Download Lecture 14-17 - U of L Class Index

Intermolecular Forces
& Liquids
and Gasses
Kinetic Molecular Theory of Matter
The kinetic-molecular theory describes the behaviour of matter:
i) Molecules are in constant motion in random directions.
ii) All molecules have the same average kinetic energy at a given
temperature.
iii) States of matter:
a) gases, distances between particles are much larger than the
particles themselves.
b) solids, particles are packed in a three-dimensional lattice. This
motion is averaged about the particle’s location in the lattice.
c) liquids, particles are much closer together than in gases, but
they are still able to change locations. Particles in a liquid undergo
significant amounts of translational, rotational and vibrational
motion.
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Kinetic Molecular Theory of Matter
The kinetic energy of molecules tends to keep them separated and disordered,
hence there must be some countervailing force(s) to pull them together – particularly in
solids and liquids.
These attractive forces are
intermolecular forces.
There are six kinds of intermolecular
forces, each of which is based on
electrostatic interactions.
The strength of an intermolecular
force is determined by the strength
of the charges/dipoles involved
and by the distance between them.
i) ion – ion forces
ii) ion – dipole forces
iii) ion – induced dipole forces
iv) dipole – dipole forces
v) dipole – induced dipole forces
vi) induced dipole – induced dipole
forces
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Bond Polarity
When the electrons in a bond are will be shared unequally a charge difference
exists over a given distance.
This resulting dipole, makes the bond polar.
Dipoles can be shown graphically using a vector.
Another way to indicate bond polarity is via partial charges (+ and -) on the
relevant atoms:
C-O
H-F
Cl-Br
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Polarity of Molecules
To determine whether a molecule is polar or nonpolar, we need to look at:
i) Bond dipoles
ii) Molecular geometry
If a molecule has no dipoles or all of the dipoles cancel out due to symmetry, it is
nonpolar.
If a molecule has dipoles that don’t cancel out, it has a permanent dipole
moment () and is polar.
Dipoles have direction! They must be added as vectors.
e.g.
H2CO
SF2
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Ion-Ion Forces
Coulombs Law:
1 ( Z  e)( Z  e)
F
4
d2
This force is the strongest force outside of those operating at subatomic levels.
Hence ionic compounds tend to form strong solid lattices.
As a result, they have very high boiling points, requiring large amounts of heat to overcome
the attractive forces holding the lattice together.
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Ion-Dipole Forces
The attractive forces between ions and dipoles are also strong.
When an ionic solid (such as the NaCl shown below) is dissolved in polar
solvent such as water, many of the solvent molecules are organized around each
ion to maximize the ion-dipole attractions:
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Dipole-Dipole Forces
Molecules with permanent dipoles also experience
attractive forces.
-
+
-
+
They will align themselves to maximize the attractions between the positive ends of
the dipoles and the negative ends of the dipoles:
Hydrogen bonding: is a special case of dipole-dipole attraction. This is due to the
very large dipole moment that occurs when a hydrogen atom is bonded to a very
small, very electronegative atom (i.e. F, O or N).
The large dipole moment results in a particularly strong dipole-dipole attraction.
Remember that for a hydrogen bond to occur both the atom bound to H and the
atom attracted to H must be either F, O or N.
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Hydrogen Bonding
Hydrogen bonding is responsible for the
open cage structure of ice along with the
unusual relationship between temperature
and density of water/ice:
Hydrogen bonds also holds the
strands of DNA together to form the
double helix
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Dipole-Induced Dipole Forces
Induced dipoles occur when the dipole
of a polar molecule forces the electrons to
move in a nearby non-polar molecule,
resulting in a net dipole on the non-polar molecule.
-
+
-
+
Atoms whose valence electrons are less strongly attracted to their nucleus are more
susceptible to induced dipoles.
Hence larger atoms are more polarizable than smaller atoms in the same group.
The polarizability of molecules also increases with the size of the molecule. This is
why large molecules tend to be more viscous and have higher boiling points than
smaller molecules of similar polarity.
Ex) The induction of a dipole in carbon disulfide, CS2, by the polar solvent acetone,
(CH3)2C=O.
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Induced Dipole-Induced Dipole Forces
Nonpolar species exist as solids
and/or liquids at low enough
temperatures.
Ex) Liquid N2 and liquid He.
Why?
+
-
+
A temporary dipole on a molecule can induce temporary dipoles on nearby molecules
The interaction between these fluctuation-induced dipoles are known as London
