CHEM1031 Study NotesAssumed Knowledge Acid - proton donor Base - proton acceptor Acidic oxides (non-metals) react with water to make acids or bases to form salts (CO2). Basic oxides (metals) react with acids to form salts but do not react with alkaline solutions (CuO, Fe 2O3). Amphoteric oxides (Al, Zn, Pb, Sn) react with acids or bases to form salts. Neutral oxides (CO, N2O) don’t react. acid + metal → H2 + salt acid + carbonate → CO2 + H2O + salt Gases Distinguishing properties of gases: very compressible flow rapidly take shape of and fill a container (liquids only take shape) expand and contract with temperature changes (more so than liquids, solids is near negligible) infinitely expandable (unlike liquids, solids) low density Gas variables: Pressure (Pa) =force/area. Due to particles in motion, colliding with momentum into each other and walls. 1Pa = 1N/m 2 = 1J/m3 (1N = 1kgm/s2) 1atm = 760mmHg/Torr Manometer - measures difference in pressure = 101325Pa = 101.325kPa = 1.01325bar = 14.7psi Barometer - measures atmospheric pressure Page 1 Volume (m3 - 103L) Oliver Bogdanovski number/Amount (mass - kg, moles) Temperature (always in Kelvin; absolute temperature) These are dependent upon each other in the three Empirical Gas Laws: Boyle’s Law - V ∝ (or P1V1 = P2V2) - as pressure increases, volume decreases Charles’ Law - V ∝ T (or = ) - as temperature increases, volume increases Avogadro’s Law (also Gay-Lussac’s - found when gases reacted volumetric ratios were small whole numbers - a stochiometric ratio) - V ∝ n (or = ) - as the number of moles increases, so does the volume Combining Boyle’s and Charles’ Law: PV ∝ T or = Combining all three forms the Ideal Gas Law: PV ∝ nT or Constant mol-1 PV = nRT where R = Universal Gas = 8.3145 J mol-1 K-1 (SI) = 0.082057 L atm K-1 Standard Temperature and Pressure (STP): 0 oC (273.15K) and 1 bar (1.00×105Pa or 0.98atm). 1 mole of gas at STP is 22.7L. We can also sub in n=m/M and density (ρ - rho) = m/V to integrate other values. Dalton’s Law of Partial Pressures - in a mixture of gases, total pressure is the sum of the pressure each gas would exert if alone under the same conditions (assuming the gases are independent and do not react): PT = Pa + Pb + Pc + … Mole Fraction - for each component A in a mixture, the mole fraction is (a value between 0 and 1 - not percentage - to express the “percentage” of moles of that substance in a mixture): XA = Partial Pressure of A PA = XAPT Each gas also obeys the Ideal Gas Law independently as if they took up all the volume, and hence were P T=PA+PB, PAV=nRT and PBV=nRT. However these conclusions in the 17 th-19th century, and it wasn’t until the 19th-20th century that a theory of atoms began to form, so these laws all looked at macroscopic ideas, influenced by what we know to be properties of microscopic atoms. Kinetic Theory of Gases: molecule size is negligible compared to distance between them molecules move randomly in straight lines in all directions at various speeds forces of attraction/repulsion are negligible (because they are very weak) except in collisions Page 2 Oliver Bogdanovski gas particle collisions are perfectly elastic Ek av ∝ absolute temperature This explains Boyle’s Law as less space means more frequent collisions, and hence higher pressure (as collisions result in a force applied), and Charles’ Law as increasing temperature, kinetic energy (molecule speed) increases, so collisions become more frequent and with greater force. Kinetic theory states Ek av is only dependent on temperature, not gas type, and difference gases at the same temperature have the same average kinetic energy. As Ēk = mū2/2, heavier gases will travel more slowly with the same energy. It can be found that (don’t need to know derivation): Ēk = NA is Avogadro’s number. Remember this is per molecule, so to find per mole multiply by Avogadro’s number. Combining this with our other formula for Ēk: Rate of Gas Movement: ūrms = Root-mean-square (rms) simply means we have square-rooted the mean value. Effusion - escape of molecules through a hole of molecular dimensions (assuming no collisions between molecules) Diffusion - mixing of gases until the mixture is homogeneous Using the above rate and these ideas (in diffusion it could be two gases reacting and producing a colour located at a particular point and speeds) we can determine molecular mass. Graham’s Law - The rates of effusion (and diffusion) of two gases at the same temperature and pressure are inversely proportional to the square roots of their densities (note time is inversely proportional to rate): = = = All gases are actually non-ideal: all particles do have volume - becomes significant at high pressure (real volume > ideal volume as ideal volume hits zero) they have attractive forces - significant at low temperatures (real volume < ideal volume as particles are brought together; gases with low interatomic dispersion forces like He do not experience this) particles do interact - negligible at high temperature (enough energy to keep bonds apart), but significant at other temperatures (real pressure < ideal gas pressure as there are less molecules - chemically bonded together - and hence less collisions) All known life depends upon the atmosphere, however the atmosphere doesn’t have a definite end, with 99% within 30km, “outer space” at ~10,000km. Atomic Structure Page 3 Oliver Bogdanovski with visible light being 3. Page 4 Oliver Bogdanovski . a narrow band of frequencies) for various scientific measurements Polychromatic Radiation .a selection of one frequency (in practicality. m or angstrom=Å=10 -10m). however also exhibits the photoelectric effect. Einstein realised light comes in packets or quanta (got Noble Prize in 1921). diffraction and interference). and a current could flow to another electrode in a vacuum.Only valence electrons determine chemical properties.9-7. however once above the threshold frequency the intensity increased current size. He also found it required a threshold frequency that was dependent on the type of metal used which