chemical bonding

metallic bonds → definition

metallic bonds refer to the electrostatic forces of attraction between a lattice of metal cations and sea of delocalised electrons

• lattice: regular repeating pattern

formation of metallic bonds

• metallic bonds are formed in metals where metal atoms lose valence electrons to form metal cations

  • metal: found mainly in group 1, 2 and transition metals

• valence electrons are delocalised → mobile within the metallic lattice

structure of metals

• metals like copper have giant metallic structures which consist of lattice of metal cations in a sea of delocalised electrons held together by strong metallic bonds

• coordination number: number of nearest neighbours of a central atom of interest

factors affecting the strength of metallic bonds

1. number of valence electrons contributed to the sea of delocalised electrons

   • the greater the number of valence electrons contributed, the stronger the metallic bonds

2. radius of metal cation

   • the larger the radius of the metal cation, the weaker the metallic bonds ⇒ the delocalised electrons are further away from the positive nuclei causing the electrostatic forces of attraction between the electrons and positive nuclei to be weaker

   • metallic radius increases down the group, and decreases across the period

physical properties of metals

1. high melting and boiling points

   • metals generally have high melting and boiling points → the stronger the metallic bonds, the higher the melting and boiling points

   • large amount of energy is required to break the strong metallic bonds (electrostatic forces of attraction between the metal cations and sea of delocalised electrons) in the giant metallic lattice

2. good electrical conductivity

   • metals are good electrical conductors in both solid and molten states → delocalised electrons function as charge carriers to conduct electricity

3. good thermal conductivity

   • metals are good conductors of heat → when heat is applied to one end of a piece of metal, kinetic energy of the electrons at that end increases, and the energy is transferred by the delocalised electrons to other parts of the metal

4. malleable (can be hammered) and ductile (can be pulled into wires)

   • when a force is applied, the layers of metal atoms can easily slide over each other without breaking the metallic bond, the metallic bonds are easily reformed and the crystal lattice is restored

alloy formation

• metals in group 1 and 2 are generally soft and some of them can be cut easily

• metals can be made much harder by alloying → mixing with another metal

• atoms of the other metal have different size and disrupt the orderly arrangement of the main metal in the lattice so that the layers of atoms do not slide over each other easily

ionic bonds → definition

ionic bonds refer to the strong electrostatic forces of attraction between the oppositely charged ions

formation of ionic bonds

• formed between elements with large electronegativity difference

• formed in ionic compounds when metal atoms (low electronegativity) lose electrons to form cations while non-metal atoms (high electronegativity) gain electrons to form anions to achieve a stable noble gas configuration

structure of ionic compounds

• giant ionic lattice structures consist of oppositely charged ions held together by strong ionic bonds

• the cations and anions are arranged alternatingly to maximise attractive forces between oppositely charged ions and minimise repulsive forces between similarly charged ions

• coordination number of an ion: determined by the total number of ions of opposite charge that surrounds it

  • depends on: relative charges of the ions (to gain electrically neutrality, a cation of a charge of +2 needs twice as many -1 ions as does a cation of charge +1) and relative sizes of ions (smaller ions may have a lower coordination number)

factors affecting the strength of ionic bonds

• ionic bonds are strong electrostatic forces of attraction and hence a lot of energy is required to break them

• strength of ionic bonds is indicated by the lattice energy of an ionic compound

lattice energy: the heat energy evolved when 1 mole of a solid ionic compound is formed from its constituent gaseous ions under standard conditions of 298K and 1 bar

• magnitude of lattice energy is dependent on: charges of ions and radii of ions

  • the greater the magnitude (numerical value) of the lattice energy, the stronger the ionic bonds

  • ionic radius increases down the group and decreases across the period

physical properties of ionic compounds

1. high melting and boiling points

   • under room conditions, ionic compounds are in the solid state as they have very high melting and boiling points → large amount of energy is required to overcome the strong ionic bonds (electrostatic force of attraction between oppositely charged ions) in the giant ionic lattice

2. good electrical conductivity

   • ionic compounds can only conduct electricity when they are in aqueous or molten states

     • in aqueous and molten state → there are free mobile ions acting as charge carriers to conduct electricity

     • in solid state → the ions can only vibrate about their fixed positions, hence there are no free mobile ions to conduct electricity

