a 5 litre vessel contains a gas at 20 atm pressure how many balloons of 0.5 litre capacity would be filled at 1 ATM pressure at same temp ? please explain
Answers
Correct option is
A
18
At same temperature,
P
1
V
2
=P
2
V
2
(Boyle's law)
P
1
=10atm;P
2
=1atm
V
1
=4l=V
2
=8l
But while filling balloons from cylinder when pressure in cylinder becomes 1 atm then further filling is not possible (P
1
′
=9atm)
Let n be the number of balloons that can be filled.
∴P
1
′
V
1
=n(P
1
V
1
)
9×8=n(4×1)
n=
4
9×8
=18balloons
Question
Answers
Related Questions
Balloons of 4L
capacity are to be filled with hydrogen at a pressure of 1atm
and 27∘C from an 8L
cylinder containing hydrogen at 10atm
at the same temperature. Find the number of balloons that can be filled.
Answer
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68.4K+ Views
Hint: We need to know the relationship between Pressure, Volume, temperature and the amount of hydrogen each balloon will require. This relationship is given by the Ideal Gas Law. It is a combination of various gas laws such as Boyle’s Law, Charles’s Law, Gay Lussac’s Law and Avogadro’s Law. The equation for the Ideal Gas Law is PV=nRT,where P is the pressure ,V is the Volume, n is the number of moles ,R is the Gas Constant and T is the temperature.
Complete step by step answer:
Given in the question:
Volume of each balloon= 4L
Pressure of hydrogen inside each balloon = 1atm
Volume of the cylinder containing hydrogen = 8L
Pressure of cylinder containing hydrogen = 10atm
Temperature is constant for both the cylinder and balloons.
The ideal gas equation states:
PV=nRT
Since the temperature is constant,
n=PV
Now we calculate the number of moles of hydrogen inside the 8L
cylinder as:
nc=10atm×8L
On multiplication we get,
⇒nc=80moles
We also calculate the number of moles of hydrogen each 4L
balloon requires as:
nb=1atm×4L
On multiplication we get,
⇒nb=4moles
Thus the number of 4L
balloons containing 4moles of hydrogen that can be filled by 80moles
of hydrogen are 804=20
Hence, the number of balloons that can be filled are 20
balloons.
Note: We must be noted that there is an alternative method for solving these type of problems by using the Boyle’s law equation which is P1V1=P2V2 . V2 calculated as the total volume of hydrogen gas the 8L cylinder can hold having pressure of 1atm inside. This total volume will be divided by the volume capacity of each balloon to give us the number of balloons that can be filled.