Topic 4 : Chemical Bonding & Structure Flashcards

1
Q

Metals and non-metals on the periodic table

A

As a general rule, metals are on the left of the Periodic Table and non-metals are on the right-hand side

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2
Q

Forming Ionic bonds

A
  1. Ionic bonds involve the transfer of electrons from a metallic element to a non-metallic element
  2. Transferring electrons usually leaves the metal and the non-metal with a full outer shell
  3. Metals lose electrons from their valence shell forming positively charged cations
  4. Non-metal atoms gain electrons forming negatively charged anions
  5. Cations and anions are oppositely charged and therefore attracted to each other
  6. Electrostatic attractions are formed between the oppositely charged ions to form ionic compounds
  7. This form of attraction is very strong and requires a lot of energy to overcome
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3
Q

Cation

A

Positive ion

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4
Q

Anion

A

Negative ion

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5
Q

Ionic Compounds (structure)

A
  1. The ions form a lattice structure which is an evenly distributed crystalline structure
  2. Ions in a lattice are arranged in a regular repeating pattern so that there are equal positive and negative charges
  3. Therefore the final lattice is overall electrically neutral
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6
Q

Examples of ionic bonding

A
  1. Sodium Chloride (salt)
  2. Magnesium Oxide
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7
Q

Ionic Bonding Physical Properties

A
  1. Strong
  2. Brittle
  3. High melting and boiling points
  4. Soluble in water
  5. Conduct electricity when molten or in solution
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8
Q

Ionic bonding - strength

A
  1. Ionic compounds are strong
  2. The strong electrostatic forces in ionic compounds keep the ions strongly together
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9
Q

Ionic bonding - brittle

A
  1. Ionic compounds are brittle as ionic crystals can split apart
  2. When a layer of ions is pushed, it will repel with the ions on top causing the material to break
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10
Q

Ionic bonding - melting + boiling points

A
  1. Ionic compounds have high melting and boiling points
  2. The strong electrostatic forces between the ions in the lattice act in all directions and keep them strongly together
  3. Melting and boiling points increase with charge density of the ions due to the greater electrostatic attraction of charges
  4. e.g. Mg2+O2- has a higher melting point than Na+Cl-
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11
Q

Ionic bonding - solubility

A
  1. Ionic compounds are soluble in water as they can form ion - dipole bonds
  2. Basically, water has a positive and negative end so ionic ions attract and dissolve
  3. Water has a positive and negative end because of the oxygen and hydrogen
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12
Q

Ionic bonding - electricity

A
  1. Ionic compounds only conduct electricity when molten or in solution
  2. When molten or in solution, the ions can freely move around and conduct electricity
  3. In the solid state they’re in a fixed position and unable to move around
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13
Q

Metal ions

A
  1. All metals form positive ions
  2. There are some non-metal positive ions such as ammonium, NH4+, and hydrogen, H+
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14
Q

Transition metals charges

A
  1. The charge on the ions of the transition elements can vary which is why Roman numerals are often used to indicate their charge
  2. Roman numerals are used in some compounds formed from transition elements to show the charge (or oxidation state) of metal ions
  3. Eg. in copper (II) oxide, the copper ion has a charge of 2+ whereas in copper (I) nitrate, the copper has a charge of 1+
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15
Q

Non-metal ions

A
  1. The non-metals in group 15 to 17 have a negative charge and have the suffix ‘ide’
  2. Eg. nitride, chloride, bromide, iodide
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16
Q

Compound negative ions

A
  1. Also known as polyatomic ions
  2. negative ions made up of more than one type of atom
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17
Q

7 polyatomic ions

A
  1. Ammonium : (NH4)+
  2. Hydroxide : (OH)-
  3. Nitrate : (NO3)-
  4. Sulfate : (SO4)2-
  5. Carbonate : (CO3)2-
  6. Hydrogen carbonate : (HCO3)-
  7. Phosphate : (PO4)3-
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18
Q

Covalent Bonds

A
  1. Covalent bonding occurs between two non-metals
  2. A covalent bond involves the electrostatic attraction between nuclei of two atoms and the electrons of their outer shells
  3. No electrons are transferred but only shared in this type of bonding
  4. When a covalent bond is formed, two atomic orbitals overlap and a molecular orbital is formed
  5. In a normal covalent bond, each atom provides one of the electrons in the bond. A covalent bond is represented by a short straight line between the two atoms, H-H
  6. Covalent bonds should not be regarded as shared electron pairs in a fixed position; the electrons are in a state of constant motion and are best regarded as charge clouds
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19
Q

Purpose of a covalent bond

A
  1. Non-metals are able to share pairs of electrons to form different types of covalent bonds
  2. Sharing electrons in the covalent bond allows each of the 2 atoms to achieve an electron configuration similar to a noble gas
  3. This makes each atom more stable
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20
Q

Octet rule

A

The octet rule refers to the tendency of atoms to prefer to have eight electrons in the valence shell.

