}{50.0} \][/tex]
Calculating the pressure:
[tex]\[ P = 0.379 \, \text{atm (approximately)} \][/tex]
Based on these calculations, the pressure of the CO₂ gas in the container is approximately 0.379 atm. Therefore, the correct answer is option C: 0.379 atm.
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