dispersion forces.
Their strength depends on the polarizability of the atoms/molecules in question.
e.g. Cl2 vs. Br2 vs. I2
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Boiling Points of P Block Hydrides
Consider the following:
i) The boiling points for the Group 14 hydrides.
ii) The anomalously high boiling points of the
hydrides of the second period elements of groups
15 to 17.
iii) The relative order of the third-period element
hydrides.
iv) The sequence of boiling points for the fourthand fifth-period elements.
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Surface Tension
Drops of a liquid tend to be round. Why?
i) Molecules within a liquid are attracted to all of the molecules around them via the IMFs.
ii) Molecules on the surface can only interact with the neighbors immediately below them
and beside them.
iii) The surface molecules feel a net pull into the liquid and thus act as a skin for the liquid.
The energy required to break through this surface skin is referred to as surface tension.
Sphere: Smallest surface area-to-volume ratio.
Hence, the smallest ratio of surface molecules to
bulk molecules.
This maximizes the IMFs, hence circular drops.
Ex) The convex meniscus of mercury (Hg) in a glass test tube.
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Surface Tension
What happens if we add a solute to the liquid?
H
H
O
H
O
H
H
H
O
H
O
H
H
H
O
O
H
H
H
H
O
smooth surface;
lots of intermolecular attractions
H
H
O
H
O
H
H
H
O
O
H
H
O
H
H H
H
O
O
H
H
surface tension broken;
intermolecular attractions interfered with
A) Solute-solvent IMFs are stronger than in solvent:
Solute will be pulled into solution.
Miscibility
(“like dissolves like”)
B) Solute-solvent IMFs are weaker than in solvent:
Solute will stay at the surface.
Surfactant (“surface active agent”).
Surfactants reduce surface tension.
Detergents are surfactants.
Long non-polar tail
and a polar head.
0
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Capillary Action
A) IMFs between liquid & surface are stronger than in liquid:
Wetting: liquid spreads over the surface to maximize attractions.
Ex. water in a glass test tube
B) IMFs in liquid are stronger than between liquid and surface:
Non-wetting: liquid beads on the surface.
Ex. Hg in a glass test tube
H
The concave meniscus of water on glass:
H
Wetting of the glass surface leads to capillary action: capillary rise.
H
The polar Si-O bonds of the glass strongly attract water
H
=> Water moves along the surface.
=> Neighboring water molecules pulled along by surface tension.
Until: Weight of the water = Surface tension
O
H
O
O
O
H O
O
H
O
H
H
Si
O
O
Si
H
O
O
O
O
H H
Si
H
O
O
H
simplified structure for glass
(it's much more 3-dimensional!)
Hence narrow capillaries allow the liquid to rise higher compared to wide
capillaries.
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Viscosity
Viscosity is a liquid’s resistance to fluid flow.
Liquids with high viscosities tend to be thick and difficult to pour.
Viscosity increases as IMFs increase.
Viscous liquids are either large or polar (or both).
Ex)
Gasoline
(nonpolar, ~8 C’s)
Ex)
Engine oil
vs.
vs.
Mineral oil
(nonpolar, ~15-40 C’s)
molasses
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Kinetic Molecular Theory of Gases/Ideal Gases
Distances between gas particles are much larger than the size of the particles.
Therefore particles therefore occupy a negligible fraction of the volume.
Gas particles are in constant motion.
Therefore particles do not interact except when colliding, where the collisions are elastic.
Gas particles move at different speeds, where the average speed is proportional to temperature.
Hence all gases have the same average kinetic energy at a given T.
Law of Large Numbers :
The behaviour of many particle system is
unlikely to deviate significantly from the
behaviour predicted by the statistical average
of the properties of the individual particles.
“The Law of Averages”
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Kinetic Molecular Theory of Gases/Ideal Gases
The kinetic energy of a particle depends on its mass and speed:
where K is kinetic energy, m is mass and v is speed.
K 
1
mv 2
2
Speeds of molecules are distributed statistically according to the Maxwell-Boltzmann
distribution:
as temperature increases, the average speed increases and the distribution of
speeds widens.
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Kinetic Molecular Theory of Gases/Ideal Gases
There are three different ways to look at the speed of gas particles in a sample:
i) vmp = most probable speed
ii) vav = average speed
iii) vrms = root mean square speed.
(similar to the variance of a statistical distribution)
As kinetic energy is proportional to
temperature calculations.
K
Where:
v2, it makes most sense to use vrms in kinetic energy and
1 2
3
mvrms  kbT
2
2
K is the average kinetic energy of gas particles,
m is the mass of one particle,
T is temperature (in K).
kb is the Boltzmann Constant, which is the ideal gas constant R for one particle.
(kb = R/A)
Therefore for one mole of gas:
Hence:
vrms
1
3
2
Mvrms
 RT
2
2
3RT

