Table of Contents
CHEM10003 - Chemistry 1
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Introduction to organic chemistry
Organic chemistry is the study of carbon containing compounds. This includes, but is not limited to hydrocarbons and is generally focused on compounds produced by living organisms, but includes synthetics like plastics. Important sources are still living beings such as plants and animals but also microorganisms such as bacteria. Crude oil and coal tar also serve as important sources of organic compounds and are often used in synthesis.
Carbon's unique properties
Carbon is able to form single, double and triple bonds with itself in varying lengths and strengths, allowing it to form a multitude of compounds. Carbon's ability to bond allows for the formation of various geometries.
Alkanes
Alkanes are the simplest hydrocarbons, consisting of single bonds between the carbon atoms. General formula of \(\ch{C_nH_{2n+2}}\). The longer a chain, the higher its boiling point.
Bonding and shape
Unpaired valence electrons are used for bonding. Molecular orbital theory determines shape. Covalent bonds are formed from the overlap of singly occupied orbitals on each atom. Sigma (\(\sigma\)) bonds are formed by direct spacial overlap. Electrons in different energy levels can hybridise to form a merged energy level presenting more unpaired electrons than in a ground state. These hybridised orbitals determine the overall geometry of the compounds. Ethane (\(\ce{CH3-CH3}\)) forms a carbon-carbon \(sp^3\) bond, which is rotatable. Below are \(s\), \(p\) and \(sp^3\) orbitals: \[\orbital{s}\orbital{p}\orbital{sp3}\]
Isomerism
Structural
Alkanes with greater than four carbons show structural isomerism. This is when the chemical formula is the same but the atoms are bonded together in a different sequence. An example of this is butane and isobutane. \[\chemfig{H3C-[:0]C(-[:90]H)(-[:270]H)-[:0]C(-[:90]H)(-[:270]H)-[:0]CH_3}\] \[\chemfig{H3C-[:0]C(-[:90]H)(-[:270]CH_3)-[:0]CH_3}\] The number of structural isomers increases quickly with the number of carbons.
Conformational
Isomers which can be converted by a rotation about single bonds. These only occur in alkane derivatives. \[\chemfig{C(<:[:0]H)(<[:90]H)(-[:180]H)(-[:270]H)}\] \[\newman{H,H,H,H,H,H}\] The second diagram is a Newman projection for ethane showing a top down view where the end hydrogens are in and out of the plane. We can rotate the rear carbon to go from the staggered conformation to the eclipsed conformation. \[\newman(-30){H,H,H,H,H,H}\] These two confirmations have different energy levels, with the eclipsed having greater energy than the staggered. This energy difference is due to non-bonded repulsion, where the like charges of the atoms repel each other. The magnitude depends on the size of the functional group and is inversely proportional to distance.
In a molecule like butane, the different conformations can be significant. \[\newman{\ch{CH3},H,H,\ch{CH3},H,H}\hspace{1cm}\newman{\ch{CH3},H,H,H,\ch{CH3},H}\] The first is the anti-confirmation and the second is the gauche-conformation. The anti-confirmation is the lowest energy.
Strain caused by bonds is torsional, strain from groups is steric.
Stereo
Atoms connected in the same order but having a different arrangement in 3d space. This has occurs when a carbon (called the chiral carbon) is bonded to 3 different groups. The chiral carbon cannot be superimposed onto its mirror image. The different versions of the molecule are known as enantiomers. These molecules lack a plane of symmetry. They share similar physical properties and some chemical properties, however for interactions which are shape oriented they cannot be substituted.
They also rotate polarised light in different directions. One enantiomer will rotate light clockwise (dextrorotation, +, S (sinister)), while the other will rotate the same amount anticlockwise (levorotation, -, R (rectus)). \(1:1\) mixtures (racemic mixtures) do not rotate. Can identify R or S from a molecular form by orienting the lowest priority group (by atomic number) perpendicular to the plane and the highest priority group at the 12 position. We then identify whether the ordering of groups is clockwise (R) or anticlockwise (S). We can also use the thumb rule to identify enantiomers. If we align our thumb with the lowest priority, if our right hand curls in the direction of descending priority, we have a R enantiomer, if left, S.
Diastereomers are stereoisomers which superimpose onto their mirror image, such as conformational and geometric isomers.
Resolution of racemic amino acids
A racemic mixture is equal parts R and L enantiomers. If we were to add a pure carboxylic acid enantiomer, we create two salts for each form. These salts are diastereomers, which have different properties unlike the enantiomers. One property is differing solubilities, allowing fractional crystallisation to separate them. After this separation, we can reform the original chemical.
Diastereomers
Molecules with multiple asymmetric centres allow for multiple configurations. Each centre has two possible configurations. Each molecule has a maximum of \(2^n\) stereoisomers. Diastereomers are when at least one asymmetric centre has the same configuration and at least one has the opposite. If all centres have opposite configurations, they are enantiomers.
Meso compounds
Diastereomers with a plane of symmetry making them achiral. The trans-isomers form enantiomers while the cis-isomers have a plane of symmetry, making them meso compounds.
Geometrical
Exist in substituted cycloalkanes where substituents are attached to two different carbons on the same ring. \[\chemfig{[:90]*3((-CH3)--(-CH3)-)}\] As each of these carbons have a tetrahedral geometry, there exist two versions of the molecule. One where both methyls are on the same side (cis) and one where they are on opposite sides (trans) of the ring. Conversion between these two states requires the breaking of bonds, so we can assume they do not inter-convert. \[\chemfig{[:90]*3((<CH3)--(<CH3)-)}\hspace{1cm}\chemfig{[:90]*3((<CH3)--(<:CH3)-)}\]
Nomenclature
IUPAC systematic nomenclature consists of a parent, derived from the longest chain in the molecule, a suffix for the family which it belongs, and a prefix for the substituents (name and location). Alkanes have the suffix “-ane”
Here is a table of the parent name's in relation to chain length:
| Number of carbon | Parent |
|---|---|
| 1 | meth- |
| 2 | eth- |
| 3 | prop- |
| 4 | but- |
| 5 | pent- |
| 6 | hex- |
| 7 | hept- |
| 8 | oct- |
| 9 | non- |
| 10 | dec- |
Alkyl substituents use the “-yl” suffix. \(\ch{-C2H5}\) is ethyl. The substituents is numbered from the end which it is closest, but where multiple substituents are present, the same end must be used so that the smallest numbers are used and the groups are ordered according to alphabetical order. For example, \(\ch{CH3CH(CH3)CH(C2H5)CH2CH2CH3}\) is 3-ethyl-2-methylhexane.
Haloalkanes are similar to alkanes, except where a halogen is replacing a hydrogen. The halogens are treated as substituents. The nomenclature is the same as alkanes. The prefixes are “fluro-” for \(\ch{F}\), “chloro-” for \(\ch{Cl}\), “bromo-” for \(\ch{Br}\), “iodo-” for \(\ch{I}\). Where multiple halogens are present, di-, tri-, penta-, etc. are used.
Drawing structures
Kekule (line bond)
Used only when showing all bonds and atoms is needed. Only used when showing Lewis structures. \[\chemfig{C(-[:90]H)(-[:180]H)(-[:270]H)-[:0]C(-[:90]H)(-[:270,2]C(-[:180]H)(-[:270]H)(-[:0]H))-[:0]C(-[:90]H)(-[:270]H)-[:0]C(-[:90]H)(-[:270]H)(-[:0]H)}\]
Condensed
\(\ch{C-H}\) and \(\ch{C-C}\) bonds are not shown. \[\chemfig{CH_{3}CHCH_{2}CH_{3}(-[:270,0.5,3]CH_{3})}\] \[\ch{CH3CH(CH3)CH2CH3}\]
Skeletal
\(\ch{C}\) and \(\ch{H}\) bonded to \(\ch{C}\) are not shown but \(\ch{H}\) bonded to other atoms are shown and all other atoms are shown. \[\chemfig{-[:30](-[:90])-[:-30]-[:30]}\]
Cycloalkanes
Carbon chains forming rings or cycles. Have a general form of \(\ch{C_nH_{2n}}\) and for naming add “cyclo-” as a prefix to the parent alkane name. Below is a skeletal structure of cyclohexane. \[\chemfig{*6(------)}\] For naming we start with the lowest number is assigned alphabetically and continued with alphabetical priority \[\chemfig{[:18]*5(--(-Cl)--(-Br)-)}\] This compound is 1-bromo-3-chlorocyclopentane. Most rings have some strain, which causes a large amount of energy to be stored in the ring. This strain comes from angle strain, torsional strain and transannular strain.