3. hard but brittle

   • ionic solids are hard → in an ionic solid, the oppositely charged ions are held together by strong electrostatic forces of attraction

   • however, they are brittle (shatter when hit) → stress applied on an ionic lattice causes the sliding of the layers of ions, and ions of similar charges come together and the repulsion shatters the ionic structure

4. solubility

   • ionic compounds are generally soluble in polar solvents (e.g. water) and insoluble in non-polar solvents (e.g. hexanes)

   • when an ionic compound interacts with water (hydration), polar water molecules are attracted to the ions, forming ion-dipole interactions (exothermic process → heat is given out), and if the solvent is not water, the process is called solvation

   • ionic compounds like sodium chloride are soluble in water

     • the ion-dipole interactions formed between ions and water molecules releases sufficient energy to overcome the ionic bonds between the oppositely charged ions and the hydrogen bonds between water molecules, the ionic lattice of the solid breaks down and the ionic compound dissolves

   • ionic compounds are generally insoluble in non-polar solvents

     • the interaction between the ions and solvent molecules is not as strong and releases insufficient energy to overcome the ionic bonds between the oppositely charged ions and the attractions between solvent molecules

intermediate bond types → ionic bonds with covalent character

• covalent character in ionic bonds arises due to the distortion/polarisation of the anion electron cloud by the cation in an ionic compound

• the greater the extent of polarisation, the greater the covalent character in the ionic bond

• extent of distortion/polarisation depends on the

  1. polarising power of the cation → ability of cation to polarise anion

  2. polarizability of the anion → to be polarised

• extent of covalent character in an ionic bond increases when

  1. the cation is small (small ionic radius) and highly charged → the cation has high charge density ⇒ high polarising power

  2. the anion is large → the anion has a higher polarizability

covalent bonds → definition

covalent bond is the electrostatic force of attraction between a shared pair of electrons and the positively charged nuclei

formation of covalent bonds

covalent bonds involve the sharing of a pair of electrons, and are formed between elements of small electronegativity differences (between non-metals) to achieve the stable noble gas configuration

sigma (σ) and pi (π) bonds

• covalent bonding arises from the overlapping of valence orbitals and occur in two ways → head-on or sideways

  • when the valence-orbitals overlap head-on with one another, a σ-bond is formed

    • σ-bond can be formed from overlapping of s orbitals, p orbitals, or hybrid orbitals

    • it can be between the same type of orbitals or different type of orbitals

    • where they overlap → where shared electrons are at most of the

  • π-bond is formed when parallel valence p orbitals overlap sideways with one another

    • although the π-bond has two lobes of electron clouds above and below the inter-nuclear axis, it constitutes only one bond

• a double bond consists of one σ-bond and one π-bond, and a triple bond consist of one σ-bond and two π-bonds → π-bonds are formed only after the σ-bond has been formed ⇒ ensures that the two atoms are close enough for sideway overlap

factors affecting the strength of covalent bonds

• strength of covalent bond depends on the extent of orbital overlap

  • the greater the extent of orbital overlap → the more effective the orbital overlap → the stronger the covalent bonds

  • σ-bond is stronger than a π-bond as there is a greater overlap of the valence orbitals

• indicators of the strength of covalent bonds

  • bond length → the shorter the bond length, the stronger the bond

    • bond length is defined as the distance (measured in nm) between the two nuclei in a covalent bond

  • bond energy → the greater the bond energy, the stronger the bond

    • bond energy: the average energy required to break one mole of covalent bonds in the gas phase (or in a gaseous molecule) into constituent gaseous atoms under standard conditions

  • bond order → greater the bond order, the stronger the covalent bonds

    • bond strength: triple bond > double bond > single bond

    • bond order: number of covalent bonds formed between 2 atoms

giant molecular structures

• a giant molecular solid consists of numerous strong covalent bonds holding the atoms together in an infinite way, and there are no discrete molecules

• e.g. diamond, graphite, silicon, silicon dioxide, silicon carbide, boron nitride

diamond

• an allotrope of carbon

• it has a giant molecular structure where each carbon atom is joined by strong covalent bonds to four other atoms in a tetrahedral arrangement (bond angle of 109.5°)

• uses: tools for drilling, cutting and grinding

diamond → physical properties

• a very high melting and boiling point → due to large amount of energy needed to break the numerous strong covalent bonds between the carbon atoms in the giant molecular structure

