# Intermolecular Forces 2

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```					                 CHM2S1-A   Intermolecular Forces
THE UNIVERSITY
OF BIRMINGHAM               Dr R. L. Johnston
Handout 2: The Importance of Intermolecular Forces

III: Intermolecular Forces in Action
8. Consequences of Intermolecular Forces
9. Anomalous Properties of Water
10. The Hydrophobic Effect
11. Protein Structure
8. Consequences of Intermolecular Forces

8.1 Real Gases

Ideal (or “perfect”) gas equation of state:
pV  nRT
where R (the gas constant) = 8.3145 J K1 mol1.

• Assumptions:           (1) atoms/molecules have no size
(2) there are no interactions between the
atoms/molecules

• Real (imperfect or non-ideal) gases don’t obey this equation, due
to the failure of both assumptions.
p,V isotherms for an ideal gas
p
Increasing T

V

Note that an ideal gas can never liquify, however low the
temperature.
The closest we get is He for which TBP = 4.2 K
van der Waals equation of state:

        n 
2
 p  a  V  nb  nRT

      V  
            
•   Introducing the molar volume, Vm = V/n, this becomes:

          
p a      V m  b   RT
    2     
  Vm      
•   van der Waals coefficients a, b > 0.
a – measures strength of attractive interactions between molecules
b – measures volume of molecules

•   These equations have the form:   peff.Veff = nRT
Ideal and Real (Non-Ideal) Gases

Ideal                        Real (Non-Ideal)

In real (non-ideal) gases, we allow for both non-zero
intermolecular forces and non-zero size of molecules.
RT       a
p           2
Vm  b  Vm
Pressure:

•   b – reduction of available volume for molecules to move in, due to non-zero size
of molecules. (Takes account of repulsive forces by modelling molecules as
hard spheres). Less volume to move in  more frequent collisions between
molecules  pressure increases.

•   a – attractive long range interactions between molecules lead to a decrease in
the frequency and the force of collisions between molecules  pressure
decreases.

•   Note:
– at high T or high Vm, vdW equation  perfect gas equation
– liquid and gas coexist when p = 0 (when 2 terms in equation balance).
p,V Isotherms for a van der Waals Gas

p
Increasing T

Tc
pc

V
Vc

vdW gases can only liquify for T  Tc (independent of p).
From the vdW equation, the following expressions can be
derived:
Tc = 8a / 27Rb

Vc = 3b ; pc = a / 27b2

i.e.   the lower a (or higher b), the lower the temperature
needs to be for liquids to form.

e.g.   CO2
Tc (observed) = 304 K

Tc (predicted by vdW) = 300 K.
Comparison of van der Waals coefficients
Gas            a / Pa m6 mol2     b / 105 m3 mol1  / kJ mol1          Tb / K
He                       0.004                 2.370           0.1             4
Ar                       0.138                 3.219           1.2            87
Xe                       0.431                 5.105           2.1           165
H2                       0.025                 2.661           0.3            20
N2                       0.143                 3.913           0.9            77
CO2                      0.369                 4.267           2.0   (subl.) 195
CH4                      0.231                 4.278           1.3           112
C6H6                     1.848                 11.54           3.1           353
H2O                      0.561                 3.049          20.0           373

•More polarisable molecules behave in a less ideal manner, due to larger
dispersion forces (reflected in a larger van der Waals a factor).
•Magnitude of b correlates to the size of the molecule.
•   There are a number of other, more accurate equations of state. Here,
we will mention only one other.
    B   C    
• Virial equation of state:           pVm  RT 1     2  
 Vm V        
        m    
B – second virial coefficient
C – third virial coefficient

•   B, C depend on T. B is more important than C (B/Vm  C/Vm2).

B (273 K)*   B (600 K)*
Ar                            21.7          11.9
CO2                          149.7         12.4
N2                            10.5          21.7
Xe                           153.7         19.6

* B has units of cm3 mol1.
Gas Compressibility
pVm
Compression factor         Z
RT
• Ideal (perfect) gases Z = 1

• Real gases
– v. low p          Z1      molecules far apart  weak interactions 
behaves like perfect gas
– medium p          Z<1      attractive forces dominate  easier to
compress
– high p            Z>1      repulsive forces dominate  harder to
compress
Gas Compression Factor (Z)

Comparison of gases          Effect of temperature
8.2 Non-Ideal Solutions and Mixtures
•   Ideal Solutions obey Raoult’s Law      pA        *
xA pA
pA = partial vapour pressure of A in liquid mixture
pA* = vapour pressure of pure liquid A
xA = mole fraction A in liquid mixture.
•   Total pressure, p      p  pA  pB  xA pA  xB pB
*       *

•   In terms of chemical potentials () we can write:

μ A   *  RT ln x A
A

•   Raoult’s law implies that all interactions AA, BB, AB are the same
(i.e. UAA = UBB = UAB).

Note: does not assume no interactions, but mixH = 0.

