Properties of gases – problem sheet
1.
Calculate the most probable speed, the mean speed, and the rootmeansquare speed for carbon
dioxide molecules at 298 K.
2.
Calculate:
(a)
the mean free path of molecules in air at 1 bar pressure and 25
°
C (take the average
collision cross section,
σ
, to be 0.43 nm
2
);
(b)
the pressure at which the mean free path in air becomes equal to 10 cm;
(c)
the number of collisions
per cm
3
in one second between oxygen and nitrogen molecules in
air at 25
°
C and 1 bar pressure (take the radii to be equal to 178 and 185 pm, respectively).
3.
Graham’s law of effusion states that the rate at which gas is lost from a vessel into a vacuum
through a small hole is proportional to
M
1/2
, where
M
is the molecular mass.
(a)
By considering the number of molecules,
N
, striking a hole of area
A
0
, show that the rate of
effusion is given by
d
N
d
t
=
p
A
0
N
A
(2
π
MRT
)
1/2
(b)
Show that the rate of change of pressure in a vessel of volume
V
is given by
dln
p
d
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This note was uploaded on 05/09/2010 for the course CHE 3051 taught by Professor Sitimachmud during the Spring '08 term at National Central University.
 Spring '08
 SitiMachmud
 Mole

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