As an example, cyclopropane has unfavourable bond angles of \(60^\circ\) (angle strain) and unfavourable eclipsing interactions (torsional strain) as all the carbons are eclipsing each other. This results in a very high energy. Cyclobutane twists itself into the z-axis, in order to reduce torsional strain, but this increases angle strain. Cyclopentane forces itself even more into the z-axis, greatly reducing the eclipsing and overall energy stored. Cyclohexane have its carbons near the optimal \(109.5^\circ\) for a tetrahedral geometry in a staggered arrangement. This is possible in a “chair” conformation and causes the overall molecule to have very little stored energy.
Cyclohexane
\[\chemfig{?-[:-50](-[:270]A)(-[:170]E)-[:10]-[:-10]-[:130](-[:90]A)(-[:-10]E)-[:190]?}\] The chair conformation of cyclohexane results in two types of hydrogen environments: axial (A) and equatorial (E). These conformations can change with a ring flip, where the hydrogens which were axial become equitorial and vice-versa. The hydrogens stay on the same face of the molecule before and after the flip; a hydrogen on the bottom stays on the bottom. If we were to introduce a methyl group in place of a hydrogen, we would find it in an equitorial position most of the time. This position reduces the transannular strain on the molecule, due to decreased steric interactions and less interference with the other hydrogens. This strain is similar to that found in a gauche conformation.
Alkenes
General formula of \(\ch{C_nH_{2n}}\). Contain a single \(\ch{C=C}\) per molecule. Has a flat, trigonal planar, geometry. Has 2 p and 1 s orbitals which hybridise to form 3 \(sp^2\) orbitals in the plane, with the remaining p orbital out of the plane. A bond consists of a \(\sigma\) bond in the plane, and a \(\pi\) bond with the \(p_z\) orbital. As a result of this \(\pi\) bond, there is no rotation.
The nomenclature is similar to alkanes, but with the suffix “-ene”. The location of the double bond is put in the prefix of the molecule name.
The lack of rotation gives rise to geometric isomerism. We can distinguish isomers according to priority. When highest priority groups are on opposite sides, we have an E isomer, on opposite, a Z.
Cycloalkenes also exist as unsaturated rings. They have the general formula \(\ch{C_nH_{2n-2}}\) and are named by adding “cyclo-” as a prefix to the parent group. The double bonded carbons are given the highest priority and the substituents are then ordered for lowest number and alphabetical priority.
Polyenes
Compounds containing two or more \(\ch{C=C}\) double bonds. These are named similarly to alkenes but a prefix denoting number is given to the suffix. e.g. 1,3-butdiene.
Polyenes can have 3 different relationships:
- Cumulated (adjacent double bonds)
- Conjugated (alternating double and single bonds)
- Non or unconjugated (2 or more single bonds between double bonds)
Conjugated are significantly more stable than their non-conjugated counterparts. This is because a partial \(\pi\) bond can form between adjacent double bonds, allowing for delocalised electrons.
Reactions
Addition reactions, particularly with halogens can occur at a \(\ch{C=C}\) bond. This can be used as a diagnostic test for a double bond.
Benzene
The observed bond lengths were equal across all carbons and an addition reaction didn't take place with a halogen, instead a substitution. Benzene was much also more stable than expected. This lead to the belief that bromine didn't behave like other cyclopolyenes. The delocalised electrons in the \(\pi\) bond formed a complete ring, allowing for great stability in resonance. Benzene forms a planar, regular hexagon with bond lengths in between those of \(\ch{C-C}\) and \(\ch{C=C}\). The resonance can be thought to alternate which carbons have a double bond, causing each carbon bond to be halfway between a single and double bond. Benzene and its derivatives are classified as aromatic compounds.
Benzene structures with a single substitution have unique structures. Disubstituted benzenes can have 3 different isomers, ortho, meta and para. \[\chemfig{[:-90]X-*6(=(-Y)-=-=-)}\hspace{1cm}\chemfig{[:-90]X-*6(=-(-Y)=-=-)}\hspace{1cm}\chemfig{[:-90]X-*6(=-=(-Y)-=-)}\]
Aromatic structures must by cyclic, conjugated, planar, have an even bond length and satisfy Huckel's rule for the number of p electrons (\(4n+2\)). An aromatic compound must also produce NMR chemical shifts.
Alkynes
Forms linear geometries. Shorter and stronger bonds than double bonds. Has \(2sp\) orbitals and 2 p orbitals. The sp and p are perpendicular to each other. The sp are opposite to each other. Named with the suffix '-yne'. There are terminal alkynes, where the alkyne is on the end of the chain, and internal where it is in the chain.
Functional groups
Functional groups define the compound class and control chemical reactivity. An example of this are groups with multiple carbon-carbon bonds, such as alkenes and alkynes. Another group are those which have a carbon singly bonded to an electronegative atom. These include:
- Alkyl Halides: carbon bonded to a halogen
- Alcohols: carbon bonded to a \(\ch{OH}\)
- Ethers: carbons joined with a bond to an oxygen
- Amines: carbon bonded to a nitrogen
- Thiols: carbon bonded to a \(\ch{SH}\)
A third category are the carbonyl group, containing \(\ch{C=O}\) These include:
- Aldehyde: \(\ch{-C(=O)H}\)
- Ketone: \(\ch{-C(=O)R}\)
- Carboxylic Acid: \(\ch{-C(=O)OH}\)
- Amide: \(\ch{C(=O)NRR'}\)
- Acid Chloride: \(\ch{-C(=O)Cl}\)
- Ester: \(\ch{-C(=O)OR}\)
Alkyl Halides
A halogen attached to a saturated \(sp^3\) carbon. Classified as primary \((1^\circ)\), secondary \((2^\circ)\) or tertiary \((3^\circ)\) based on the number of carbon substituents attached to the same carbon as the halogen. When naming, the halogen is always a substituent. The degree is given as an addition at the end of the name.
Alcohols
A hydroxyl attached to a saturated \(sp^3\) carbon. Classified as primary, secondary or tertiary, similarly to the alkyl halides. The hydroxyl must be on the parent chain. The suffix for the chain is “-ol”.
Ethers
Two organic residues attached to an oxygen. Named by naming the residues and adding the suffix “ether”.
Amines
Organic derivatives of ammonia (\(\ch{NH3}\)). Classified as primary, secondary or tertiary based on the number of carbon substituents attached to the same nitrogen atom. Named with the suffix “amine”.
Thiols
A thiol (\(\ch{SH}\)) attached to a saturated \(sp^3\) carbon. Classified as primary, secondary or tertiary based on the number of carbon substituent attached to the same carbon as the thiol. Named with the suffix “-thiol”.
Carbonyl
The carbon is \(sp^2\) hybridised, forming a trigonal planar geometry. This is similar to alkenes, but have different reactivity. The electronegativitiy of the oxygen causes a polar bond, distorting the bond and creating a partial negative charge at the oxygen and a partial positive at the carbon.
Aldehydes and Ketones
Aldehydes contain a carbonyl group at the end of the molecule. The parent chain must contain the carbonyl, and is named with the suffix “-al”. Ketones have the carbonyl group with two carbon substituents attached to the carbonyl carbon. They must be on the parent chain and are named with the suffix “-one”.
Carboxylic acids
Contain a carbonyl group with one carbonyl substituent and one hydroxyl attached to the carbonyl carbon. Open chain carboxylic acids must contain the acid in the parent chain and are named with the suffix “-oic acid”. Cyclic carboxylic acids are carboxylic acids attached to a cycloalkane. These are named with the suffix “carboxylic acid”.
