CHALLENGE 7 A 30 g gas sample of CO₂ occupies 27 L and exerts a pressure of 5.6 atm. Additionally, the temperature measured is exactly 263 K within the container. The pressure is then tripled, the volume is reduced by its original value, and 25% of the gas leaks out. Calculate the new resulting temperature.
CHALLENGE 7 A 30 g gas sample of CO₂ occupies 27 L and exerts a pressure of 5.6 atm. Additionally, the temperature measured is exactly 263 K within the container. The pressure is then tripled, the volume is reduced by its original value, and 25% of the gas leaks out. Calculate the new resulting temperature.
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Problem 7E
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![### Challenge 7
A 30 g gas sample of CO₂ occupies 27 L and exerts a pressure of 5.6 atm. Additionally, the temperature measured is exactly 263 K within the container. The pressure is then tripled, the volume is reduced by ⅓ its original value, and 25% of the gas leaks out. Calculate the new resulting temperature.
**Detailed Explanation of the Problem:**
1. **Initial Conditions:**
- Mass of gas \( m = 30 \) g
- Volume \( V_1 = 27 \) L
- Pressure \( P_1 = 5.6 \) atm
- Temperature \( T_1 = 263 \) K
2. **Changes Applied to the Gas:**
- Pressure is tripled: \( P_2 = 3 \times P_1 \)
- Volume is reduced to ⅔ of its original value: \( V_2 = \frac{2}{3} V_1 \)
- 25% of the gas leaks out, so 75% of the original gas remains.
**Hint:**
You may need to use the Ideal Gas Law and the relationships between pressure, volume, and temperature to solve for the new temperature after the changes have been applied.
#### Ideal Gas Law:
\[ PV = nRT \]
Where:
- \( P \) is the pressure
- \( V \) is the volume
- \( n \) is the number of moles
- \( R \) is the ideal gas constant
- \( T \) is the temperature in Kelvin
Use the initial conditions to find the number of moles \( n \) of the gas, and then apply the changes and the new conditions to calculate the resulting temperature \( T_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3f0c16-4bc2-4005-8b34-f5a8ba23d8d8%2F3d4528e8-9f45-4265-94d7-3417c894167d%2Ftib2e6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Challenge 7
A 30 g gas sample of CO₂ occupies 27 L and exerts a pressure of 5.6 atm. Additionally, the temperature measured is exactly 263 K within the container. The pressure is then tripled, the volume is reduced by ⅓ its original value, and 25% of the gas leaks out. Calculate the new resulting temperature.
**Detailed Explanation of the Problem:**
1. **Initial Conditions:**
- Mass of gas \( m = 30 \) g
- Volume \( V_1 = 27 \) L
- Pressure \( P_1 = 5.6 \) atm
- Temperature \( T_1 = 263 \) K
2. **Changes Applied to the Gas:**
- Pressure is tripled: \( P_2 = 3 \times P_1 \)
- Volume is reduced to ⅔ of its original value: \( V_2 = \frac{2}{3} V_1 \)
- 25% of the gas leaks out, so 75% of the original gas remains.
**Hint:**
You may need to use the Ideal Gas Law and the relationships between pressure, volume, and temperature to solve for the new temperature after the changes have been applied.
#### Ideal Gas Law:
\[ PV = nRT \]
Where:
- \( P \) is the pressure
- \( V \) is the volume
- \( n \) is the number of moles
- \( R \) is the ideal gas constant
- \( T \) is the temperature in Kelvin
Use the initial conditions to find the number of moles \( n \) of the gas, and then apply the changes and the new conditions to calculate the resulting temperature \( T_2 \).
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