HW 11-IR spectroscopy key

HW 11-IR spectroscopy key - (1) 

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Unformatted text preview: (1)  The
IR
spectrum
of
CO
shows
a
vibra:onal
band
centered
at
2170
cm‐1.
 (a)  What
is
the
force
constant
for
the
CO
bond?
 Wavenumbers
(in
cm‐1)
=
5.3
x
10‐12
s/cm
(k/µ)1/2
 With
k
in
N/m
and

µ
in
kg
 µ
=

1.1
x
10‐26
kg
and
k
=
1843.6
N/m
 (b)
At
what
wavenumber
would
the
corresponding
peak
for
14CO
occur?
 µ
=

1.25
x
10‐26
kg,
and
with
the
force
constant
from
above
the
vibra:on
would
occur
at
2035
cm‐1
 (2)
How
many
vibra:onal
modes
does
sulfur
dioxide
have?
How
many
are
IR
ac:ve?

 SO2
is
bent
so
3N‐6
=
3
possible
modes.
 To
be
IR
ac:ve
the
mode
must
involve
a
change
in
dipole
moment.
The
dipole
changes
during
 all
3
vibra:ons
so
all
are
ac:ve.
 (3)
Consider
the
possible
C‐H
stretching
modes
of
the
ethene
molecule,
C2H4.
 The
symmetric
stretch
has
all
four
H’s
moving
away
from
their
respec:ve
C
atoms
simultaneously
while
in
 the
assymetric
stretch
two
H
on
one
C
move
away
while
the
other
two
are
moving
in.
 Which
of
these
vibra:ons
is
IR
ac:ve?
 The
asymmetric
stretch
is
ac:ve.
 (4)
What
length
of
mirror
drive
in
an
FTIR
spectrometer
would
be
required
to
provide
a
resolu:on
of
0.050
 cm‐1?
 The
wavenumber
resolu:on
=
1/δ,
where
δ
is
called
the
retarda:on.The
mirror
drive
required
for
a
desired
 resolu:on
is
½
the
retarda:on.

 Thus,
δ
=
20
cm
and
the
mirror
drive
=
10
cm.
 ...
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This note was uploaded on 11/16/2011 for the course CHEM 4011 at Colorado.

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