CHEM1002 Answers to Problem Sheet 9
1.
Which intermolecular forces are present in CH3Cl(s)?
•
•
•
(a)
(b)
(c)
(d)
(e)
2.
CH3Cl is polar with δ- Cl and δ+ C so dipole-dipole forces will be present.
As H is bonded to C, there are no hydrogen bonds. H bonding only exists
when hydrogen is bonded to one of the most electronegative elements (N,
O or F).
Dispersion forces are present between all molecules:
London dispersion only
dipole-dipole only
hydrogen bonding only
London dispersion and dipole-dipole
London dispersion, dipole-dipole and hydrogen bonding
Which intermolecular force or bond is responsible for the density of H2O(s) being less
than that of H2O(l)?
Hydrogen bonding leads to strongly directional bonding between the molecules
and an ordered structure in ice. The weaker interactions in liquid water lead to a
much less ordered structure with the molecules free to move closer.
(a)
(b)
(c)
(d)
(e)
3.
hydrogen bonding
London dispersion forces
covalent bonding
ionic bonding
dipole/induced dipole forces
A phase diagram is shown on the right
LIQUID
(b)
(c)
(d)
(e)
(f)
Letter D lies at the critical point –
C
beyond this temperature, the gas
A
B
E
cannot be liquidied whatever
pressure is applied.
GAS
SOLID
Letter F lies at the triple point
where solid, liquid and gas all exist.
F
G
Letter H lies on the equilibrium
between solid and gas (as does the
H
triple point F).
Temperature
Moving from G to C corresponds to
moving from gas liquid:
condensation.
Liquid and solid coexist at B
F corresponds to the triple point so solid, liquid and gas all coexist.
Pressure
(a)
4.
The smallest repeating structure in a crystalline solid is called the ‘unit cell’. If
the unit cell is repeated in all three directions, the crystal is generated.
5.
(a)
74% of the space is occupied in a face-centred cubic cell.
D
(b)
68% of the space is occupied in a body-centred cubic unit cell.
(c)
52% of the space is occupied in a simple cubic unit cell.
The calculations used to obtain these numbers are detailed below.
(a)
In a face centred cubic lattice, there are
atoms on each corner and at the centre of
each face, but there is no atom at the
centre of the cube.
The atoms on the corners are shared
between 8 cells so 1/8 is located in this
cell. The atoms on the corners are shared
between 2 cells so 1/2 is in this cell. The
total number of atoms in the cell is
therefore:
a
8 × 1/8 (corners) + 6 × 1/2 (faces) = 4.
If the spheres have radii r, their volume
4
16
is πr3 The total volume occupied is
3
3
πr3.
The atoms touch along the diagonal of
one of the faces so that the length of the
diagonal is 4r. Using Pythagoras’
theorem, the length of the side of the
cube is:
a2 + a2 = (4r)2 or a =
8r
Hence the cube volume = a3 = (8)3 2 r 3 . The percentage of this which is
occupied is therefore:
percentage occupied =
(b)
(16 3)πr 3
(8)3 2 r 3
× 100 = 74%
In a body centred cubic lattice, there are
atoms on each corner and at the centre of
the cube. The atoms on the corners are
shared between 8 cells so 1/8 is located in
this cell. The atoms in the centre is totally
in this cube. The total number of atoms
in the cell is therefore
8 × 1/8 (corners) + 1 (centre) = 2.
The spheres touch along the body
diagonal.
A similar calculation to that in (a) gives the percentage occupied = 68%
(c)
In a simple centred cubic lattice, there
are only atoms on each corner. These
atoms are shared between 8 cells so 1/8 is
located in this cell.
8 × 1/8 (corners) = 1.
The spheres touch along the edges.
A similar calculation to that in (a) gives the percentage occupied = 52%
Note that the face centred cubic unit cell gives the highest percentage occupation
– it is the only closed packed structure out of these three.
6.
The eight atoms on the corners are shared with eight other unit
cells. The total number of this atom type in this unit cell is
therefore 8 × 1/8 = 1.
The atom at the centre is only in this cube so the total number
of this atom type is also 1.
The stoichiometry is 1:1 so the formula is XY.
7.
There are 12 nearest neighbours in a closed packed structure (in both cubic and
hexagonal close-packed structures).