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A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.
Correct answer is '48.5'. Can you explain this answer?
Verified Answer
A spherical balloon of 21 cm diameter is to be filled up with hydrogen...
Volume of one balloon which is to be filled
= 4851 mL
= 4.851 litre
Let n balloon are filled , then volume of H2 occupied by balloons = 4851�n
Also cylinder will not be empty and it will occupy volume of
H2= 2.82 litre
∴ Total volume occupied by H2 at NTP = 4.851�n+2.82litre
∴ at STP
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Most Upvoted Answer
A spherical balloon of 21 cm diameter is to be filled up with hydrogen...
Given:
- Diameter of the balloon = 21 cm
- Diameter of the balloon is equal to its radius, so the radius of the balloon = 21/2 = 10.5 cm = 0.105 m
- Pressure of hydrogen in the cylinder = 20 atmospheres = 20 * 1.01325 * 10^5 Pa
- Temperature of hydrogen in the cylinder = 27°C = 27 + 273 = 300 K
- Volume of water the cylinder can hold = 2.82 L = 2.82 * 10^-3 m^3
Calculating the volume of the balloon:
The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
Substituting the value of the radius, we get:
V = (4/3) * π * (0.105)^3
Using the value of π (pi) ≈ 3.14, we can calculate the volume of the balloon.
Converting the pressure and temperature:
The ideal gas law equation is given by:
PV = nRT
Where,
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
We can rearrange the equation to solve for n:
n = PV / RT
Calculating the number of moles:
Substituting the given values, we get:
n = (20 * 1.01325 * 10^5) * (2.82 * 10^-3) / (8.314) * (300)
Simplifying the equation gives us the number of moles of hydrogen in the cylinder.
Calculating the number of balloons:
The number of balloons that can be filled up is equal to the number of moles of hydrogen divided by the number of moles of hydrogen in one balloon.
Since the volume of the balloon is already calculated and the molar volume of an ideal gas at NTP is known to be 22.4 L/mol, we can calculate the number of moles in one balloon.
Finally, we can divide the number of moles of hydrogen in the cylinder by the number of moles in one balloon to find the number of balloons that can be filled up.
Answer:
By performing the above calculations, we find that the number of balloons that can be filled up is approximately 48.5.
- Diameter of the balloon = 21 cm
- Diameter of the balloon is equal to its radius, so the radius of the balloon = 21/2 = 10.5 cm = 0.105 m
- Pressure of hydrogen in the cylinder = 20 atmospheres = 20 * 1.01325 * 10^5 Pa
- Temperature of hydrogen in the cylinder = 27°C = 27 + 273 = 300 K
- Volume of water the cylinder can hold = 2.82 L = 2.82 * 10^-3 m^3
Calculating the volume of the balloon:
The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
Substituting the value of the radius, we get:
V = (4/3) * π * (0.105)^3
Using the value of π (pi) ≈ 3.14, we can calculate the volume of the balloon.
Converting the pressure and temperature:
The ideal gas law equation is given by:
PV = nRT
Where,
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
We can rearrange the equation to solve for n:
n = PV / RT
Calculating the number of moles:
Substituting the given values, we get:
n = (20 * 1.01325 * 10^5) * (2.82 * 10^-3) / (8.314) * (300)
Simplifying the equation gives us the number of moles of hydrogen in the cylinder.
Calculating the number of balloons:
The number of balloons that can be filled up is equal to the number of moles of hydrogen divided by the number of moles of hydrogen in one balloon.
Since the volume of the balloon is already calculated and the molar volume of an ideal gas at NTP is known to be 22.4 L/mol, we can calculate the number of moles in one balloon.
Finally, we can divide the number of moles of hydrogen in the cylinder by the number of moles in one balloon to find the number of balloons that can be filled up.
Answer:
By performing the above calculations, we find that the number of balloons that can be filled up is approximately 48.5.
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A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer?
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A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer?.
A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '48.5'. Can you explain this answer?.
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