Esters
Same as a carboxylic acid except replacing the hydrogen on the hydroxyl with an R group. Named with the suffix “-ate”.
Amides
Same as the carboxylic acids but with a nitrogen instead of the hydroxyl. Named with the suffix “-amide”.
Acid chloride
Same as the carboxylic acid but with a chlorine instead of the hydroxyl. Named with the suffix “-oyl chloride”.
Anhydride
Same as the carboxylic acid but with the hydroxide hydrogen replaced by another carbonyl. Named with the suffix “-anhydride”.
Priority
Where multiple functional groups are present, the following priority is followed:
- Carboxylic acids
- Esters
- Acid Chlorides
- Amides
- Aldehydes
- Ketones
- Alcohols
- Amines
- Alkynes
- Alkenes
- Halogens
- Alkanes
Spectroscopy
Qualitative Organic Analysis are a set of techniques used to determine the structure of an unknown compound. These include:
- Combustion Analysis: Empirical Formula
- Mass Spectrometry (MS): Molecular weight and molecular formula
- Ultraviolet Spectroscopy (UV):
- Infrared Spectroscopy (IR): Functional Groups present
- Nuclear Magnetic Resonance Spectroscopy (NMR): C/H framework
- X-Ray Diffractometry (X-Ray):
Combustion analysis
Used to determine the empirical formula by combusting under conditions where the resulting combustion products can be quantitatively analysed. From the combustion products, we can find a molar ratio between carbon, hydrogen and oxygen which gives the molecular formula.
Mass spectrometry
Used to determine the molecular mass of an organic compound based on their mass to charge ratio (m/z). Charged ions of the molecule are accelerated and deflected to be detected at various positions. The amount of deflection is dependent on the mass and charge of the ion. The molecule can fragment once ionised, however the fragments are unique to each molecule.
We can also use the double bond equivalent calculation to help to determine more about the molecule's structure. \[DBE=\frac{1}{2}(n_4+n_2-n_1+2)\] Here the subscript denotes the number of bonds that atom can make (carbon makes 4, hydrogen makes 1). The final number gives us the number of double bonds or rings present.
Spectroscopy
Atoms and molecules can interact with electromagnetic radiation in a variety of ways. They can absorb or emit EMR. The absorption or emission spectra can divulge information about the structure of the atom or molecule.
IR Spectroscopy
Absorption of IR radiation causes chemical bonds to vibrate. The bonds can bend or stretch, they can do this symmetrically or asymmetrically. This can distinguish between functional groups as different groups respond to different wavelengths (energies). The wavelength is given by a wavenumber in the IR region (400-4000 \(cm^{-1}\)).
NMR
Used to determine a compound's unique structure. Identifies the carbon-hydrogen framework of an organic compound. Works by aligning the nuclear spin with an external magnetic field, and determining the energy given off by their oscillation between energy states. The amount of energy lost in a transition gives information about the molecular environment. \(\ch{^{13}C}\) and \(\ch{^1H}\) are commonly used in NMR, \(\ch{^{12}C}\) is not NMR active despite being the most common isotope. Their relative strength is given compared to a reference of tetramethylsilane, located at 0 ppm. The location of the NMR signal is known as the chemical shift, in ppm.
Hydrogen NMR provides information on hydrogens on \(\ch{C_H}\) framework. The peaks can give information on adjacent atoms. Resonance coupling between hydrogens gives multiple signals for a hydrogen depending on adjacent hydrogens. Resonance coupling uses the \(N+1\) rule, the number of lines observed in a signal is \(N+1\). where N is the number of hydrogens on nearby atoms. A lack of shielding from electrons causes a downshift on the spectra, like for carbon NMR. Symmetry in a molecule causes the spectra to overlap for the same environment. The number of hydrogens on the adjacent carbon causes singlet, doublet, triplet or quartet splitting. The area under the peak indicated the number of hydrogens present in that environment.
Physical chemistry
Gases
Definitions
The fundamental states of matter are:
- Solid: Fixed volume and shape
- Liquid: Takes the shape of its container but has a fixed volume at a given temperature and pressure
- Gas: Takes shape of its container and expands to completely fill its container
Gasses are quantitatively described by volume and pressure. There is SATP (standard ambient temperature and pressure), which is a standard of 298.15 K (25 C) and 1 bar (100 kPa).
Ideal gas laws
We can also consider that the number of gas particles can affect the overall gas. There is Avogadro's Law, which relates the volume and amount of gas particles at constant temperature and pressure: \[V\propto n\] This relationship holds regardless of the gas examined. At SATP, 1 mole of a gas has a volume of 24.8 L. \(n\) denotes the number of particles in mole, where 1 mole is \(6.02*10^{23}\) particles. The number of particles in a mole is Avogadro's constant, \(N_A\). Boyle's law relates the pressure and volume of a fixed amount of gas at a constant temperature: \[p\propto \frac{1}{V}\] Gay-Lussac's law relates temperature and pressure of a fixed gas at a constant volume: \[p\propto T\] Charles' Law relates the volume and temperature of a fixed gas at a constant pressure: \[V\propto T\] These relations rely on absolute temperature, being the kelvin scale where 0 K is -273.15 C.
We can combine these proportionalities to give the ideal gas equation: \[pV=nRT\] R is the universal gas constant and has a value of \(8.314Jk^{-1}mol^{-1}\). This assumes pressure is in Pa, volume in \(m^3\), amount in mol and absolute temperature in K.
Mixtures of gasses
Dalton's law of partial gases states that mixing two gases in the same contianer results in the pressure being the sum of the individual gas pressures: \[p_{total}=\sum p_i=(n_A+n_B+n_C)\frac{RT}{V}\] We can work out the partial pressures from the ideal gas equation of each gas individually. This is equivalent of adding the amount of gas in each gas. If we know the total pressure and amount of an individual gas compared to the whole, we can calculate the pressure of that gas. \[p_A=\frac{n_A}{n_{total}}p_{total}\]
Kinetic Molecular Theory
The kinetic molecular theory assumes:
- A gas consists of particles in constant motion in all directions
- These particles collide with each other and the walls of the container causing pressure
- The path of a single particle is random and can be modelled as a random walk
- Gas particles have negligible size and can be modelled as point masses
- All collisions are elastic, where no energy is lost or gained
- There are no interactions between molecules
Using these assumptions we can relate the various properties of the particles and the quantities present in the ideal gas equation. For example, a gas with high pressure has fast moving particles, which have high kinetic energy which must have high temperature.
The distribution of speed of particles can be measured and gives a Maxwell-Boltzmann distribution. It's peak is the most probable speed, the mean is slightly greater and the root mean squared is slightly greater again. We can find the root mean squared from the ideal gas equation as follows: \[\sqrt{\overline{u^2}}=\left(\frac{3RT}{M}\right)^{\frac{1}{2}}\] This shows that greater temperatures correlate with greater speeds. Likewise, larger masses decrease speeds. This allows us to find the average molecular kinetic energy: \[\overline{E}_{k,molecular}=\frac{1}{2}m\sqrt{\overline{u^2}}^2=\frac{3RT}{2N_A}\] We can also find the average molar kinetic energy: \[\overline{E}_{k,molar}=\overline{E}_{k,molecular}*N_A=\frac{3RT}{2}\] These show that the average kinetic energies depend only on temperature, not the mass of the substance like the speed.
The random motion of particles gives rise to effusion and diffusion. Effusion is the escape of a gas through a hole in the container. The rate of effusion is proportional to the square root of its molar mass. Diffusion is the mixing of gasses. Diffusion seeks to equalise the concentration of a gas throughout the container. The rate of diffusion is dependent on the speed of the particles.
Real Gases
Real gasses deviate slightly from ideal ones at the extremes. For example, ideal gases do not undergo phase changes. Real gases interact with each other and have size, unlike real gases. An example of an adapted ideal gas equation for real gases is the van der Waals equation for gases: \[\left(p+a\left(\frac{n}{V}\right)^2\right)(V-nb)=nRT\] Here there is an attempt to adapt for the inter-molecular attractions in the modification of pressure and the size of molecules in volume.
