418 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at EquilibriumPROBLEMS
Section 9.6: Effusion and Wall Collisions
9.40 Assume that one of the doors of a classroom is 36 inches
by 80 inches (91 cm by 203 cm). Find the number of N 2
molecules and the number of moles of N 2 molecules
striking one side of the door in 90 minutes. Assume that the
partial pressure of N 2 is 0.78 atm and that the temperature
is 25◦C.
9.41 The equilibrium vapor pressure of a substance is the
pressure of the vapor phase at equilibrium with the
solid or liquid phase. The vapor pressure of solid
tungsten (wolfram) at 4763 K is equal to 10.0 torr.
A sample of solid at equilibrium with its vapor is
maintained at this temperature in a container that has a
circular hole of diameter 0.100 mm leading to a vacuum
chamber. Find the loss of mass through the hole in
1.00 hour.
9.42 a.The equilibrium vapor pressure of water at 25◦Cis
equal to 23.8 torr. If the relative humidity is 50.0%,
calculate the number of water molecules per second
striking an area of 1.00 cm^2 at 25◦C.
b.Calculate the number of water molecules per second
leaving an area of 1.00 cm^2 at 25◦C. Calculate the net
loss of mass per second at an area of 1.00 cm^2 at 25◦C
if the relative humidity is 50.0%.
9.43 In a certain vacuum system, a pressure of 1. 0 × 10 −^10 torr
is achieved. Assume that the air inside the vacuum system
is 80 mol% N 2 and 20 mol% O 2.
a.Find the number density in molecules per cubic meter
for each substance if the temperature is 298 K.
b.Find the number of molecules striking 1.00 cm^2 of wall
per second at 298 K.9.44 A spherical vessel of radius 10.0 cm contains argon at
0.980 atm pressure and 298.15 K. Calculate the number of
argon atoms striking the inner surface of the container per
second.
9.45 Assume that the mole fraction of carbon dioxide in the
earth’s atmosphere is 0.000306. The area of the earth’s
oceans is roughly 3. 61 × 108 km^2. Estimate the number of
moles of carbon dioxide molecules striking the earth’s
oceans in 1.00 s.
9.46 Calculate the number of N 2 molecules striking an area of
1.00 m^2 in 1.00 s if the pressure is 1.00 bar and the
temperature is
a.78 K
b.298 K
c.1000.0 K
9.47A container with a volume of 1.00 L contains carbon
monoxide gas, and a sample of a solid catalyst is suddenly
placed into the container.
a.If the total surface area of the catalyst is 1.00 m−^2 , and
if the initial rate of collisions of CO molecules with the
catalysts surface is 6. 0 × 1023 s−^1 , find the initial
pressure of the carbon monoxide.
b. If every CO molecule that strikes the catalyst surface
sticks to the surface, how long will it take for the
pressure of CO to drop to 50.0% of its initial value?
Assume that enough surface sites are available for this
to be the case.
9.48Assume that in a certain automobile the exhaust gas has a
carbon monoxide mole fraction of 0.0140 and a
temperature of 500 K when it reaches the catalytic
converter, which contains a solid platinum catalyst coated
on a ceramic material with a large surface area. Calculate
the number of carbon monoxide molecules and the amount
of carbon monoxide in moles that strikes 50.00 m^2 of
catalyst surface in 1.000 minute.
9.49A 1.000-liter container full of neon gas and maintained at
298 K is placed in a large vacuum chamber, and a circular
hole with a diameter of 20 micrometers is punched in the
container. If the initial pressure in the container is 1013 Pa,
find the time required for half of the neon gas to effuse
from the container.Hint:Remember that the pressure will
be dropping as the gas escapes.
9.50 Estimate the time required for a bicycle tire to go flat as a
result of a circular hole of 50μm diameter. State your
assumptions.9.7 The Model System with Potential Energy
Until now, we have assumed that the particles in our model gas have no forces acting
on them except those due to collisions with the container. We now modify our model
to include additional forces on the particles.