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21
Q

Breaking the octet rule

A
  1. In some instances, the central atom of a covalently bonded molecule can accommodate more or less than 8 electrons in its outer shell
  2. Being able to accommodate more than 8 electrons in the outer shell is known as ‘expanding the octet rule’
  3. Accommodating less than 8 electrons in the outer shell means than the central atom is ‘electron deficient’
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22
Q

How to predict between covalent and ionic bond character

A
  1. The differences in Pauling electronegativity values can be used to predict whether a bond is covalent or ionic in character
  2. A difference of less than around 1.0 in electronegativity values will be associated with covalent bonds, although between 1.0 and 2.0 can be considered polar covalent
  3. A difference of more than 2.0 will be considered an ionic bond
  4. All bonds have ionic or covalent character but some have less than others
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23
Q

Diatomic molecules (electronegativity difference)

A
  1. In diatomic molecules the electron density is shared equally between the two atoms
  2. Eg. H2, O2 and Cl2
  3. Both atoms will have the same electronegativity value and have an equal attraction for the bonding pair of electrons leading to formation of a covalent bond
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24
Q

Coordinate bonds

A
  1. In simple covalent bonds the two atoms involved share electrons
  2. Some molecules have a lone pair of electrons that can be donated to form a bond with an electron-deficient atom
  3. An electron-deficient atom is an atom that has an unfilled outer orbital
  4. In other words, both of the “shared” electron come from the same atom
  5. This type of bonding is called dative covalent bonding or coordinate bond
  6. An example is an ammonium ion
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25
Q

Ammonium ion (coordinate bonds)

A
  1. The hydrogen ion, H+ is electron-deficient and has space for two electrons in its shell
  2. The nitrogen atom in ammonia has a lone pair of electrons which it can donate to the hydrogen ion to form a dative covalent bond
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26
Q

Multiple covalent bonds

A
  1. Non-metals are able to share more than one pair of electrons to form different types of covalent bonds
  2. Sharing electrons in the covalent bond allows each of the 2 atoms to achieve an electron configuration similar to a noble gas
  3. This makes each atom more stable
  4. There are single (2 shared electrons), double, and triple covalent bonds
  5. It is not possible to form a quadruple bond as the repulsion from having 8 electrons in the same region between the two nuclei is too great
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27
Q

Bond energy

A
  1. The bond energy (or enthalpy) is the energy required to break one mole of a particular covalent bond in the gaseous states
  2. Bond energy has units of kJ mol-1
  3. The larger the bond energy, the stronger the covalent bond is
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28
Q

Bond length

A
  1. The bond length is internuclear distance of two covalently bonded atoms
  2. It is the distance from the nucleus of one atom to another atom which forms the covalent bond
  3. The greater the forces of attraction between electrons and nuclei, the more the atoms are pulled closer to each other
  4. This decreases the bond length of a molecule and increases the strength of the covalent bond
  5. Triple bonds are the shortest and strongest covalent bonds due to the large electron density between the nuclei of the two atoms
  6. This increase the forces of attraction between the electrons and nuclei of the atoms
  7. As a result of this, the atoms are pulled closer together causing a shorter bond length
  8. The increased forces of attraction also means that the covalent bond is stronger
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29
Q

Bond polarity

A
  1. When two atoms in a covalent bond have the same electronegativity the covalent bond is non-polar
  2. When two atoms in a covalent bond have different electronegativities the covalent bond is polar and the electrons will be drawn towards the more electronegative atom
  3. The greater the difference in electronegativity the more polar the bond becomes
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30
Q

Result of a bond being polar

A
  1. The negative charge centre and positive charge centre do not coincide with each other
  2. This means that the electron distribution is asymmetric
  3. The less electronegative atom gets a partial charge of δ+ (delta positive)
  4. The more electronegative atom gets a partial charge of δ- (delta negative)
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31
Q

Dipole moment

A
  1. The dipole moment is a measure of how polar a bond is
  2. The direction of the dipole moment is shown by an arrow which points to the partially negatively charged end of the dipole
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32
Q

Lewis Structures

A

Lewis structures are simplified electron shell diagrams and show pairs of electrons around atoms.