Thermodynamics
Introduction
Thermodynamics explains the transformation of energy from one form to another. Energy is the quantitative property that provides the ability to do work. There are potential energies (stored forms of energy) and kinetic energy (movement). Energy can be transferred as heat through temperature differences or as work as a result of motion against an opposing force. Energy is measured in Joules, although calories, being the amount of energy required to increase the temperature of a gram of water by a degree is also used. Reactions can either be endothermic (absorbing energy) or exothermic (releasing energy.)
The first law of thermodynamics states that energy is conserved though all interactions. The sum of energies in the universe is constant. There are closed, isolated and open systems. Open systems can transfer matter and energy out of the system. Closed systems contain matter but can transfer energy. Isolated systems do not transfer matter or energy, their energy is constant. An isothermal change is when heat is exchanged between the system and the surroundings so their temperatures are equal. An adiabatic change is when there is no heat change between the system and its surroundings, their temperatures may not be equal.
Heat (\(q\)) is the energy transferred due to a temperature difference. The transfer occurs from the higher temperature object to the lower temperature object. The temperature is the measure of an object's heat energy (kinetic energy) and the ability to transfer that heat. It is an intensive property (independent of amount of material). Work (\(w\)) is the energy exchange as a result of motion against an opposing force. For this subject, work is related to the pressure and volume changes. \[w=-p_{ext}\Delta V\] Thermochemistry is involved with the energy changes of chemical reactions.
Exothermic reactions are when the energy required in forming the reactants are greater than the products so energy is released. Endothermic reactions are when the energy required in forming the reactants is lesser than the products so energy is added. The activation energy is the energy required to break the bonds of the reactants. The total energy of a system is the sum of the kinetic and potential energies present. This is called the internal energy (\(U\)). This is an extensive property (depends on the amount of substance). \[\Delta U=U_{final}-U_{initial}=q+w\] The change in internal energy is a state function, depending only on the initial and final states of the system, not the pathway between them. If the change is positive, the system gains energy. If the change is negative, the system loses energy. In an isolated system, \(\Delta U=0\).
Enthalpy
Enthalpy is the heat in a system at a given pressure and volume. The enthalpy change is the heat transferred between the system and its surroundings during a process at constant pressure if no work other than expansion is done. \[\Delta H=\Delta U+p\Delta V\] Enthalpy is measured in \(kJmol^{-1}\). The enthalpy change of fusion, \(\Delta_{fus}H\) is the energy required to melt one mole of a pure substance at its melting point (latent heat of fusion). The enthalpy change of vaporisation, \(\Delta_{vap}H\) is the energy required to vaporise one mole of a pure substance at its boiling point (latent heat of vaporisation). We can find the change in energy corresponding to a temperature change with: \[q=mc\Delta T\] \[q=nc\Delta T\] Here \(c\) is the specific and molar heat capacities respectively, being the amount of energy required to raise one gram (mole) of a substance by 1 K. For gasses, we have molar heat capacities at constant pressure and volume which can differ.
Trying to measure the enthalpy changes is done with a calorimeter, which tries to isolate the system. This is done by using insulating materials and can use water as a substance to absorb the heat.
A reaction is exothermic (endothermic) if its change in enthalpy is negative (positive). \[\Delta_rH=\sum H_{products}-\sum H_{reactants}\] A reverse reaction has the same magnitude change in enthalpy with the opposite sign. The enthalpy change of a reaction depends on the states of the reactants. The standard states are:
- 1 M at 1 bar for a solution
- 1 bar for a gas
- Whatever state is most stable at 1 bar and the temperature of interest for a pure substance
The standard enthalpy is denoted by \(\Delta_rH\).
Hess' Law can make it useful to find a reaction enthalpy provided we know the initial and final states. This is because the route taken between states doesn't matter. This allows us to add reactions together to produce each side of the reaction. \[\Delta_rH^\circ=\sum ni\Delta_fH^\circ(products)-\sum ni\Delta_fH^\circ(reactants)\] Here \(\Delta_fH^\circ\) is the enthalpy of formation, being the enthalpy change in producing the compound from the elements in their base state. The enthalpy of formation of elements is used a reference and thus is 0. We can also work out the enthalpy for a compound from the enthalpy of the bonds present. \[\Delta_rH=\sum D(\text{bonds broken})-\sum D(\text{bonds formed})\] When the temperature changes during the reaction we can use the Kirchhoff equation: \[\Delta_rH^\ominus_{T_2}=\Delta_rH^\ominus_{T_1}+\Delta C_p(T_2-T_1)\] Where \[\Delta C_p=\sum v_iC_p(products)-\sum v_iC_p(reactants)\]
Entropy
Entropy is the degree of disorder within a system. The universe tends towards disorder, so states with greater entropy are more likely to occur. We can quantise entropy with \[S=k_B\ln W\] Where \(k_B=\frac{R}{N_A}\) is the Boltzmann constant and \(W\) is the number of ways to arrange the molecules in the system. The larger the \(W\), the more likely that macro-state is. The degrees of freedom within a substance affects its entropy, a solid has less than a gas. Hence the entropy increases as temperature is raised. The reference point for entropy is at 0 K in a perfect crystal, where it is 0. Likewise, the more complex a molecule, the higher its entropy compared to a simpler one.
Entropy is a state function and can be measured by the heat required to raise the temperature from 0 K by a reversible process: \[\Delta S_{sys}=\frac{q_{rev}}{T}\] Its units are \(JK^{-1}\). The entropy of an isolated system like the universe is constant. \[\Delta S_{isolated}=\Delta S_{system}+\Delta S_{surroundings}=0\] We can find the entropy change of the surroundings from the change in enthalpy from a reaction, as any change in heat comes from the surroundings. We can also find the entropy of a reaction: \[\Delta_rS^\ominus_{298}=\sum v_iS^\ominus_{298(products)}-\sum v_iS^\ominus_{298(reactants)}\]
Spontaneity
Using entropy and enthalpy, we can find the following \[\Delta G=-T\Delta S_{universe}=\Delta H^\ominus_sys-T\Delta S_{system}\] Here \(\Delta G\) is the Gibbs free energy, a state function with units of joules per mole. The Gibbs free energy gives us information about the spontaneity of a reaction, with it being spontaneous if \(\Delta G<0\) and not if not. If \(\Delta G\) is 0, there is no preference for direction. The free energy changes can only be calculated for a constant pressure process. We can tell if a reaction is enthalpy or entropy driven by the sign of the enthalpy.
The following table describes the spontaneity of reactions by the sign of \(\Delta S\) and \(\Delta H\).
| \(+\Delta S\) | \(-\Delta S\) | |
| \(+\Delta H\) | Spontaneous at all temperatures | Spontaneous at high temperatures |
| \(-\Delta H\) | Spontaneous at low temperatures | Non-spontaneous at all temperatures |
We can find standard free energies of formation \(\Delta_fG^\ominus\) as that of 1 mol of a pure substance formed in standard state from its component elements at their standard states at 1 bar. As a result \(\Delta_fG^\ominus=0\) for all elements. We can use this to find: \[\Delta_rG^\ominus=\sum ni\Delta_fG^\ominus_{(products)}-\sum ni\Delta_fG^\ominus_{(reactants)}\] We can also use Gibbs free energy with Hess' law as it is a state function.
The Gibbs free energy is equivalent to the maximum non-expansion work that can be obtained from a change. \[\Delta_rG=w_{max}\] This is the maximum work a change can do after the change in volume has been accounted for. This can be useful in electrical work, such as the energy available in a cell.
Chemical Equilibrium
Equilibrium constant
A reaction approaches an equilibrium between the reactants and products. This equilibrium is the same regardless of the direction of the reaction. The rate of reaction reduces as the reaction nears equilibrium. The equilibrium is constant, given constant temperature. Given a reaction at constant temperature, we can express the thermodynamic equilibrium constant \(K_p\) with respect to pressure as: \[K_p=\frac{p_{eqm}(\text{products})}{p_{eqm}(\text{reactancs})}\] Being the ratio of partial pressures at equilibrium of the reactants to the products. The stoichiometric ratios appear as exponents in the equilibrium constant. We can also express the equilibrium in terms of concentration. \[K_c=\frac{\prod c_{eqm}(\text{products})^{\nu_p}}{\prod c_{eqm}(\text{reactants})^{\nu_r}}\] Depending on the reaction, the units of \(K\) are different and are often left out. The units of concentration used must be \(molL^-1\), however the units for pressure can be different.
