CHM2S1-A Intermolecular Forces Dr R. L. Johnston

Handout 2: The Importance of Intermolecular Forces

III: Intermolecular Forces in Action8. Consequences of Intermolecular Forces9. Anomalous Properties of Water10.The Hydrophobic Effect11.Protein Structure

THE UNIVERSITYOF BIRMINGHAM

8. Consequences of Intermolecular Forces

8.1 Real Gases

Ideal (or “perfect”) gas equation of state:

where R (the gas constant) = 8.3145 J K1 mol1.

• 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.

nRTpV

p,V isotherms for an ideal gas

Note that an ideal gas can never liquify, however low the temperature.

The closest we get is He for which TBP = 4.2 K

p

V

Increasing T

van der Waals equation of state:

• Introducing the molar volume, Vm = V/n, this becomes:

• van der Waals coefficients a, b > 0.a – measures strength of attractive interactions between moleculesb – measures volume of molecules

• These equations have the form: peff.Veff = nRT

nRTnbVVnap

2

RTbVVap mm

2

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.

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).

2mm Va

bVRTp

p,V Isotherms for a van der Waals Gas

vdW gases can only liquify for T Tc (independent of p).

p

V

Increasing T

Tc

Vc

pc

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 coefficientsGas a / Pa m6 mol2 b / 105 m3 mol1 / kJ mol1 Tb / KHe 0.004 2.370 0.1 4Ar 0.138 3.219 1.2 87Xe 0.431 5.105 2.1 165H2 0.025 2.661 0.3 20N2 0.143 3.913 0.9 77CO2 0.369 4.267 2.0 (subl.) 195CH4 0.231 4.278 1.3 112C6H6 1.848 11.54 3.1 353H2O 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.

• Virial equation of state:

B – second virial coefficientC – third virial coefficient

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

* B has units of cm3 mol1.

21

mmm

VC

VBRTpV

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

Gas Compressibility

• 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

RTpV

Z mCompression factor

Gas Compression Factor (Z)

Comparison of gases Effect of temperature

8.2 Non-Ideal Solutions and Mixtures

• Ideal Solutions obey Raoult’s Law

pA = partial vapour pressure of A in liquid mixturepA

* = vapour pressure of pure liquid AxA = mole fraction A in liquid mixture.

• Total pressure, p

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

• Raoult’s law implies that all interactions AA, BB, AB 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.

*AAA pxp

A*AA ln xRTμ

*BB

*AABA pxpxppp

• 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)

negative deviation

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

positive deviation

• In terms of chemical potential:

where aA is the activity (= effective mole fraction) of liquid A in the mixture.

*AAA pxp

*AAA pxp

A*AA ln aRTμ

Vapour Pressures of Solutions

Benzene-Toluene CS2-AcetoneIdeal Solution

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

between surfaces and adsorbed molecules.

9. Anomalous Properties of Water9.1 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:

• The dipole moment () of the isolated water molecule is 1.85 D.• Water forms hydrogen bonds: the OH 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.

O

H H

rOHrOH = 0.96 Å

= 104.45

• In the gas-phase optimal H-bond bond strength between water molecules ~ 23 kJ mol1.

• H-bonding in condensed phases of water is cooperative (non-additive): the strength of H-bonding increases with increasing number of water molecules, as this increases the polarization of the OH bonds.

• This shows up in the increase in the average dipole moment per water molecule, which increases from 1.85 D (isolated H2O) to 2.42.6 D (liquid H2O at 0C).

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 4C. Above 4C, 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:

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

• This may contribute to enabling ice skating!

C)OatKatm133(0 1

solliq

solliq

VV

SS

VS

dTdp

Other properties of liquid water

• Liquid water is less compressible than ice. Compressibility decreases with T until 46C.

• 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 mol1) and entropy of vaporization (109 JK1 mol1), 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 Effect10.1 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 25C. (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 K1 mol1

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

• For T 25C, 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.

• 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.

CH4

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.

Clathrate water cage around a long chain hydrocarbon

Spherical micelle

Clathrates and Micelles

11. Protein Structure11.1 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 NHO=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 SS 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.

Sequence

hydrophobic

hydrophilic

Folded proteinhydrophobic core

hydrophilic shell