$conf['savedir'] = '/app/www/public/data'; ======= CHEM10003 - Chemistry 1 ======= {{tag>notes unimelb chemistry}} /*$$\require{chemfig,chemmacros}\chemsetup{modules={newman,orbital}}$$*/ $$\require{mhchem}$$ ====== 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((>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 \(QK\), 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^-