• very hard substance → due to the very strong carbon-carbon covalent bonds and rigid tetrahedral structure

• does not conduct electricity → it has no mobile delocalised electrons as all the valence electrons of the carbon atoms are localised in the covalent bonds

• does not dissolve in water → the energy released from the formation of instantaneous dipole-induced dipole interactions between water molecules and carbon atoms is insufficient to overcome the strong covalent bonds between the carbon atoms

graphite

• an allotrope of carbon

• has a giant molecular structure, within each layer each carbon atom forms strong covalent bonds with three other carbon atoms in a trigonal planar arrangement (bond angle of 120°), using three of its valence electrons, while the fourth electron from the outer shell of the carbon atom is delocalised in a π bond that extends over the whole layer

• uses: as a lubricant and in pencils

graphite → physical properties

• a very high melting and boiling point → due to large amount of energy needed to break the numerous strong covalent bonds between the carbon atoms within each layer and the instantaneous dipole-induced dipole attractions between layers in the giant molecular structure

• slippery → the layers of graphite can slide over each other by breaking the weak instantaneous dipole-induced dipole attractions between the layers

• good electrical conductor only along/parallel to the layers because of the presence of the mobile delocalised electrons within each plane of carbon atoms, and graphite cannot conduct electricity perpendicular to the layers because the delocalised electrons cannot move across the layer

• insoluble in water → the energy released from the formation of instantaneous dipole-induced dipole interactions between water molecules and carbon atoms is insufficient to overcome the strong covalent bonds between the carbon atoms

silicon dioxide

• occurs in quartz

• each Si atom is tetrahedrally bonded to four other O atoms while each O atom is bonded to two Si atoms

silicon dioxide → physical properties

• a very high melting and boiling point → due to large amount of energy needed to break the numerous strong covalent bonds between the Si and O atoms in the giant molecular structure

• very hard substance → due to the very strong silicon-oxygen covalent bonds and rigid tetrahedral structure

• does not conduct electricity → it has no mobile delocalised electrons as all the valence electrons of the Si and O atoms are localised in the covalent bonds

• does not dissolve in water → the energy released from the formation of instantaneous dipole-induced dipole interactions between water molecules, and Si and O atoms is insufficient to overcome the strong covalent bonds between the Si and O atoms

simple molecular structure

• simple discrete molecules are found in the structure

  • within each molecule, the atoms are joined together by strong covalent bonds

  • the separate molecules are attracted to each other by weak intermolecular forces of attraction (instantaneous dipole-induced dipole attractions)

dative bonds

a covalent bond in which the shared pair of electrons is provided by only one of the bonded atoms

• a dative bond, once formed, is no different from the usual covalent bond

• A = electron-pair donor atom (Lewis base) → electron rich

• B = electron-pair acceptor atom (Lewis acid) → electron deficient

• arrow always points from donor to acceptor

criteria for dative bonding

• the donor atom must have at least a lone pair of electrons in its valence shell

• the acceptor atom must have a vacant and energetically accessible orbital to accept the lone pair of electrons

polar covalent bond → intermediate bond types

a covalent bond, bond polarity is a measure of how equally the electrons are shared between the two bonded atoms

• depends on the difference in electronegativity between the atoms

• if the two atoms have same electronegativity, the bonding electrons are equally shared, and a non-polar covalent bond is formed

• if the two atoms have different electronegativity, the bonding electrons are not equally shared, and a polar covalent bond is formed

  • the atom with greater electronegativity pulls the electrons of the covalent bond towards itself, and the other atom is depleted of electrons ⇒ this atom acquires a partial negative charge δ-, and the other atom acquires a partial positive charge δ+

• permanent partial separation of charges result in the formation of a dipole

dipole moment

• dipole moment is a measure of:

  • the separation of charges between the partial positive and negative ends in one covalent bond

  • the extent of polarisation or distortion of electron cloud of a covalent bond

• most electronegative: F > O > N; Cl > I > C

• dipole moments are vector quantities and denoted by an arrow pointing from the δ+ atom to the δ- atom along the bond

• the magnitude of the dipole moment depends on the difference in electronegativity between the two atoms sharing the covalent bond

