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A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.?
Most Upvoted Answer
A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this b...
Given Data
- Volume of the initial bulb (V₁) = 0.5 L
- Initial pressure (P₁) = 1 atm = 760 mm Hg
- Final pressure after opening the stop cock (P₂) = 380 mm Hg
- Volume of the second bulb (V₂) = V (unknown)
Using Ideal Gas Law
Since the temperature is constant, we can apply Boyle's Law, which states that \( P₁V₁ = P₂V₂ \).
Calculating the Total Volume
When the stop cock is opened, the gas expands to fill both bulbs. Therefore, the total volume after the stop cock is opened becomes:
- Total Volume (V_total) = V₁ + V₂ = 0.5 L + V
Setting Up the Equation
Using Boyle's Law:
\[
P₁V₁ = P₂V_{total}
\]
Substituting the known values:
\[
760 \, \text{mm Hg} \times 0.5 \, \text{L} = 380 \, \text{mm Hg} \times (0.5 + V)
\]
Solving the Equation
1. Calculate the left side:
- \( 760 \times 0.5 = 380 \, \text{mm Hg L} \)
2. Set the equation:
- \( 380 = 380 \times (0.5 + V) \)
3. Divide both sides by 380:
- \( 1 = 0.5 + V \)
4. Solve for V:
- \( V = 1 - 0.5 = 0.5 \, \text{L} \)
Final Result
The volume of the second bulb (V) is **0.5 L**.
- Volume of the initial bulb (V₁) = 0.5 L
- Initial pressure (P₁) = 1 atm = 760 mm Hg
- Final pressure after opening the stop cock (P₂) = 380 mm Hg
- Volume of the second bulb (V₂) = V (unknown)
Using Ideal Gas Law
Since the temperature is constant, we can apply Boyle's Law, which states that \( P₁V₁ = P₂V₂ \).
Calculating the Total Volume
When the stop cock is opened, the gas expands to fill both bulbs. Therefore, the total volume after the stop cock is opened becomes:
- Total Volume (V_total) = V₁ + V₂ = 0.5 L + V
Setting Up the Equation
Using Boyle's Law:
\[
P₁V₁ = P₂V_{total}
\]
Substituting the known values:
\[
760 \, \text{mm Hg} \times 0.5 \, \text{L} = 380 \, \text{mm Hg} \times (0.5 + V)
\]
Solving the Equation
1. Calculate the left side:
- \( 760 \times 0.5 = 380 \, \text{mm Hg L} \)
2. Set the equation:
- \( 380 = 380 \times (0.5 + V) \)
3. Divide both sides by 380:
- \( 1 = 0.5 + V \)
4. Solve for V:
- \( V = 1 - 0.5 = 0.5 \, \text{L} \)
Final Result
The volume of the second bulb (V) is **0.5 L**.
Community Answer
A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this b...
0.5L
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A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.?
Question Description
A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.?.
A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bulb of volume 0.5 L contains an ideal gas at 1 atm pressure. this bulb was connected to another evacuated bulb of unknown volume V through a stop cock. when the stop cock was opened, the pressure at each bulb became 380mm Hg while the temperature remained constant. calculate V.?.
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