Phys 221 SI :
Ideal Gas
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Michael
Phys 221
Prell
April 15th, 2012
Useful Equations
✔ Ideal Gas Law : p V =n RT
◦ R=8.314 J /(mol⋅K )=0.08206 (L⋅atm) /(mol⋅K )
✔ Standard Temperature and Pressure (STP) : 0o C , 1 atm
n
✔ Partial Pressure : p X = X pall (The pressure contributed by gas X)
nall
1
3
m〈 v 2 〉= k T
✔ Kinetic Energy :
2
2
R
−23
=1.38×10 J / K
◦ k=
NA
Problems :
1. (*) What is the volume of two moles of an ideal gas at STP?
2. (**) We take 1 mol of oxygen gas (O2) at STP and put it into a container of fixed volume
with liquid nitrogen (77 K). What is the pressure inside the container?
3. (**) If we take a balloon filled with nitrogen (N2) at room temperature (20oC) with a
volume of 32.1 Liters, if it is lowered to a temperature of -30oC – what is its new
volume?
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4. (**) 20% of our atmosphere (by volume) is composed of oxygen gas (O2). What is the
partial pressure of oxygen at the surface of the Earth?
5. (**) What is the average speed of oxygen molecules (O2) at STP?
6. (***) Recall that the escape velocity from the surface of the Earth is 11.2 km/s. Use this
to explain why our atmosphere does not contain detectable amounts of hydrogen and
helium gases.
7. (***) Let's model a hot-air balloon as a ball of air at a temperature TH moving through
the atmosphere which is at STP. If the total mass of our balloon and payload is 200 kg
and the balloon has a volume of 600 m3 (this is actually a relatively small hot-air balloon
– just to give you an idea), how hot does the air need to be? (Assume the density of air at
STP to be 1.3 kg/m3)