  • greater electronegativity difference ⇒ larger dipole moment ⇒ covalent bond more polar

dot-and-cross diagrams → electron pair

• an electron pair that is shared between the bonded atoms is called a bond pair

• an electron pair that is part of an atom’s valence shell but not ‘shared’ with another atom is called a lone pair

rules when drawing dot-and-cross

• show only the valence electrons, including those valence electrons not involved in bonding → both lone pairs and bond pairs

• use only dots and crosses to represent electrons

• alternate different electron symbols for atoms adjacent to each other

  • two dots or crosses are used to represent the two electrons from the donor atom used to form a dative bond

• elements with one to four valence electrons form the same number of covalent bonds as the number of valence electron it has (H - 1 bond, B - 3 bonds, C - 4 bonds)

• for period 2 atoms, if the number of valence electrons is greater than 4, then it forms the number of covalent bonds that corresponds to the number of electrons it requires to gain an octet structure (eg N - 3 bonds, O - 2 bonds, F - 1 bond)

• always try single covalent bonds first, followed by double and triple bonds to attain the octet configurations in the dot-and-cross diagram, and dative bond is (usually) assigned the last in particular for elements which cannot expand octet configuration

general steps in drawing

1. determine the central atom → the central atom is usually the atom that needs the greatest number of electrons to be stable

   • the other atoms are the surrounding atoms

2. if it is an ion, use the following:

   • cation: for each + charge, remove 1 electron from the less electronegative atom

   • anion: for each - charge, add 1 electron to the more electronegative atom

3. complete the valence shell of each atom via covalent bond formation

4. check that all the valence electrons for each atom have been accounted for and remember to draw lone pairs (if any) around both the central and surrounding atoms

electronegativity

• increases from the left to right across a period

• decreases down a group

exceptions to octet rule in covalent bonding

• molecules with central atom of < 8 valence electrons

  • for example, group 2 and 13 elements such as Be, B and Al may form molecules with central atoms of < 8 valence electrons

• molecules with central atom of > 8 valence electrons

  • elements in period 3 and onwards can expand their octet structure

  • in a period 3 element (e.g. P), it has energetically accessible vacant 3d orbitals, which it can use to accommodate the extra electrons

  • elements in period 2 cannot expand its octet structure due to the absence of energetically accessible vacant orbitals in its valence shell, and can only have a maximum of 8 electrons in the valence shell

• molecules with central atom having unpaired electrons

  • such species are called radicals and are very reactive

principles of valence shell electron pair repulsion (vsepr) theory

1. electron pairs in the outer/valence shell of the central atom arrange themselves as far as possible to minimise repulsion and maximise stability → account for shape of molecule

2. strength of repulsion between electrons pairs decreases in the order: lone pair-lone pair repulsion > lone pair-bond pair repulsion > bond pair-bond pair repulsion

3. a central atom, which is more electronegative, will give rise to a larger electronic repulsion between two bond pairs, hence larger bond angle between the bond pairs

4. a multiple bond (e.g. double or triple bond) can be considered to be like a single bond

approach to predict the shape of molecules

1. draw the dot-and-cross diagram for the molecule

2. count the total number of electron pairs around the central atom

   • a single bond, double, triple bond and dative bond are counted as 1 electron pair

   • a lone pair is also counted as 1 electron pair

3. apply vsepr theory principle 1 to determine the molecular shape based on the exact number of bond pairs and lone pairs around the central atom, and draw the structure if required

   • drawing includes only the lone pairs on central atom, shows the correct shape and include the dotted lines (if applicable) to show that the atoms in the same plane

reason for the difference in bond angles of CH₄ and NH₃

although the number of electron pairs are the same, NH_3 has a smaller bond angle than CH_4 because of the greater repulsion between lone pair and bond pair of electrons, this forces the bond pairs closer together resulting in a smaller bond angle of 107°

steps to explain shapes and bond angle of molecules

1. state the number of electron pairs in the outer/valence shell of the central atom

2. apply vsepr principle to determine the electron geometry

3. to minimise repulsion and maximise stability,

   • electron geometry for 2 electron pairs is linear

   • electron geometry for 3 electron pairs is trigonal planar

   • electron geometry for 4 electron pairs is tetrahedral

   • electron geometry for 5 electron pairs is trigonal bipyramidal

   • electron geometry for 6 electron pairs is octahedral

4. state the number of bond pairs and lone pairs (if any) and the shape

5. to explain bond angle, apply vsepr principle 2

   • if 1 lone pair is present ⇒ lone pair-bond pair repulsion > bond pair-bond pair repulsion

