Problem Set #9
-1-
Chem 444 B
Homework Set #9 - Solutions
DUE:
Friday, April 11, 2008
1)
A 1.0L glass bulb contains 1.0x10
23
H
2
molecules.
If the pressure exerted by the gas
is 100 kPa…
a)
what is the temperature (K) of the gas?
3
Solve for T using the ideal gas equation:
100
10
Pa
PV
T
nR
×
=
=
5
1
1.01 10
atm
Pa
×
×
(
)
23
1.0
1.0
10
L
molecules
⎛
⎞
⎜
⎟
⎝
⎠
×
23
1
6.022
10
mol
molecules
×
×
72.6
0.0821
K
L atm
mol K
=
⎛
⎞
⋅
⎛
⎞
⎜
⎟
⎜
⎟
⋅
⎝
⎠
⎝
⎠
b)
what is the root mean square speed of the molecules (m/s)?
(
)
1/ 2
1/2
1/ 2
2
5
2
3 8.314
72.6
3
From Eq. 27.14,
9.06
10
0.002
952
/
rms
rms
J
K
RT
m
mol K
u
kg
M
s
mol
u
m s
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎛
⎞
⋅
⎛
⎞
⎝
⎠
⎜
⎟
=
=
=
×
⎜
⎟
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
⎜
⎟
⎝
⎠
=
c)
Would the temperature be different if the molecules were O
2
?
Why/Why
not?
The temperature follows the ideal gas law and does not depend on molecular
weight.
The parameters P, V and n are given to us in the problem, so the
temperature will be the same regardless of the substance used
d)
Would the root mean square speed be different if the molecules were O
2
?
Why/Why not?
The root mean square speed does depend on molecular weight, and is inversely
proportional to it (as shown in Eq. 27.14).
Therefore, since O
2
is heavier than H
2
,
it will have a smaller root mean square speed.

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