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33
Q

How to draw a lewis structure

A
  1. Count the total number of valence
  2. Draw the skeletal structure to show how many atoms are linked to each other.
  3. Use a pair of crosses or dot/cross to put an electron pair in each bond between the atoms.
  4. Add more electron pairs to complete the octets around the atoms ( except H which has 2 electrons)
  5. If there are not enough electrons to complete the octets, form double/triple bonds.
  6. Check the total number of electrons in the finished structure is equal to the total number of valence electrons
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34
Q

Incomplete octets

A
  1. For elements below atomic number 20 the octet rule states that the atoms try to achieve 8 electrons in their valence shells, so they have the same electron configuration as a noble gas
  2. However, there are some elements that are exceptions to the octet rule, such a H, Li, Be, B and Al
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35
Q

Hydrogen octet rule

A
  1. H can achieve a stable arrangement by gaining an electron to become 1s2, the same structure as the noble gas helium
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36
Q

Lithium octet rule

A

Li loses an electron thus going from 1s2,2s1 to 1s2 to become a Li+ ion

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37
Q

Beryllium octet rule

A

Be from group 2, has two valence electrons and forms stable compounds with just four electrons in the valence shell

38
Q

Boron and Aluminium octet rule

A

B and Al in group 13 have 3 valence electrons and can form stable compounds with only 6 valence electrons

39
Q

Lewis structures with incomplete octets (examples need to know in IB)

A
  1. BeCl2
  2. BF3
40
Q

BeCl2 lewis structure

A
  1. Has a total of 16 valence electrons
  2. Beryllium will only have four electrons in its valence shell (2 pairs of shared electrons)
41
Q

BF3 lewis structure

A
  1. Has a total of 24 valence electrons
  2. Boron will only have 6 valence electrons (3 pairs of shared electrons)
42
Q

Delocalised electrons

A

Delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or one covalent bond

43
Q

Resonance structures

A
  1. Due to delocalised electrons, some structures/species don’t fit with a Lewis structure
  2. There may be more than 1 possible lewis structure
  3. When this occurs, we use resonance structures
  4. It describes two or more possible structures interchanging so rapidly (resonating) as to be indistinguishable.
  5. Dotted lines are used to show the position of the delocalised electrons
  6. The criteria for forming resonance hybrids structures is that molecules must have a double bond (pi bond) that is capable of migrating from one part of a molecule to another
44
Q

Resonance hybrid (examples needed in IB)

A
  1. nitrate (V) ion
  2. Carbonate ion : (CO3)2-
  3. Benzene : C6H6
  4. Ozone : O3
  5. Carboxylate ion : RCOO-
45
Q

Why molecules have different shapes

A
  1. When an atom forms a covalent bond with another atom, the electrons in the different bonds and the non-bonding electrons in the outer shell all behave as negatively charged clouds and repel each other
  2. In order to minimise this repulsion, all the outer shell electrons spread out as far apart in space as possible
  3. The regions of negative cloud charge are known as domains and can have one, two or three pairs electrons
46
Q

VSEPR theory

A
  1. valence shell electron pair repulsion theory
  2. This theory is used to predict molecular shapes and angles between bonds
47
Q

VSEPR theory rules

A
  1. All electron pairs and all lone pairs arrange themselves as far apart in space as is possible.
  2. Lone pairs repel more strongly than bonding pairs.
  3. Multiple bonds behave like single bonds
48
Q

Linear

A
  1. 2 atoms attached to a center atom
  2. 0 long pairs
  3. 180 bond angle
  4. Type: AB2 (A being the central atom and B being the atoms bonded to the central
  5. e.g. CO2
49
Q

Trigonal planar

A
  1. 3 atoms attached to the center atom
  2. 0 long pairs
  3. Bond angle : 120
  4. Type AB3L0 (L being lone pair of electrons)
  5. e.g. AlF3
50
Q