If \(K>>1\) the reaction goes nearly to completion. If \(K>1\), the equilibrium consists mostly of products. If \(K<1\), the equilibrium consists mostly of reactants. If \(K\approx 1\), similar amount of reactants and products exist. The \(K\) of the forward reaction is equal to \(1/K\) of the reverse reaction. Stoichiometric multiplication is an exponentiation of the original \(K\).
The size of \(K\) is solely determined by thermodynamic factors, such as the energy difference between the products and reactants. The activation energy affects the reaction rate and time taken for the reaction, so does not affect \(K\).
A homogeneous equilibrium is one where all chemical species are in the same phase. A heterogeneous equilibrium is one where the chemical species have different phases. When working with liquids or solids with gas, it can be useful to ignore the solid or liquid, as their concentration and pressure barely change throughout the reaction. Likewise, when working with liquids (or aqueous solutions) and solids, the solid can be ignored. The solubility product is an example of this, and is \[K_{sp}=[A]^a[B]^b\] Where \(A\) and \(B\) are the components in solution. The smaller \(K_{sp}\), the harder it is to dissolve the substance in solution.
Reaction quotient
We can find a number analogous to \(K\) at any given time for a reaction. \[Q_c=\frac{[P]}{[Q]}\] \(Q\) informs as to the extent of the reaction's completion, as it will tend to \(K\) as time tends to infinity. If \(Q<K\), the forward reaction is favoured. If \(Q>K\), the reverse reaction is favoured.
Gibbs free energy and equilibrium
We can express Gibbs free energy as: \[\Delta_rG^\ominus=\Delta H^\ominus-T\Delta S^\ominus\] This is the standard form relating enthalpy and entropy. We can also express Gibbs free energy using the equilibrium constant: \[\Delta_rG^\ominus=-RT\ln K\] Where \(R\) is the universal gas constant, \(T\) is the absolute temperature and \(\ln K\) is the natural logarithm of the equilibrium constant. We can rearrange this to find the equilibrium constant. \[K=e^{-\frac{\Delta_rG^\ominus}{RT}}\]
Le Chatelier's principle
A system at equilibrium will act to partially oppose changes made upon it. This means that given a system at rest, any changes will be partially undone. If the temperature of a reaction mixture is increased, the reaction will move its equilibrium to reduce the temperature of the environment. If the pressure is increased, the reaction will act to reduce the pressure of the environment. The reaction will not be able to completely undo any changed made, so a new, different equilibrium will form.
Inorganic chemistry
Acids and bases
Lewis acids and bases
Lewis acids are molecules capable of donating electron pairs and bases are capable of receiving them. Often this forms covalent bonds.
Bronsted acids and bases
The traditional acids and bases. The acid donates a \(\ch{H+}\) and the base donates \(\ch{OH^-}\), or accepts the \(\ch{H^+}\). The Bronsted acid and base is a subclass of Lewis acid and base involving hydrogen ions. A Bronsted acid is a proton donor and a Bronsted base is a proton acceptor. A Bronsted acid-base reaction is a proton transfer reaction. The hydrogen ion as a naked ion does not exist in an aqueous solution and instead is hydrated to a certain degree. Despite this, it is commonly referred to as \(\ch{H^+}\) or \(\ch{H3O^+}\), a hydronium ion.
In reactions between an acid and a base, we form a conjugate base and acid respectively. \[\ch{A + HA <=> A^- + HB^+}\] Here, \(\ch{HA}\) and \(\ch{A^-}\) are a conjugate pair, like \(\ch{B}\) and \(\ch{HB+}\). Water autoionsises into a proton and a hydroxide. At \(25^\circ C\), we can express this autoionsisation rate from the concentrations of the ions as \(K_w\). \[\Kw=[\ch{H^+}][\ch{OH^-}]=10^{-14}@25^\circ C\] In pure water at \(25^\circ C\), \([\ch{H^+}]=[\ch{OH^-}]=10^{-7}\). When the concentration of protons is equal to hydroxides, the solution is said to be neutral. If \([\ch{H^+}]>10^{-7}\), the solution is said to be acidic, if \([\ch{OH-}]>10^{-7}\), the solution is said to be basic. Due to the small number, a logarithmic scale is used, called the \(\pH\). \[\pH=-\log[\ch{H+}]\] \[\pOH=-\log[\ch{OH-}]\] We can relate \(\pH\) to \(K_w\) as \(\pH+\pPH=14=p\Kw\)
We can express the strength of an acid with its acid dissociation constant. \[\Ka=\frac{[\ch{H3O+}][\ch{A-}]}{[\ch{HA}]}\] \[\pKa=-\log\Ka\] We can do the same for bases. \[\Kb=\frac{[\ch{OH-}][\ch{BH+}]}{[\ch{B}]}\] \[\pKb=-\log\Kb\] In all of these, water is ignored as it is the solvent.
Strong acids completely ionise in an aqueous solution. As a result, their conjugate bases are weak bases. They have a large \(\pKa\). As a result, we can assume complete dissociation of the acid. The same applies for a base. Weak acids undergo a small degree of dissociation. As such, the equilibrium lies towards the middle, so complete disassociation cannot be assumed. We can express the \(\pH\) of a weak acid in solution as: \[\pH=-\log(\sqrt{\Ka[\ch{HA}]})=1/2\pKa-1/2\log[\ch{HA}]\] For weak acids, we can assume that the concentration of the acid is close to the number of model divided by the volume. This approximation improves the weaker the acid. We can use the rule of thumb of 5% dissociation to check whether the approximation is valid, i.e. if the amount dissociated is less than 5%. We can do the same for weak bases.
Polyprotic acids
Acids with more than one acid proton are called polyprotic. Disassociation occurs in a step-wise manner. For most polyprotic acids, we can assume that only the first acidic proton is donated as the successive \(\Ka\) are reduced.
In a series of oxyacids, the acidity increases as the oxidation state of the central atom increases. This would mean sulfuric acid (\(\ch{H2SO4}\))is more acidic than sulfurous acid (\(\ch{H2SO3}\)).
Buffer solutions
A buffered solution is one that resists a change in \(\pH\) when either \(\ch{OH-}\) or \(\ch{H+}\) ions are added. If we add more \(\ch{OH-}\) or \(\ch{H+}\) than buffer, we exceed the buffer and it fails. A buffer is formed from a solution of an acid and a base. We can use the Henderson-Hasselbach equation to give the \(\pH\) of a buffered solution. \[\pH=\pKa+\log\left(\frac{[\ch{A-}]}{[\ch{HA}]}\right)\] Note that the ratio is important in determining the \(\pH\), not the amount of concentration. A buffer is formed from a weak acid and its weak conjugate base.
Lewis structures
Covalent bonding
Valence electrons are shared between nuclei. Molecules are attracted to each other by the electrostatic attraction of the positively charged nuclei for the shared electrons. Bonding will occur if the energy of the molecule is lower than that of the separate atoms. Lewis structures compose a simple model concerned with the arrangement of electrons in a molecule. In many stable compounds, the atoms achieve an octet of electrons like the noble gasses.
Writing Lewis structures
The steps required to write a Lewis structure are:
- Sum the valence electrons in the molecule
- Place a single bond between each pair of bonded atoms
- Complete the octet rule for all the atoms using lone pairs and multiple bonds
- If electrons remain, place them on atoms with available d orbitals
- Check atoms for formal charge
This allows us to draw structures like: \[\chemfig{H-\lewis{0:2:6:,F}}\] \[\chemfig{H-\lewis{2:,N}(-[6]H)-H}\] \[\chemfig{\lewis{4:,N}~\lewis{0:,N}}\] \[\chemfig{\lewis{2:4:6:,F}-C(-[2]\lewis{0:2:4:,F})(-[6]\lewis{0:4:6:,F})-\lewis{0:2:6:,F}}\]
Elements in period 3 or above are capable of accommodating more than 8 electrons as they put them in the d orbital. Similarly they are capable of forming more than 4 bonds.
