All Chapters Covered
SOLUTION MANUAL
, 1.2
An approximate solution can be found if we combine Equations 1.4 and 1.5:
_! _ mJ7 2 = e; olecular
2
Kit = e; olecular
2
.-. v l:
Assume the temperature is 22 °C. The mass of a single oxygen molecule is m = 5.14 x 10-26 kg.
Substitute and solve:
V = 487.6 [miss]
The molecules are traveling really, fast (around the length of five football fields every second).
Comment:
We can get a better solution by using the Maxwell-Boltzmann distribution of speeds that is
sketched in Figure 1.4. Looking up the quantitative expression for this expression, we have:
4; r
F (v) dv =
312
Expr -_!!! V 2} v 2 dv
{
(_!!!_)
2; rkT 2kT
Whereof (v) is the fraction of molecules within dv of the speed v. We can find the average speed
by integrating the expression above
JF (v) vivo=
0 0
-=
V 0
8kT = 449 [m/s ]
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 2
, F (v) dv MN
J
00
0
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 3
, 1.3
Derive the following expressions by combining Equations 1.4 and 1.5:
Therefore,
VA
2
mb
-2
VB ma
Since mob is larger than ma , the molecules of species A move faster on average.
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 4
SOLUTION MANUAL
, 1.2
An approximate solution can be found if we combine Equations 1.4 and 1.5:
_! _ mJ7 2 = e; olecular
2
Kit = e; olecular
2
.-. v l:
Assume the temperature is 22 °C. The mass of a single oxygen molecule is m = 5.14 x 10-26 kg.
Substitute and solve:
V = 487.6 [miss]
The molecules are traveling really, fast (around the length of five football fields every second).
Comment:
We can get a better solution by using the Maxwell-Boltzmann distribution of speeds that is
sketched in Figure 1.4. Looking up the quantitative expression for this expression, we have:
4; r
F (v) dv =
312
Expr -_!!! V 2} v 2 dv
{
(_!!!_)
2; rkT 2kT
Whereof (v) is the fraction of molecules within dv of the speed v. We can find the average speed
by integrating the expression above
JF (v) vivo=
0 0
-=
V 0
8kT = 449 [m/s ]
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 2
, F (v) dv MN
J
00
0
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 3
, 1.3
Derive the following expressions by combining Equations 1.4 and 1.5:
Therefore,
VA
2
mb
-2
VB ma
Since mob is larger than ma , the molecules of species A move faster on average.
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 4