Tetrahedral

A
  1. 4 atoms attached to the centre atom
  2. 0 long pairs
  3. Bond angle : 109.5 (3D geometry)
  4. Type : AB4Lo
  5. e.g. CH4
51
Q

Trigonal Bipyramidal

A
  1. 5 atoms attached to the centre atom
  2. 0 long pairs
  3. Bond angle : Equatorial is 120 and axial is 90
  4. Type : AB5
  5. e.g. PF5
52
Q

Octahedral

A
  1. 6 atoms attached to centre atom
  2. 0 long pairs
  3. Type : AB6
53
Q

Trigonal Pyramidal

A
  1. 3 atoms attached to centre atom
  2. 1 long pair
  3. Bond angle : 107 (due to the pair of lone electrons, it’s smaller than 109.5 because lone pairs are pulled more closely to the central atoms so they exert a greater repulsive force than bonding pairs)
  4. Type : AB3L1
  5. e.g. NH3
54
Q

Bent

A
  1. 2 atoms attached to centre atom
  2. 2 long pairs (repel each other more than bonding pairs)
  3. Bond angle : 104.5
  4. Type : AB2L2
  5. e.g. H20
55
Q

Electron domain geometry/shape

A
  1. Includes the lone pair of electrons as well as the bonding pairs
56
Q

Molecular geometry

A
  1. does not include long pairs of electrons
57
Q

Assigning polarity to molecules

A
  1. There is a difference between bond polarity and molecular polarity
  2. To determine whether a molecule is polar, the following things have to be taken into consideration: the polarity of each bond and how the bonds are arranged in a molecule
  3. Some molecules have polar bonds but are overall not polar because the polar bonds in the molecule are arranged in such way that the individual dipole moments cancel each other out
  4. HINT: count the number of molecules that actually belong to that atom
58
Q

Covalent Lattices

A
  1. Covalent bonds are bonds between nonmetals in which electrons are shared between the atoms
  2. In some cases, it is not possible to satisfy the bonding capacity of a substance in the form of a molecule; the bonds between atoms continue indefinitely, and a large lattice is formed.
  3. Such substances are called giant covalent substances, and the most important examples are C and SiO2
59
Q

Allotrope

A
  1. An allotrope is a different form of an element
  2. Same chemical properties but different physical properties (different structures)
  3. Bonded through giant covalent bonding structure held together by strong covalent bonds
  4. e.g. diamond, graphite, and buckminsterfullerene - carbon allotropes
60
Q

Diamond bonding

A
  1. Diamond is a giant lattice of carbon atoms
  2. Each carbon is covalently bonded to four others in a tetrahedral arrangement with a bond angle of 109.5
  3. The result is a giant lattice with strong bonds in all directions
  4. Due to the many covalent bonds, Diamond is the hardest substance known. For this reason it is used in drills and glass-cutting tools
61
Q

Graphite bonding

A
  1. In graphite, each carbon atom is bonded to three others in a layered structure
  2. The layers are made of hexagons with a bond angle of 120
  3. The spare electron is delocalised and occupies the space in between the layers (also allows for graphite to conduct electricity)
  4. All atoms in the same layer are held together by strong covalent bonds, and the different layers are held together by weak intermolecular forces
62
Q

Buckminsterfullerene

A
  1. Buckminsterfullerene is one type of fullerene
  2. It contains 60 carbon atoms, each of which is bonded to three others by single covalent bonds
  3. The fourth electron is delocalised so the electrons can migrate throughout the structure making the buckyball a semi-conductor
  4. It has exactly the same shape as a soccer ball, hence the nickname the football molecule
63
Q

Graphene

A
  1. Some substances contain an infinite lattice of covalently bonded atoms in two dimensions only to form layers. Graphene is an example
  2. Graphene is made of a single layer of carbon atoms that are bonded together in a repeating pattern of hexagons
  3. Graphene is one million times thinner than paper; so thin that it is actually considered two dimensional
64
Q

Silicon(IV) oxide

A
  1. Silicon(IV) oxide is also known as silicon dioxide
  2. Silicon(IV) oxide adopts the same structure as diamond - a giant structure made of tetrahedral units all bonded by strong covalent bonds. This makes it have similar properties with diamond
  3. Each silicon is shared by four oxygens and each oxygen is shared by two silicons (contains silicon and oxygen atoms instead of carbon)
  4. This gives an empirical formula of SiO2
65
Q