When assigning a formal charge, the number of electrons when in a neutral form must be considered. This is done after otherwise normally constructing the Lewis structure. An atom with a different number of electrons in the bonded state to its neutral state has a formal charge. When drawing structures, we try to minimise formal charges.
Resonance occurs when it is possible to write more than one Lewis structure for a molecule. In this case, the Lewis structures are valid, but are not accurate. The resonance results in a delocalisation of the electron pairs.
Some atoms have less than 8 valence electrons, so fail the octet rule (e.g. Boron). This forms electron-deficient molecules, which react with electron-rich molecules with a dative (coordinate) bond forming with electrons entirely from the electron-rich molecule.
Species with unpaired electrons are radicals. These are often very reactive. All species with an odd number of electrons are radicals.
Covalent Bonding
Valence Shell Electron Pair Repulsion (VSEPR) theory
A simple model to determine molecular structure. Can be used to determine shape from a Lewis structure. In predicting shape, we need to first determine the electron pair geometry, being the spacial arrangement of electron pairs including lone non-bonding pairs. This can be used to predict the molecular geometry, being the spacial arrangement of atoms. The fundamental idea is that electron pairs arrange themselves to be as far apart as possible.
The following table describes the electron geometry and names:
| Number of pairs (electron domains) | Number of atoms | Name | Bond Angle | Example |
|---|---|---|---|---|
| 6 | 6 | Octahedral | 90,180 | Sulfur Hexafluoride |
| 5 | 5 | Trigonal Bipyramid | 90,120,180 | Phosphorus Pentachloride |
| 4 | 4 | Tetrahedral | 109.5 | Methane |
| 4 | 3 | Trigonal Pyramidal | 107 | Ammonia |
| 4 | 2 | Bent | 104.5 | Water |
| 3 | 3 | Trigonal Planar | 120 | Boron Trifluoride |
| 3 | 2 | Bent | Sulfur Dioxide | |
| 2 | 2 | Linear | 180 | Carbon Dioxide |
It turns out that lone pairs occupy more space than bonding pairs. As a result, the bond angles decrease as atoms are removed from a geometry. This cause a molecule like Xenon Tetrafluoride (6 pairs, 4 atoms) to have a square planar shape, as the lone pairs are oriented as far from each other as possible. In the case with 5 electron domains, there is more space in the equatorial plane, so a molecule like \(\ch{I3-}\) (5 domains, 2 atoms) is linear. Multiple bonds reduce the number of electron domains, so Carbon Dioxide is linear. Multiple bonds, however do affect the bond angles as their increased electron density causes them to take up more space.
Polarity
A bond between two atoms of different electronegativities is a polar bond. A highly electronegative atom pulls electrons towards it, causing its end of the bond to be partially negative. This leaves the less electronegative atom as partially positive. The degree of polarity can be measured as the dipole moment, in Debye (D). A bond between atoms of large electronegativitiy difference have a large dipole moment.
A symmetrical molecule has equal and opposite polarities from its bonds, resulting in no polarity overall. In cases where the molecule isn't symmetrical, the bond polarities sum to give an overall polarity.
Covalent bonding
Covalent bonds are formed from the electrostatic attraction of positively charged nuclei for shared electrons. Bonding will occur of the energy of the molecule is lower than that of the separate atoms. The energy of two atoms that bond is at a minimum when the atoms are near to each other as when they are too close they repel and when they are too far the electromagnetic force is too weak to interact meaningfully. The energy difference where the atoms are together is the bond energy and is normally in the magnitude of 100-1000 kJ.
The overlap of orbitals forms sigma bonds. The hybridisation of orbitals allows sigma bonds at angles other than those the s, p, d or f orbitals are at.
Valence bond theory and hybridisation
It is possible to combine orbitals to form multiple equivalent orbitals. An \(s\) and 3 \(p\) orbitals can combine to give 4 \(sp^3\) orbitals of equivalent energy. We say that the atom has become \(sp^3\) hybridised. Each \(sp^3\) orbital is 25% \(s\) and 75% \(p\) character. This results in the orbital having a large and small lobe, which they can overlap with other orbitals to form a sigma bond. These orbitals are directed towards the vertices of a tetrahedron. The electron pair geometry determines the hybridisation. The following table relates electron pair geometries and hybridisation:
| EPG | Hybridisation |
|---|---|
| Linear | \(sp\) |
| Trigonal | \(sp^2\) |
| Tetrahedral | \(sp^3\) |
| Trigonal bipyramid | \(sp^3d\) |
| Octahedral | \(sp^3d^2\) |
The more s character a hybridised orbital has, the rounder the orbital. pi bonds are formed from orbitals that do not engage in hybridisation.
Molecular orbital theory
A more sophisticated model than Valence bond theory to describe bonding. The models are harder to visualise. Generally the molecular orbitals can be obtained from a linear combination of atomic orbitals.
The behaviour of electrons in atoms is best described by wave (quantum) mechanics. At the heart of this is the Schrodinger equation, which yields solutions as wave functions. The wave function (\(\psi\)) itself has no meaning, but its square (\(\psi^2\)) describes the probability of finding it at a point in space. Each wave function corresponds to an orbital of a particular energy. The phase of the wave function is indicated by + or - signs. The atomic orbitals are solutions to the quantum treatment of atoms. When the wave functions interfere constructively we get a bonding orbital and when destructively an antibonding orbital. The shapes of these orbitals can be obtained from the square of the wave functions. The energy of a bonding orbital is lower than the individual orbitals, while the energy of the antibonding orbital is higher. Orbitals are conserved, i.e. every starting orbital results in a mixed orbital. The electrons in bonding orbitals have opposite spins and are stable, while the electrons in antibonding orbitals are unstable. If the number of electrons in bonding orbitals exceeds the number in antibonding orbitals, the molecule is predicted to be stable. The bond order is an indicator of the stability of a bond. \[\text{Bond order}=\frac{\text{No. of bonding e}-\text{No. of antibonding e}}{2}\] The larger the bond order, the larger the bond energy and the more likely the structure is to exist.
p orbitals can interact remotely forming \(\pi_p\) bonds. The p orbital can also overlap forming \(\sigma_p\) bonds, which are stronger than the pi bonds. Likewise we can get antibonding interactions between p orbitals. Unpaired electrons are paramagnetic, and can be used to verify a molecular orbital structure.
The MO theory often works when Lewis fails, but quickly becomes very complex. As a result, Lewis is often used due to its simplicity and ease of visualisation.
Metals
The electron sea model is a simple model used to explain metal bonding. It consists of metal cations in a sea of electrons. The mobile electrons conduct heat and electricity. We would expect a higher group metal to have stronger interactions than a lower one.
MO theory and the band model is better to explain the bonding of metals. Basically, the overlap of atomic orbitals from a large number of metal atoms results in a virtual continuum of energy levels, known as bands. The Fermi level is the highest filled level at 0K. Above 0K, higher orbitals are occupied, resulting in holes left below the Fermi level. The holes and electrons move in opposite directions, resulting in electrical conduction. The closeness of the energy levels allows for the absorption and emission of virtually any frequency of light, resulting in their characteristic lustre.
In semiconductors, there is a band gap separation between the filled valence band and the empty conduction band. At a small band gap, we have a semiconductor and a large band gap results in an insulator.
Trends in the periodic table
Atomic size
The size of an atom depends on the volume of space the electrons are allowed to occupy. The nature of electrons in orbitals means that the atomic boundaries are hard to define and are fizzy, We can define the size with the covalent radius or the van der Waals radius. The covalent radius is considered to be half the length of a single bond to itself. Going down a group, the radius of an atom increases in size. Across a period, atoms decrease in size.
As we go down a group, the shell number (principle quantum number) increases. The higher the principle quantum number, the larger the volume occupied by the orbitals and the greater the distance of the outer electrons from the nucleus. As we go across a period, the shell number stays the same while the nuclear charge increases. Electrons in the outer shell are drawn closer to the radius by the increasing positive charge from left to right. Electron-electron repulsion is responsible for far right elements being similar in size within a period.
