45
11.65)
NaF has the NaCl structure. That means the F! ions are in a fcc structure (F! ions
in the corners and on the faces) with the Na+ ions between them on the edges and 1
Na+ in the body center. Also, the cations and anions touch along an edge so the
edge length and ionic radii are related by,
R = 2 r+ + 2 r!
a) Using ionic radii given in chapter 7 we can estimate the edge length.
rNa+ = 1.16 D
rF! = 1.19 D
R = 2 r+ + 2 r! = 2 (1.16 D) + 2 (1.19 D) = 4.70 D
b) In this NaCl structure there are 4 f.u. per unit cell, so there are 4 NaF f.u./u.c.
4 NaF formula units per u.c. (4 Na+ and 4 F! ions)
edge length, R = 4.70 D = 4.70 x 10&8 cm; FW = 41.988 g/mol
D
=
m
x
1/V
g
41.988 g NaF
1 mol NiO
4 NaF units
1 u.c.
? ------=
-----------------x
---------------------------x
---------------x
---------------------cm3
1 mol NaF
6.02 x 1023 NaF units
1 u.c.
(4.70 x 10&8 cm)3
= 2.6871 g/cm3
= 2.69 g/cm3
46
11.68)
a) Cinnabar, HgS, has the ZnS (zinc blende) type structure (Fig. 11.42b).
What is density of HgS?
4 HgS formula units per u.c. (4 Hg2+ and 4 S2! ions)
edge length, R = 5.852 D = 5.852 x 10&8 cm; FW = 232.655
D
=
m
x
1/V
g
232.655 g HgS
1 mol HgS
4 HgS units
1 u.c.
? ------=
------------------x
--------------------------x
---------------x
----------------------1 mol HgS
6.022 x 1023 HgS units
1 u.c.
(5.852 x 10&8 cm)3
cm3
= 7.7111 g/cm3
= 7.711 g/cm3
47
11.68) (cont.)
b) Tiemmanite, HgSe, has the ZnS (zinc blende) type structure (Fig. 11.42b).
Since Se2! has a larger ionic radius than S2! we would expect the edge length of the
HgSe to be larger than that of HgS. This means the HgSe would have the larger
volume.
c) What is density of HgSe?
4 HgSe formula units per u.c. (4 Hg2+ and 4 Se2! ions)
edge length, R = 6.085D = 6.085 x 10&8 cm; FW = 279.55
D
=
m
x
1/V
g
279.55 g HgSe
1 mol HgSe
4 HgSe units
1 u.c.
? ------=
------------------x
--------------------------x
---------------x
----------------------cm3
1 mol HgSe
6.022 x 1023 HgSe
1 u.c.
(6.085 x 10&8 cm)3
= 8.2413 g/cm3
= 8.241 g/cm3
The unit cell of HgSe is larger (greater volume) than HgS, due the larger size of
Se2! compared to S2- giving HgSe a unit cell longer edge length. Thus one might
expect HgSe to have a smaller density (inversely proportional to volume, d=m/V).
However, Se2! has a much larger mass the S2- (more than twice the mass) giving
HgSe a greater molar mass. This larger mass is enough to give HgSe the greater
density even though it has the larger volume. The mass of HgSe is about 20%
larger but the volume is only about 12% larger).
48
11.72)
See next page
49
11.72) (cont.)
ZrO2 may also have some covalent character (covalent network solid).
d) C12H22O11 (table sugar)
See next page
Molecular solid (lots of OH groups, LF, DD
and lots of H-bonding)
50
11.72) (cont.)
51
11.77)
52
11.77) (cont.)
53
11.78) Which of the following pairs has the higher m.p. and why?
a)
HF
MW
20
molecular
polar
LF
DD
H-bonding
higher m.p.
<
>
HCl
36.5
molecular
polar
LF
DD
You would expect HF to have the stronger AF. HCl is larger so it has larger
LF (but not that much larger). However, HCl is not as polar as HF and more
importantly HF forms H bonds between HF molecules while HCl doesn’t.
HF thus has stronger AF and higher m.p.
b)
C (graphite)
covalent network
strong covalent bonds
high m.p.
CH4
molecular
nonpolar
LF
low m.p. (gas at room temp.)
C (graphite) is a covalent network solid. It has layers of C atoms covalently
bonded in fused benzene type rings and the layers are held together by very
strong London Forces. CH4 is a small molecular compound. It is nonpolar
and has only LF between CH4 molecules. Thus the C(graphite) has a higher
m.p. The CH4 is a gas at room temperature.
c)
KCl
ionic
high m.p.
Cl2
molecular
nonpolar
LF
low m.p. (liquid at room temp.)
KCl is an ionic compound. Ionic compounds have relatively high m.p. that
depend on the charges on the ions and the distance between them. The Cl2 is
a nonpolar molecular compound that has only LF. These LF are much
weaker than the ionic AF between the ions in KCl. Thus, KCl with ionic AF
has a higher m.p. All ionic compounds are solids at room temperature.
54
11.78) (cont.)
d)
LiF
ionic
or
MgF2
ionic
Ionic Solids - m.p. & hardness (and solubility) depends on Lattice Energy
Q+ Q&
LE % ------d
Q: charge on ion
d: distance between centers of ions & usually
determined by adding ionic radii.
The Mg2+ has a +2 charge while Li+ has a +1 charge.
The F& has a &1 charge and is present in both compounds.
ˆ Numerator for MgF2 % |(+2)(&1)| = 2
&
for LiF % |(+1)(&1)| = 1
so numerator for MgF2 is 2 times larger than that for LiF
r(Mg2+) . r(Li+)
Also,
Mg2+ and Li+ are almost the same size (Mg2+ is actually slightly smaller).
so
d(MgF2) < d(LiF)
ˆ LE(MgF2) > LE(LiF)
&
(d is sum of ionic radii)
(mostly based on the charges)
MgF2 has higher m.p.
greater LE => higher m.p.
(Also, generally less soluble.)