Properties of giant covalent bonds

A
  1. High melting and boiling points
  2. Can be hard or soft
  3. More are insoluble in water
  4. Most don’t conduct electricity but some do (graphite)
66
Q

Examples of giant covalent bonds

A
  1. Diamond
  2. Graphite
  3. Buckminsterfullerene
  4. Graphene
  5. Silicon Dioxide
67
Q

Giant covalent bonds - melting and boiling points

A
  1. Giant covalent lattices have very high melting and boiling points
  2. These compounds have a large number of covalent bonds linking the whole structure
  3. A lot of energy is required to break the lattice
68
Q

Giant covalent bonds - hard or soft

A
  1. The compounds can be hard or soft
  2. Graphite is soft as the forces between the carbon layers are weak
  3. Diamond and silicon(IV) oxide are hard as it is difficult to break their 3D network of strong covalent bonds
  4. Graphene is strong, flexible and transparent which it makes it potentially a very useful material
69
Q

Giant covalent bonds - electricity

A
  1. Most compounds do not conduct electricity however some do
  2. Graphite has delocalised electrons between the carbon layers which can move along the layers when a voltage is applied
  3. Graphene is an excellent conductors of electricity due to the delocalised electrons
  4. Buckminsterfullerene is a semi-conductor
  5. Diamond and silicon(IV) oxide do not conduct electricity as all four outer electrons on every carbon atom is involved in a covalent bond so there are no free electrons available
70
Q

Intermolecular forces

A
  1. There are no covalent bonds between molecules in molecular covalent compounds. There are, however, forces of attraction between these molecules, and it is these which must be overcome when the substance is melted and boiled
  2. These forces are known as intermolecular forces
71
Q

Types of intermolecular forces

A
  1. London(dispersion) forces
  2. Permanent Dipole-dipole attraction
  3. Hydrogen bonding
72
Q

London dispersion forces

A
  1. The electrons in atoms are not static; they are in a state of constant motion
  2. It is therefore likely that at any given time the distribution of electrons will not be exactly symmetrical - there is likely to be a slight surplus of electrons on one side of the atoms
  3. The side with a surplus of electrons is known as a temporary dipole (It lasts for a very short time as the electrons are constantly moving and are constantly appearing and disappearing)
  4. Due to the temporary dipole, the adjacent atom will be repelled and attracted to the positive part of the atom causing a temporary induced dipole
  5. This resulting attraction is known as london dispersion forces
73
Q

London dispersion forces strength

A
  1. London (dispersion) forces are present between all atoms and molecules, although they can be very weak
  2. They are the reason all compounds can be liquefied and solidified
  3. London (dispersion) forces tend to have strengths between 1 kJmol-1 and 50 kJmol-1.
  4. The strength of the London( dispersion) forces in between molecules depends on two factors: number of electrons and surface area of the molecules
74
Q

Number of electrons effect on london dispersion forces

A
  1. The greater the number of electrons in a molecule, the greater the likelihood of a distortion and thus the greater the frequency and magnitude of the temporary dipoles
  2. The dispersion forces between the molecules are stronger and the melting and boiling points are larger
75
Q

Surface area effect on london dispersion forces

A
  1. The larger the surface area of a molecule, the more contact it will have with adjacent molecules
  2. The greater its ability to induce a dipole in an adjacent molecule, the greater the London (dispersion) forces and the higher the melting and boiling points
76
Q

Permanent dipole-dipole attraction

A
  1. Temporary dipoles exist in all molecules, but in some molecules there is also a permanent dipole
  2. In addition to the London (dispersion) forces caused by temporary dipoles, molecules with permanent dipoles are also attracted to each other by permanent dipole-dipole bonding
  3. This is an attraction between a permanent dipole on one molecule and a permanent dipole on another.
  4. Dipole-dipole bonding usually results in the boiling points of the compounds being slightly higher than expected from temporary dipoles alone as it slightly increases the strength of the intermolecular attractions
77
Q

Permanent dipole-dipole vs london dispersion forces

A
  1. For small molecules with the same number of electrons, dipole-dipole attractions are stronger than dispersion forces
  2. e.g. butane and propanone have the same number of electrons but butane is non-polar and propanone is polar. Therefore more energy is required to break the intermolecular forces between propanone and butane so propanone has a higher boiling point than butane
78
Q