M
K
where M is the molar Mass.
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Kinetic Molecular Theory of Gases/Ideal Gases
Pressure is force exerted on an area. P = F/A
The Maxwell-Boltzmann equation can be derived from the kinetic-molecular theory of
gases, which states that:
2
Nmvrms
P
3V
2
Nmvrms
PV  KE 
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or
where P is pressure, V is volume, N is the number of gas particles,
particle, and vrms is the root-mean-square speed.
m is the mass of one
Combining the Maxwell-Boltzmann equation and the Ideal Gas Law
PV 
2
Nmv rms
Therefore:
3
2
Nmv rms
 nRT
3
PV  nRT
and
2
Nmv rms
 3RT
n
or
The mass of one particle (m) multiplied by the number of particles (N) gives the
total mass of gas particles.(mN = M)
2
Mv rms
 3RT
or
v rms 
3RT
M
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Kinetic Molecular Theory of Gases/Ideal Gases
Ex) At a constant temperature room temperature of 25 oC:
O2 particles with mass of 32 amu will have __________ vrms
He particles with mass of 4 amu will have __________ vrms
Speed of sound ________ => ________ the frequency of sound.
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Kinetic Molecular Theory of Gases/Ideal Gases
You have a sample of helium gas at 0.00 ˚C. To what temperature should the gas
be heated in order to increase the root-mean-square speed of helium atoms by
10.0%?
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Non-ideal Gases
The ideal gas law and kinetic molecular theory are based on two simplifying assumptions:
i) The actual gas particles have negligible volume.
ii) There are no forces of attraction between gas particles.
Are these assumptions are not always valid?
Ideally the volume of a container of gas is 100% empty space – so the volume available for
gas particles to move into is the entire volume of the container.
Actually there is less available volume, which can be corrected via an excluded volume
term to the ideal gas law:
P V  nb   nRT
where b is an experimentally determined constant specific to the gas.
This constant tends to scales with the size of the gas particles.
The excluded volume is a downward correction to the actual volume thus increasing the
actual pressure of the gas.
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Non-ideal Gases
Under ideal conditions, particles in a gas sample don’t experience IMFs.
Under non-ideal conditions, the gas particles are close enough together that they do
experience IMFs.
The Ideal Gas Law is corrected accordingly:

n2 
 P  a 2  V  nRT
V 

where a is an experimentally determined constant specific to the gas.
This constant tends to increase as the polarity of the gas particles increases.
The effect of the IMFs is to decrease the pressure of the gas.
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Non-ideal Gases
When both corrections are applied, we get the van der Waals equation:

n2 
 P  a 2 V  nb   nRT
V 

The table below gives some sample values for a and b
a (Pa·m6·mol-2)
b (m3·mol-1)
Hydrogen
H2
0.0245
2.65  10-5
Methane
CH4
0.2303
4.31  10-5
Ammonia
NH3
0.4225
3.71  10-5
Water
H2O
0.5537
3.05  10-5
Sulfur dioxide
SO2
0.6865
5.68  10-5
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Non-ideal Gases
You have two 1.00 L containers at 298 K. One contains 1.00 mol of hydrogen
gas while the second contains 1.00 mol of ammonia gas.
(a)
Calculate the pressure in each container according to the ideal gas law.
(b)
Calculate the actual pressure in each container.
a (Pa·m6·mol-2)
b (m3·mol-1)
Hydrogen
H2
0.0245
2.65  10-5
Ammonia
NH3
0.4225
3.71  10-5
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Brownian Motion
The kinetic-molecular theory doesn’t just apply to gases. Brownian
motion is the random motion of small particles (e.g. micrometer-sized)
in a fluid.
Einstein showed that the mean squared displacement is given by:
x 2  2Dt
where D is the diffusion coefficient of the particle in that fluid. It can be
found using the equation below
D 
k BT
6r
where r is the radius of the particle and  is the viscosity coefficient of the
solvent
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Brownian Motion
The HIV-1 virus has a radius of about 50 nm. The viscosity
coefficient of water at 20 °C is 1.00 mPa·s. How far will a particle
of HIV-1 typically travel in 1 minute?
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