Positive ions (cations) are always smaller than the parent atom. Negative ions (anions) are always larger than the parent atom.
Isoelectronic series, being ions with the same number of electrons, can have varying sizes. The size of the ion is negatively correlated with its charge, i.e. a large positive charge results in a small ion and a large negative charge results in a large ion.
Ionization energy
It will always require energy to remove an electron from an atom. As we go down a group, the first ionization energy decreases. The outermost electrons are further from the nucleus, explaining the difference. The ionization energy increases across a period. This is because the number of core electrons (electrons in lower shells) is constant but the nuclear charge is increasing, causing more attraction between the electrons and the core. A high ionization energy correlates with a small size, and a small ionization energy correlates with a large size.
Electron affinity
Electron affinity is the energy required to add an electron to an atom. Electron affinity generally decreases down a group since the electron being added is being added to the atom at an increased distance from the nucleus.
Electronegativitiy
The ability of an atom in a molecule to attract shared electrons to itself. Measured on the Pauling scale from 4.0 (F) to 0.79 (Cs). Electronegativitiy generally increases across a period and decreases down a group.
Metallic character
Metallic character is the ease of removing an electron from an atom. Increase in metallic character moving down a group and from right to left in a period.
Inter-molecular forces
Could be considered a type of secondary bonding. Significant in solids and liquids. Much weaker to bonding within molecules. Also known as van der Waals forces. Range from dipole-dipole forces to London dispersion forces. Although they are weak, they are important.
London dispersion forces
Occur between all molecules, both polar and non-polar. Relatively weak forces. Originate from instantaneous dipoles from electron fluctuation, which creates a similar dipole in neighbouring molecules. Can scale up to being relatively strong.
Stronger for atoms that are more easily polarised. The polarisability relates to the ability of a molecule or atom to undergo a distortion of its electron clouds. Molecules with extended electron clouds can be polarised to a greater extend than those with smaller clouds. Tend to be weak as polarisability of most species isn't very large, so only works over short distances.
The shape of a molecule can also affect dispersion forces. The larger the surface area of the molecule, the larger the dispersion forces.
Dipole-dipole forces
Occur in polar molecules. Polar molecules possess a dipole moment, causing an electrostatic attraction to other molecules. The dipoles align to the lowest energy state. About 1% the strength of covalent/ionic bonds.
Hydrogen bonding may be considered a special type of dipole-dipole bonding. When a hydrogen atom is attached to a small electronegative atom, the interaction between the bond dipole and polar molecules is greater than expected from ordinary dipole interactions. The interaction depends on the polarity of the \(\ch{X-H}\) dipole. The strongest occur when hydrogen is bonded with Nitrogen, Oxygen or Fluorine. Here the Hydrogen is bonded to a NOF, and interacts with another NOF. Hydrogen bonds are often close to linear, strong, generally asymmetric and are longer than covalent bonds but shorter than dipole interactions. H-bonding increases the boiling point, working against the trend going down a group.
Gas solubility
Generally, solubility increases with temperature. With gasses, the solubility decreases with temperature. Increasing the pressure has little effect on the solubility of solids and liquids but can significantly affect gasses. Henry's law describes the relationship between gas pressure and concentration of a dissolved gas. \[s=k_Hp\] Where \(s\) is the gas solubility, \(p\) is the partial pressure of the gas above the solution and \(k_H\) is a constant characteristic of a particular solution. The amount of gas dissolved is proportional to the pressure of the gas above the solution.
Solubility of ionic solids
Using a symbol \(K_s\) or \(K_{sp}\), we can express the solubility of a compound: \[K_{sp}=[ions]\] The equilibrium constant for the dissolution of a sparingly soluble ionic solid is called the solubility product. The solubility of a sparingly soluble salt is reduced in the presence of a common ion. This increases the concentration of the ion, so decreases the amount dissolving. pH of a solution can affect the solubility of salts that dissolve into hydroxide ions, as basic solutions are common salts and protons reduce the concentration of hydroxide in solution. The opposite will happen for acidic salts. We can also consider the ion product, \(Q\): \[Q=[ions]_0\] The ion product is the initial concentration of the ions.
Formation of ionic compounds
There is a continuum from pure covalent to pure ionic bonding depending on the degree of sharing electrons. Although it may take energy to make the ions, there is energy to be gained from storing the atoms in a lattice. The lattice energy can be calculated as \[\text{Lattice energy}-k(q_1q_2)/r\] Where \(k\) is a constant related to the structural arrangement of ions, \(q_1\) and \(q_2\) are the charges on the ions and \(r\) is the inter-ionic centre to centre distance. The lattice energy is inversely correlated with ionic size.
Lattice enthalpy can be determined from the Born-Haber cycle. This is using a group of equations and Hess' law to find the difference in energy between the gaseous state of the atoms and the ionic state of the compound.
X-ray crystallography
Allows us to “see” molecular structure. X-rays are scattered by the regular array of atoms in a crystal to give a diffraction pattern. By measuring the position and intensity of the scattered X-rays it is possible to determine the arrangement of atoms in the crystal. The diffraction is caused by the constructive and destructive interference of the X-rays reflected from the lattice planes. The conditions required for reflection are represented by Bragg's Law: \[n\lambda=2d\sin\theta\] Where \(n\) is an integer (order of reflection), \(\lambda\) is the wavelength of the radiation, \(d\) is the inter-planar separation and \(\theta\) is the angle of incidence.
Sphere packing
Close packing occurs when rafts of spheres stack on top of each other. When 2 layers stack together, a sphere from one layer sits above an indentation formed from the three spheres of another layer.
There is hexagonal close packing (AB). Here, the odd layers are directly above each other and the even layers are above each other. Every sphere is surrounded by 12 other spheres.
There is also cubic close packing (ABC). Here, every third layer is replicated. Also referred to as face centred cubic.
The basic repeating unit within a structure is called the unit cell. A crystal structure is made of related unit cells by pure translations in 3 dimensions. A sphere may belong to more than one unit cell. In a cubic close packing arrangement, the axis of stacking aligns with the body diagonal of an overall cubic structure, but with a sphere in the middle of every face. This produces a face centred cubic unit cell, consisting of 4 spheres per unit cell. Hexagonal close packing produces a more complex unit cell. When there are only spheres at the corners of the cell, resulting in only one sphere per unit cell, we get a simple cubic structure. This has a packing efficiency of 54%. There is also a body centred cubic, where there is a sphere in the centre of the unit cell and one on every vertex. This results in 2 spheres per unit cell and a 68% packing efficiency.
In metals, the most common structures are body-centred cubic, cubic close packing and hexagonal close packing. Alloys contain a mix of elements and has metallic properties. A substitutional alloy has some of the host metal atoms replaced by other metal atoms with a similar size. Interstitial alloys are when atoms are inserted in between the space left in the packing arrangement. This is done with much smaller atoms, like carbon in iron for steel.
Ionic solids
The structure of ionic solids can be easily related to close packed or simple cubic packing pf ions. In a 1:1 ratio of anions to cations, the cation can occupy the interstitial space as the anions are generally larger. There is a tetrahedral site in the centre of a tetrahedron formed by the atoms in hexagonal packing. Octahedral sites are formed in the space between atoms in layers in cubic close packing. Ionic solids tend to maximise anion-cation interactions. To achieve this, the cations occupy holes that are slightly smaller than the ion. This forces the anions slightly apart, so that the ions of opposite charges are touching but none of the same charge are touching. Ions if radius \(0.225R^-<r^+<0.414R^-\) will form tetrahedrons, with the cation in the tetrahedral hole. If the cation is larger than 0.414 times the radius of the anion, it will occupy a octahedral hole. If the ions are of a similar size (\(0.732R^-<r^+\)), no close packing occurs and instead a simple cubic packing arrangement occurs. Ions with a ratio of 1:1 tend to have octahedral/cubic packing, while ions with a ratio of 2:1 tend to have tetrahedral packing. We call the number of ions of opposite charge surrounding an ion the coordination number of the structure.