Hydrogen bonding

A
  1. Hydrogen bonding is a special type of permanent dipole – permanent dipole bonding and is the strongest type of intermolecular force
  2. When hydrogen is covalently bonded to an electronegative atom, such as O or N, the bond becomes very highly polarised
  3. The H becomes so δ+ (delta positive) charged that it can form a bond with the lone pair of an O or N atom in another molecule
79
Q

Requirements for hydrogen bonding to take place

A
  1. A species which has an O or N or F (very electronegative) atom with an available lone pair of electrons
  2. A hydrogen attached to the O, N or F
80
Q

Properties of covalent compounds (solubility)

A
  1. The general principle is that ‘like dissolves like’ so non-polar substances mostly dissolve in non-polar solvents, like hydrocarbons and they form dispersion forces between the solvent and the solute
  2. Polar covalent substances generally dissolve in polar solvents as a result of dipole-dipole interactions or the formation of hydrogen bonds between the solute and the solvent
  3. Polar covalent substances are unable to dissolve well in non-polar solvents as their dipole-ipole attractions are unable to interact well with the solvent
  4. Giant covalent substances generally don’t dissolve in any solvents as the energy needed to overcome the strong covalent bonds in the lattice structures is too great
81
Q

Properties of covalent compounds (conductivity)

A
  1. As covalent substances do not contain any freely moving charged particles they are unable to conduct electricity in either the solid or liquid state
  2. However, under certain conditions some polar covalent molecules can ionise and will conduct electricity
82
Q

Metallic bonding

A
  1. Metal atoms are tightly packed together in lattice structures
  2. When the metal atoms are in lattice structures, they lose their valence electrons which freely move around
  3. The free-moving electrons are called ‘delocalised’ electrons and they are not bound to their atom
  4. When the electrons are delocalised, the metal atoms become positively charged
  5. The positive charges repel each other and keep the neatly arranged lattice in place
  6. There are very strong electrostatic forces between the positive metal centres and the ‘sea’ of delocalised electrons
83
Q

Properties of metals

A
  1. Malleable (able to be hammered or pressed permanently out of shape without breaking or cracking.)
  2. Ductile (can be drawn into a wire)
  3. Strong and hard
  4. High melting and boiling point.
  5. Can conduct electricity
84
Q

Metals - malleable and ductile

A
  1. Metallic compounds are malleable and ductile
  2. When a force is applied, the metal layers can slide
  3. The attractive forces between the metal ions and electrons act in all directions (bonding is non-directional). The particles will not repel each other as there are delocalised electrons
  4. So when the layers slide, the metallic bonds are re-formed
  5. The lattice is not broken and has changed shape
85
Q

Metals - strength

A

Metallic compounds are strong and hard due to the strong attractive forces between the metal ions and delocalised electrons

86
Q

Metals - boiling and melting point

A

As metals are giant lattice structures, the number of electrostatic forces to be broken is extremely large, and so metals have high melting and boiling points.

87
Q

Metals - conductivity

A
  1. Metals can conduct electricity when in the solid or liquid state
  2. As both in the solid and liquid state there are delocalised electrons which can freely move around and conduct electricity
  3. When a potential difference is applied to the metallic lattice, the delocalised electrons repel away from the negative terminal and move towards the positive terminal cause an electrical current
88
Q

How to increase electrostatic attraction in metals

A
  1. Increasing the number of delocalised electrons per metal atom
  2. Increasing the positive charges on the metal centres in the lattice
  3. Decreasing the size of the metal ions
89
Q

Alloys

A
  1. Alloys are mixtures of metals, where the metals are mixed together physically but are not chemically combined
  2. They can also be made from metals mixed with nonmetals such as carbon
  3. Ions of the different metals are spread throughout the lattice and are bound together by the delocalised electrons
  4. It is possible to form alloys because of the non-directional nature of the metallic bonds
90
Q

Pure metals

A

All atoms in a pure metal are exactly the same as they are elements (uniform shape)

91
Q

Why alloys are stronger than metals

A
  1. Alloys contain atoms of different sizes, which distorts the regular arrangements of cations
  2. This makes it more difficult for the layers to slide over each other, so they are usually much harder than the pure metal