# CHM2S1-A Intermolecular Forces Dr R. L. Johnston Handout 2: The Importance of Intermolecular Forces III: Intermolecular Forces in Action 8.Consequences.

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CHM2S1-A Intermolecular Forces 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 THE UNIVERSITY OF 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 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 Note that an ideal gas can never liquify, however low the temperature. The closest we get is He for which T BP = 4.2 K p V Increasing T

van der Waals equation of state: Introducing the molar volume, V m = V/n, this becomes: 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: p eff.V eff = nRT

Ideal and Real (Non-Ideal) Gases IdealReal (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 V m, 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 vdW gases can only liquify for T  T c (independent of p). p V Increasing T TcTc VcVc pcpc

From the vdW equation, the following expressions can be derived: T c = 8a / 27Rb V c = 3b ; p c = a / 27b 2 i.e. the lower a (or higher b), the lower the temperature needs to be for liquids to form. e.g.CO 2 T c (observed) = 304 K T c (predicted by vdW) = 300 K.

Comparison of van der Waals coefficients Gasa / Pa m 6 mol  2 b / 10  5 m 3 mol  1  / kJ mol  1 T b / K He0.0042.3700.14 Ar0.1383.2191.287 Xe0.4315.1052.1165 H2H2 0.0252.6610.320 N2N2 0.1433.9130.977 CO 2 0.3694.2672.0(subl.) 195 CH 4 0.2314.2781.3112 C6H6C6H6 1.84811.543.1353 H2OH2O0.5613.04920.0373 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 coefficient C – third virial coefficient B, C depend on T. B is more important than C (B/V m  C/V m 2 ). * B has units of cm 3 mol  1. B (273 K)*B (600 K)* Ar  21.7 11.9 CO 2  149.7  12.4 N2N2  10.5 21.7 Xe  153.7  19.6

Gas Compressibility Ideal (perfect) gasesZ = 1 Real gases –v. low pZ  1 molecules far apart  weak interactions  behaves like perfect gas –medium pZ < 1 attractive forces dominate  easier to compress –high pZ > 1 repulsive forces dominate  harder to compress Compression factor

Gas Compression Factor (Z) Comparison of gases Effect of temperature

8.2 Non-Ideal Solutions and Mixtures Ideal Solutions obey Raoult’s Law p A = partial vapour pressure of A in liquid mixture p A * = vapour pressure of pure liquid A x A = mole fraction A in liquid mixture. Total pressure, p In terms of chemical potentials (  ) we can write: Raoult’s law implies that all interactions A  A, B  B, A  B are the same (i.e. U AA = U BB = U AB ). Note: does not assume no interactions, but  mix H = 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. CS 2 /acetone (U AA  U BB  U AB ). U AB > U AA, U BB   mix H < 0(exothermic mixing) negative deviation U AB 0(endothermic mixing) positive deviation In terms of chemical potential: where a A is the activity (= effective mole fraction) of liquid A in the mixture.

Vapour Pressures of Solutions Benzene-Toluene CS 2 -Acetone Ideal 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 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: 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. O HH  r OH r OH = 0.96 Å  = 104.45  

In the gas-phase optimal H-bond bond strength between water molecules ~ 23 kJ mol  1. 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 O  H bonds. This shows up in the increase in the average dipole moment per water molecule, which increases from 1.85 D (isolated H 2 O) to 2.4  2.6 D (liquid H 2 O 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 H 2 O 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!

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 H 2 X molecules from the same group)  relatively high boiling and melting points (same true for HF and NH 3 ). 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 (U AB < U AA, U BB ). 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 CH 4 and CO 2 ) surrounded by a polyhedral cage of water molecules. At high P, low T, these clathrates can precipitate out as solids. Examples: CH 4 -H 2 O clathrates in oil pipelines. CO 2 -H 2 O clathrates in deep ocean sites. CH 4

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 Structure 11.1 Proteins: natural polymers = polypeptides = chains of amino acids (H 2 NCHRCO 2 H) 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1 22 33 4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 protein hydrophobic core hydrophilic shell

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