Network solids
Network solids are infinite covalent solids which may be 1D (chain), 2D (sheet), or 3D. Silicon dioxide is an example network solid. Due to the size difference between the silicon and oxygen, pi bonds are unable to form, resulting in silicon bonding to 4 oxygens unlike 2 in carbon dioxide. Silicates are anionic \(\ch{Si-O}\) networks formed of oxyanions of silicon which are usually very large. Metallic ions can be packed between the oxyanions and complex structures can be explained in terms of the \(\ch{SiO4^{4-}\) unit. Silicates can link to form chains, as in \(\ch{Si2O7^{2-}}\), or form rings as in \(\ch{Si6O_{18}^{12-}}\). We can combine this into double chains, with repeating units of \(\ch{Si4O11^{6-}}\) We can form sheets with three linking oxygens and one terminal oxygen, with a repeating \(\ch{Si4O10^{4-}}\). Using all 4 oxygens for linking creates 3D arrays. Quartz consists of interwoven, crosslinked, helical chains of \(\ch{SiO4}\).
Mineral silicates usually crystallise slowly. Forcing them to cool quickly causes solidification without crystallisation, resulting in a supercooled liquid, a glass. Over long periods, glasses may slowly crystallise.
Structure of elements
Hydrogen
Simple diatomic molecule normally existing as \(\ch{H2}\). Typically a nonmetal, but transformed into a conducting solid with 3 million atm of pressure. Forms more compounds than any other element and of great interest.
Noble gasses
The noble gasses are extremely stable, monoatomic elements. If cooled sufficiently, they form close packing solids. Most have cubic close packing, argon has a metastable hexagonal state. Helium transitions from body centred cubic to hexagonal to cubic with increasing pressure.
Metals
Metals commonly are body-centred cubic, cubic close or hexagonal close packing. This leads to efficient space usage.
Boron
Boron is the only group 13 element that is a non-metal. It has a large number of allotropic forms which is a result of it having fewer valence electrons than bonding orbitals. Most similar elements adopt metallic bonding but due to its high ionisation energy, Boron forms covalent bonds. Boron can form a 12 atom icosahedron in many of its allotropes.
Carbon
Carbon has a number of alltropic forms, including diamond, lonsdaleite, graphite and fullerenes. The different allotropes have a variety of properties.
Diamond is formed from a tetrahedral structure. Diamond has adamantane-like rings, formed from 4 fused cyclohexanes. Diamond is formed if all tetrahedral centres are connected and perfectly staggered. The unit cell can be considered a cubic close packing arrangement of carbon atoms. The electrons are locked into sigma bonds, resulting in poor electrical conductivity. It is an excellent conductor of heat, has a high refractive index and is extremely hard.
Lonsdaleite is a rare form of carbon. The atoms are eclipsed, looking at only one of the four bonds. It has a similar structure to ice and is only found in meteor craters. Graphite are carbon atoms linked to form an infinite 2D planar hexagonal grid of carbon. Each carbon is \(sp^2\) hybridised, with p orbitals perpendicular to the grid and the electrons contributing to the delocalised pi electron system. Each carbon-carbon bond can be considered a 1.33 bond.
Graphite is soft, opaque and an electrical conductor. It is possible for ions or molecules to slide in between the layers, known as intercalation. The sheets stack loosely, bonded by van der Waals interactions.
Fullerenes are a recent class of carbon allotropes. The simplest of these is \(\ch{C60}\) buckminsterfullerine, discovered from its sole carbon NMR environment. It only has dispersion forces between molecules and is soluble in organic solvents. Sometimes atoms or molecules can be trapped inside the molecule. All the carbons are \(sp^2\) hybridised. Carbon nanotubes belong to the fullerene family. Nanotubes consist of tessellated six membered rings, with generally at least one end capped with 5 and 6 membered rings. There are single walled nanotubes, with a diameter of 1nm, which have excellent electrical conductivity and tensile strength, they are directional thermal conductors and are expensive. Multi-walled nanotubes are insulators and are less interesting.
Group 14
The rest of the group 14 elements share some of their properties with carbon. Silicon is a semiconductor without a graphite counterpart due to ineffective p-pi bonding. At high pressure silicon becomes denser with distorted tetrahedral geometries between atoms.
Germanium is similar to silicon. Tin has a metallic structure above \(13^\circ C\) but below is forms a diamond-type network. Lead is a blue-grey malleable metal. Overall there is an increase in metallic character.
Group 15
Nitrogen forms a diatomic molecule with a very strong triple bonds, but only has weak dispersion forces between molecules. Diatomic nitrogen is very stable and is often used to provide an inert atmosphere. Its low boiling point also lends itself to use as a cryogenic liquid.
Phosphorus has 3 major allotropic forms, white, red and black, and all of these have pyramidal geometries. Above \(1100^\circ C\) it can exist as \(\ch{P2}\), analogous to \(\ch{N2}\). White phosphorus (\(\ch{P4}\)) is the most reactive, is volatile and is highly toxic. The highly strained bond angle of \(60^\circ\) accounts for its reactivity. Red phosphorus forms from chaining white phosphorus by breaking one of the internal bonds. As a result it has less strain. Black phosphorus has even less strain by braking another of the bonds, removing a ring to form 6 membered rings.
Arsenic, antimony and bismuth exhibit more metallic character.
Group 16
Oxygen has 2 major allotropes, \(\ch{O2}\) and \(\ch{O3}\), both as discrete covalent molecules that are essential to life. Dioxygen is a diatomic gas with a double bond, it is paramagnetic due to unpaired electrons from Molecular Orbital theory. It is pale blue when condensed at \(-183^\circ C\). Although oxygen is a good oxidiser, there is a large kinetic barrier to reacting, due to its electron configuration. The MO ground state of dioxygen corresponds to triplet dioxygen, which is not very reactive with species that have all their electrons paired. The singlet state is much more reactive. The kinetic stability and high bond energy contribute to a high activation energy, although reactions tend to be exothermic so encourage further reactions. Ozone is a V shaped molecule, with an internal angle of \(117^\circ\). It is polar, diamagnetic, toxic and is a strong oxidant. The structure resonates between two forms with a double bond from the central oxygen to each of the side oxygens. It is less stable than dioxygen, is a stronger oxidant, has a strong odour. When acting as an oxidant, only one oxygen is released. It is often used as a bleach or to sterilise water and purify air by oxidising the compounds in the air. In the environment, ozone absorbs UV light from reaching the surface of the earth, which can be detrimental to life.
Sulfur has two main forms, most commonly cyclic \(\ch{S8}\) and chains of sulfur. \(\ch{S2}\) is formed in the gas phase at high temperatures, as does \(\ch{S3}\). Additionally the rings can have different sizes greater than 6.
Selenium has six distinct structural forms. Three of the forms are based on \(\ch{Se8}\) rings. The most stable is a “metallic” form of hexagonal selenium. Helical chains with weak interactions exist which are photosensitive.
Tellurium has one crystalline form of a network of spirals with strong interchain interactions. Polonium has $\alpha$-polonium with a simple primitive structure. Down the group, there is a decrease in directional influences and an increase in metallic character.
Group 17 (Halogens)
All atoms form diatomic molecules with single covalent bonds. The attraction between molecules increases down the group.
General observations
Pi bonding can be important in period 2 elements, with decreasing importance in successive periods. Elements tend towards metallic structures down the group. Physical and chemical behaviour is related to the structure of the element, not so much the identity of the element.
Group 15 & 16 compounds
Oxygen chemistry is dominated by the -2 oxidation state. Occasionally oxygen can be in the -1 oxidation state, where is can act as an oxidant or a weak reductant. Sulfur has oxidation states -2, +2, +4 and +6. In the -2 state it is chemically similar to oxygen. Nitrogen takes a -3 state in ammonia and -2 in hydrozene. Nitrous oxides vary from +1 to +5. Phosphorus has an analogue to ammonia called phosphene, but it is a weaker base. Phosphorus forms adamantane oxides, which form strong phosphoric and phosphonic acids.