•   Raoult’s law is obeyed well by mixtures of similar (shape and bonding)
molecules – e.g. benzene/toluene.
•   Non-Ideal Solutions: strong deviations from ideality (positive or negative)
shown by mixtures of dissimilar liquids – e.g. CS2/acetone (UAA  UBB 
UAB).

•   UAB > UAA , UBB  mixH < 0        (exothermic mixing)

pA  xA pA
*           negative deviation

•   UAB < UAA , UBB  mixH > 0        (endothermic mixing)

pA  xA pA
*           positive deviation

•   In terms of chemical potential:       μA   A
*
 RT ln a A
where aA is the activity (= effective mole fraction) of liquid A in the
mixture.
Vapour Pressures of Solutions

Ideal Solution              Benzene-Toluene      CS2-Acetone
8.3 Other Consequences of IMFs

• Different phases adopted by various elements and compounds.
• Structures of solids and liquids.
• Liquid crystals – unusual properties due to anisotropic
intermolecular interaction (e.g. disk-like or cigar-shaped
molecules).
• Transport properties (viscosity, thermal conductivity, diffusion).
• Properties of electrolyte solutions (solvated ions).
• Supramolecular chemistry (aggregation, self-ordering, molecular
recognition, protein folding, drug-protein interactions, DNA …).
8.4 Some Experimental Techniques for Investigating IMFs

•   Molecular Beams – study collisions and scattering between individual
molecules.
•   X-ray and neutron diffraction – determine long range structures of
crystalline solids and short range structure of liquids.
•   Spectroscopy – determine structures, binding energies and electronic,
vibrational and rotational energies of loosely bound “van der Waals
molecules”.
•   Measurement of gas imperfection – e.g. pV isotherms, Joule-Thomson
effect, compressibility.
•   Measurement of solution non-ideality – deviations from Raoult’s law and
Henry’s law.
•   Measurement of transport properties
•   Atomic Force Microscopy – direct measurement of intermolecular forces
9. Anomalous Properties of Water
9.1 Water
•   Water is the most abundant liquid on Earth.
•   But: it is considered to be “anomalous” because it behaves differently
from simple liquids (e.g. Ar).
•   Differences are due to hydrogen bonding in water.
•   The water molecule is small and compact, with two H atoms and two
lone pairs arranged tetrahedrally around the O atom:

        rOH   O                rOH = 0.96 Å
 = 104.45
H               H

•   The dipole moment () of the isolated water molecule is 1.85 D.
•   Water forms hydrogen bonds: the OH bonds act as H-bond donors and
the O lone pairs act as H-bond donors.
•   Each water molecule can take part in up to 4 H-bonds.
• In the gas-phase optimal H-bond bond strength between water
molecules ~ 23 kJ mol1.

• H-bonding in condensed phases of water is
H-bonding increases with increasing number
of water molecules, as this increases the
polarization of the OH bonds.

• This shows up in the increase in the average dipole moment per
water molecule, which increases from 1.85 D (isolated H2O) to
2.42.6 D (liquid H2O at 0C).
Phase Diagram for Water
9.2 Ice (Solid Water)
• The structure of ice is based on tetrahedral coordination of the
water molecules, which each take part in 4 H-bonds.
• There are a number of different solid ice phases. At 1 atm. the
most stable form is hexagonal ice Ih.
9.3 Liquid Water
• For water, the liquid is more dense than the solid (ice). This is in
contrast to most liquids. Maximum density of liquid is at around
4C. Above 4C, water behaves like other liquids – expanding as
it gets warmer.

• This is due to the disruption of the long-range ordered tetrahedral
network in liquid water. The average number of nearest
neighbours around each H2O molecule increases from 4 to
approx. 4.4 on melting.

• There is a fluctuating network of H-bonds in liquid water.

• Higher densities are favoured by increasing van der Waals (D-D
and dispersion) interactions, though H-bonding favours lower
coordination and lower density.  on melting, the H-bonding is
weaker but the vdW bonding is stronger.

• Consequences: ice-bergs; burst water pipes in winter…
• Applying pressure to ice causes melting. According to the
Clapeyron equation:

dp S S liq  S sol
                 0 (  133 atm K 1 at O  C)
dT V Vliq  Vsol

 every 133 atm. of applied pressure, decreases the melting
temperature of ice by 1 K.