   • if 2 lone pairs or more are present ⇒ lone pair-lone pair repulsion > lone pair-bond pair repulsion > bond pair-bond pair repulsion

6. state the bond angle (specify the value → slightly less for < )

steps to explain difference in bond angles

1. determine which central atom is more electronegative → bond pairs are drawn closer to the central atom

2. higher electron density and the bond pairs experience greater repulsion ⇒ greater bond angle

to determine the overall polarity of molecules

• use the shape of the molecules to determine

• the overall polarity of simple molecules enables one to determine the intermolecular forces of attraction between simple molecules

• the terms ‘polar’ and ‘non-polar’ do not apply to polyatomic ions like NH₄⁺, CO₃^2-, SO₄^2-

method to determine the overall polarity of molecules

1. does the molecule has polar bonds

   • no: molecule is non-polar

2. if yes, does the molecule have a net dipole moment?

   • no: molecule is non-polar

   • yes: molecule is polar

how to check if the molecule has a net dipole moment

• the net dipole moment in a molecule is obtained by resolving the individual dipole moments of each polar bond

  • if the dipole moments do not cancel out → the molecule has a net dipole moment

  • if the dipole moments cancel out → the molecule has no net dipole moment

• shapes of molecules which would result in the dipole moments cancelling out

  • linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, square planar

  • only applies where all atoms surrounding the central atom are identical

• shapes of molecules which would result in the dipole moments not cancelling out

  • bent, trigonal pyramidal, see-saw, T-shaped, square pyramidal

  • all atoms surrounding the central atom are not identical

intermolecular forces between molecules

• substances with simple molecular structure have intermolecular forces between the discrete simple molecules

  • instantaneous dipole-induced dipole (id-id) attractions → for all molecules

  • permanent dipole-permanent dipole (pd-pd) attractions → polar molecules only

  • hydrogen bonds

• for molecules with similar electron cloud size (comparable Mr)

  • strength of intermolecular forces: hydrogen bonding > pd-pd attractions > id-id attractions

instantaneous dipole-induced dipole attractions

• it is the electrostatic forces of attraction between the instantaneous dipoles and induced dipoles present in molecules

• although they are observed in both polar and non-polar molecules, they are only significant for non-polar molecules

factors affecting id-id attractions

size of electron cloud → indicated by Mr

• the greater the size of the electron cloud (larger Mr):

  • the greater the extent of polarisation of the electron cloud

  • the stronger and more extensive id-id attractions

surface area of contact between the molecules

• straight chain molecules have a greater surface area of contact between the molecules compared to branched molecules, which are more spherical

• straight chain molecules form more extensive id-id attractions

• only considered if the molecules have the same type of intermolecular forces of attraction (id-id) and have similar electron cloud size

permanent dipole-permanent dipole attractions

• it is the electrostatic forces of attraction between permanent dipoles of polar molecules

• the greater the dipole moment, the stronger the pd-pd attractions

hydrogen bonding

electrostatic forces of attraction between an H atom covalently bonded to a highly electronegative atom (i.e. N, O or F) and a lone pair of electrons on a second highly electronegative atom (i.e. N, O or F)

case study: structure and properties of water and ice

• due to hydrogen bonding between water molecules, water has:

  1. the behaviour of expanding when it freezes

  2. an unusually high melting and boiling point

  3. high surface tension

• ice is less dense than water at 0°C

  • the presence of two hydrogen atoms and two lone electron pairs in each water molecule results in a regular three-dimensional tetrahedral structure in ice

  • the arrangement of water molecules in ice creates a very open structure where the molecules are further apart than they are in liquid water

• liquid water has a higher density than ice

  • when ice melts, the regular lattice breaks up and the water molecules can then pack more closely

melting and boiling points → simple molecules

• melting and boiling only involve overcoming the intermolecular forces of attraction

