A cylinder of compressed He originally has a pressure of 20 atm and a volume 10 L at a temperature of 25°C. It is used to fill 10, 1 L balloons at a pressure of 0.99 atm at 25°C. After filling the balloons what is the pressure in the tank?
12.0 atm
17.2 atm
18.0 atm
19.0 atm
19.8 atm
Explanation:
Cylinder:
PV=nRT
P is pressure
V is volume
n = number of moles
R is the ideal gas constant which would be given
T is temperate and must be in Kelvin
(20atm)(10L)= n(0.08306 L atm/ mol K) ( 25+273.15)
n = 8.1745 moles of He in the cylinder originally
Balloons:
PV=nRT
We will use the volume for all 10 balloons, which would be 10 L to calculate the total number of moles used in all of the balloons.
(0.99 atm)(10 L) = n(0.08306 L atm/ mol K) ( 25+273.15)
n = 0.40464 moles of He were used to fill the balloons.
Initially, there were 8.1745 moles of He in the cylinder.
0.40464 moles of He were used to fill the balloons.
There were, 8.1745 moles - 0.40464 moles = 7.76991 moles of He left in the cylinder after the balloons were filled.
Now we can use, P1/n1 = P2/n2 since the volume of the cylinder and temperature stayed the same.
(20atm)/8.1745 moles = P2/ 7.76991 moles
P2 = 19.01 atm
Alternatively, we could use PV= nRT to calculate the pressure of the cylinder, since we have volume, moles of gas, ideal gas constant and temperature.
Choice D