• This may contribute to enabling ice skating!
Other properties of liquid water

•   Liquid water is less compressible than ice. Compressibility decreases
with T until 46C.
•   Liquid water has a high dielectric constant:
(because H-bonds are polarizable) so it is
a good solvent for ions.
•   H-bonding leads to higher cohesive energies than
for similar-sized molecules (especially compared with
H2X molecules from the same group)  relatively high
boiling and melting points (same true for HF and NH3).
•   The extended H-bonded network in liquid water leads to rapid transfer of
H+ and OH  changes of pH move rapidly through aqueous solutions.
•   Water has a high enthalpy (40 kJ mol1) and entropy of vaporization
(109 JK1 mol1), indicating that the liquid still has quite a lot of the order
(and cohesion) of the solid  water has a very high liquid range (100 K).
This is critical for life on Earth!
Comparison of boiling points of group 16 and group 18 hydrides
10. The Hydrophobic Effect
10.1 Definitions
•   Hydrophobic Effect: The low solubility of hydrocarbons and other non-
polar molecules in water and their increased tendency to aggregate.
•   Hydrophobic Interaction: Enhanced effective attractions between
hydrocarbon molecules etc., when in water.
•   Simple enthalpy explanation: immiscibility (lack of solubility) of solute B
in solvent A occurs when the A-B interactions are weaker than the A-A
and B-B interactions (UAB < UAA, UBB).
•   This might be expected to be the case for B = hydrocarbon (quite strong
dispersion forces between long chain hydrocarbons) and A = water
(strong H-bonds), with A-B interactions being primarily dipole-induced
dipole in nature (relatively weak).
•   BUT – this does not explain why solubility of oil in water, as a function of
T, goes through a minimum at T  25C. (Normally expect solubility  as
T ).
10.2 Origin of the Hydrophobic Effect
•   Note: the overall enthalpy of interaction of a non-polar solute with water is not
particularly unfavourable (H  0) because the non-polar molecules induce
cage-like ordering of the first shell of water molecules, strengthening their H-
bonding.

•   The origin of the hydrophobic effect is mostly entropic.

•   The ordering of the shell of water molecules around the hydrocarbon solute (so
as to minimise “dangling” H-bonds), causes a significant decrease in the entropy
of the water (S < 0).

•   Typically, the total change in entropy in dissolving small hydrocarbon molecules
in water (at 298 K):
S  100 J K1 mol1

•   For T < 25C, entropy term dominates and becomes more unfavourable with
increasing T  solubility decreases as T rises.

•   For T  25C, the water cages start to break up (weakening H-bonds) so H,
S increase  solubility increases as T rises (enthalpy starts to dominate).
10.3 Clathrates: single hydrocarbon or other non-polar molecules
(even small ones, such as CH4 and CO2) surrounded by a
polyhedral cage of water molecules.

CH4

• At high P, low T, these clathrates can precipitate out as solids.

• Examples:     CH4-H2O clathrates in oil pipelines.
CO2-H2O clathrates in deep ocean sites.
10.4 Micelles: (examples of colloids) = pseudo-spherical clusters of
surfactant molecules – consisting of hydrophilic heads (polar or charged
groups) and hydrophobic tails (hydrocarbon chains) dispersed in water.

•   Hydrophobic tails aggregate together (dispersion forces) – this also
minimizes the unfavourable hydrophobic entropy effect on the solvent
(water). Centre of micelle is oil-like.

•   Hydrophilic heads form a close-packed shell and have strong
intermolecular interactions with the water molecules.

•   Sizes range from 100’s (charged heads) to 1000’s of molecules.
•   Used to solubilize hydrocarbons in aqueous solution:
– e.g. detergents, drug carriers, organic synthesis, petroleum
recovery.
•   Analogous to biological membranes.
Clathrates and Micelles

Clathrate water cage around              Spherical micelle
a long chain hydrocarbon
11. Protein Structure
11.1 Proteins: natural polymers = polypeptides = chains of amino acids
(H2NCHRCO2H) joined by peptide links CO-NH.

•   Protein folding: the folding up of the polypeptide chains under the
influence of “intermolecular” forces.
Note: the chemical function of the protein is dependent on its 3D
structure – which depends on its folding.

•   Primary structure: sequence of amino acids.

•   Secondary structure: coiling into -helices or folding into -sheets, due
to NHO=C hydrogen-bonding between peptide groups (which are
close in the sequence).

•   Tertiary structure: folding of the polypeptide chain by forming
interactions (e.g. covalent disulfide SS links, ionic interactions, H-
bonds) between side chains (R) of amino acids which are relatively far
apart in the sequence. In aqueous solution, the hydrophobic effect may
also be important.
• Quaternary structure: aggregation of more than one polypeptide
chain due to similar interactions to those responsible for tertiary
structure.

• Protein aggregation
– sometimes beneficial (e.g. for the function of haemoglobin –
an aggregate of 4 polypeptide chains)
– sometimes harmful (e.g. in “protein misfolding” diseases such
as BSE, CJD).

1        2        3               4
Secondary Protein Structure

Conformational Flexibility               -helix
Secondary and Tertiary Protein Structure
11.2 The hydrophobic effect in protein folding
• Globular proteins in aqueous solution have pseudo-spherical
shapes:
– cores rich in hydrophobic residues (amino acids with non-
polar alkyl or aryl side-chains, R)
– outer shell rich in hydrophilic residues (polar side chains).

• Protein folding is partially driven by the hydrophobic effect –
“burying”  ½ of hydrophobic residues reduces the unfavourable
decrease in entropy of the surrounding water molecules.
hydrophobic

Sequence

hydrophilic           hydrophilic shell

Folded protein
hydrophobic core

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