  • as intermolecular forces of attraction are relatively weak, only a small amount of heat energy is required ⇒ low melting and boiling points (<200°C)

answering format for bp/mp questions

1. state the type of structure and bonding

2. state the intermolecular forces of attractions present

3. compare the relative strength of the intermolecular forces of attraction

4. compare the amount of energy required to overcome these interactions

different question types for melting and boiling points → simple molecules

1. non-polar vs polar molecules with comparable size of electron cloud

   • more energy is required to overcome the stronger permanent dipole-permanent dipole attractions between polar molecules compared to the weaker instantaneous dipole-induced dipole attractions between non-polar molecules

2. molecules with different electron cloud size

   • as size of electron cloud increases, extent of polarisation of the electron cloud increases, leading to stronger and more extensive instantaneous dipole-induced dipole attractions

   • more energy is required to overcome the instantaneous dipole-induced dipole attractions and boiling point increases

3. straight vs branched chain isomers

   • as the molecules become more spherical, the surface area of contact between molecules decreases, and the instantaneous dipole-induced dipole attractions become less extensive

   • less energy is required to overcome these forces, thus the boiling point decreases

4. molecules with different bonds

   • boiling involves overcoming the stronger hydrogen bonds between molecules, which requires the highest amount of energy, followed by pd-pd and then id-id

5. dimerisation of carboxylic acids

   • exist as dimers because of the formation of intermolecular hydrogen bonding

   • boiling involves breaking both the instantaneous dipole-induced dipole interactions between the dimers and the hydrogen bonds within the dimers, which requires more energy to overcome, and hence has a higher boiling point

6. intermolecular (between different molecules) vs intramolecular hydrogen bonds (within the same molecule)

   • in 2-nitrophenol, the –OH and –NO2 groups are close to each other giving rise to intramolecular hydrogen bonding, reducing the extent of intermolecular hydrogen bonding between 2-nitrophenol molecules

   • extent of intermolecular hydrogen bond: 2-nitrophenol < 4-nitrophenol

   • as the energy required to overcome intermolecular hydrogen bond: 2-nitrophenol < 4-nitrophenol, boiling point of 2-nitrophenol < 4-nitrophenol

   • due to the difference in their boiling points, these two isomers can be separated by fractional distillation

non-conductors of electricity → simple molecules

• simple molecular compounds do not conduct electricity due to absence of delocalised electrons or free mobile ions to function as charge carriers

• however, covalent substances which can ionise in water can conduct electricity in the aqueous form

softness → simple molecules

due to the weak intermolecular forces between discrete molecules

solubility → simple molecules

concept:

• a solute is soluble if the solvent-solute interaction is stronger/similar in strength when compared to the solute-solute and solvent-solvent interactions

• energy released by the solvent-solute interaction is sufficient to overcome both the solvent-solvent and solute-solute interactions

• most substances with simple molecular structure do not dissolve in water

• those that dissolve in water do so by the following methods:

  1. form ions in water (e.g. HCl, H2SO4)

  2. form hydrogen bonds with water molecules

approach to explain solubility

1. identify each of the following interactions:

   • solute-solute interactions

   • solvent-solvent interactions

   • solute-solvent interaction

2. consider if the solute-solvent interaction is similar / stronger / weaker in strength than both the solute-solute and solvent-solvent interactions </aside>

answering format for solubility questions

• formation of [solute-solvent interactions] between [solute] and [solvent] releases sufficient/insufficient energy to overcome the [solute-solute interactions] between [solute] and [solvent-solvent interactions] between [solvent]

liquefaction of gas

the process of converting a gas into liquid state, where gas molecules have to come closer and will be held by intermolecular forces of attraction

• the ease of liquefaction of gases depends on the strength of intermolecular forces

  • the weaker the intermolecular forces of attraction, the easier for these attractions to be overcome and the substance to become gaseous → harder to liquefy

factors affecting liquefaction of gases

high pressure

• gases with stronger intermolecular forces are liquefied by applying pressure at room temperature, e.g. butane, ammonia

• high pressure causes the gas molecules to be closer together and experience significant intermolecular forces of attraction ⇒ the gas converts to liquid and liquefication takes place

low temperature

• most gases can be easily liquefied by lowering the temperature at standard pressure, e.g. oxygen, nitrogen

• at low temperatures, the gas molecules have less kinetic energy, the gas particles move more slowly and are near each other long enough for intermolecular forces of attraction to be more significant ⇒ the gas converts to liquid and liquefication takes place

high pressure and low temperature

• required for gases with very weak intermolecular forces e.g. helium