was independent of the intensity. discovered in 1887 by Hertz who found light could eject electrons from the surface of a metal. where each quantum of energy is proportional to frequency: E = hν where h = Planck’s constant = 6. and is characterised by its frequency (ν . which are related by c=νλ. and the energy of the electrons emitted depended on the frequency. whilst gamma rays are around 10-12m and long radio waves 104. When heating a gas by electrical discharge. producing a current. This is because electrons occupy discrete energy states that they move up or down. and only one with enough energy could overcome the attraction of the atom.nu. and hence much weaker at the detecting screen. and hence isotopes have nearly identical chemical properties. Monochromatic Radiation . Hz or sec-1) or wavelength (λ. In 1905.consisting of many frequencies Light has typical wave-like properties (refraction. The spectra vary with the gas used and pressure (proximity alters energy of shells).626×10-34Js A photon with enough energy could be absorbed and eject an electron. forming an absorption spectrum (the release of the photons once electrons fall is in all directions. it produces these series of lines in an emission spectrum. The energy of a particular orbital can be found by the Rydberg Equation: = RH where RH = Rydberg constant for H (on data sheet) n1 = lower shell n2 = upper shell For hydrogen the shell is a good indicator of electron energy: E = -RH/n2 White (polychromatic) light passing through a gas composed of single atoms gas lines (or specific frequencies) removed. Light is electromagnetic radiation (a self-sustaining oscillation of electric and magnetic fields). the remainder energy being converted to kinetic (E k = hν-W).0 10-7m. a prism can be used to distinguish between colours). 1. There are four quantum numbers to label each electron: principal quantum number (n) . …. ±2. and this surface is thought of as the spatial limit of the atomic orbital. …. 0. ±l (but counted from negative to positive: -l. l-1. The ground state is an atom’s lowest state. ±1. -l+1. These are unstable and result in the lowering of energy levels by emission of photons. 2. These are wave-like states with 3D shape and amplitude (this form is a direct consequence of the Schrödinger equation.±½ A set of orbitals with the same n are called a shell (in hydrogen all orbitals are in the same shell as there is one electron).0. The electron density (probability of an electron being at a certain point) is given by the square of the wavefunction (however the Heisenberg uncertainty principle limits the ability to know both the position and energy (thus speed) of a quantum particle like an electron): ψψ∗=ψ2 As the electron could be at any distance from the nucleus (although further is less probable. l) spin quantum number (ms) . labelled by letters (called orbital symbols): if l=0 → s orbital if l=1 → it’s a p orbital Remember: Spadoof! if l=2 → it’s a d orbital Page 5 Oliver Bogdanovski . …. Solutions to the Schrödinger equation have exact analytical forms for the hydrogen atom: Ĥψ=Eψ where Ĥ = Hamiltonian (an operator that corresponds to the total energy of the system .Lyman = UV Balmer = visible light Paschen = IR The value of n for each energy level/shell is the principal quantum number.encompasses nature of proton and electron particles and their Coulombic attraction [the electrostatic attraction or repulsion between protons and electrons]) E = energy of the state (a constant of proportionality) ψ (psi) = the wavefunction An eigenstate (or orbital) is an allowed energy (or shell) under the contraints of the Schrödinger equation (labelled by quantum numbers .0. ∞ azimuthal (angular momentum) quantum number (l) . …. and a set of orbitals with the same n and l are part of the same sub-shell. Complete removal of an electron means the electron has been moved to n=∞. 1. however it can undergo transitions to higher excited states by heating or colliding energetically with other bodies. the volume with a 90% chance of an electron being there is called the boundary surface. (n-1) magnetic quantum number (ml) .they are the outcomes or results when solving the equation). …. The energy required to move a valence electron upwards is called the ionisation energy. 3. 2. Multi-electron atoms are more difficult to obtain analytical solutions of through the Schrödinger equation as the electrons repel each other. i and so on This is written as: (n)(orbital symbol)no. then d. h. py and pz. As there are three ml values. These repulsions are considered electronic shielding.g. of electrons e. d orbitals have either a cloverleaf shape (d xy. then f. dx -y ) or two lobes and a torus (dz ). 2 2 2 The Coulombic attraction between the nucleus and electrons leads to a contraction of shells as you move to the right of the periodic table. however the inner orbitals often deflect the outer orbitals (by Coulombic repulsion) resulting in their electron densities peaking further away. and so on Thus the degree of shielding goes s<p<d<f (opposite is degree of penetration) Page 6 Oliver Bogdanovski . there are three types of orbitals: px. dxz. dyz. p orbitals consist of two lobes of electron density on opposite sides of the nucleus with a nodal plane (zero electron density) between them. and do not affect the electrons of an outer shell equally: s electrons of an outer shall have at least one smaller lobe of density closer to the nucleus (inside the region of shielding electron) and hence are less affected as they are more often closer in and not further out the effect is smaller for p orbitals. 2s2 s orbitals are spherically symmetric. requiring more energy to pull the electron out due to the increasing nuclear charge. if l=3 → it’s an f orbital then g. however we can still approximate orbitals that resemble the hydrogen atom. following the aufbau principle. so all their valence electrons reside in Page 7 Oliver Bogdanovski . and this only occurs in two transition metals and the ones below them (Group VI and XI): Cr (Chromium) [Ar]4s13d5 NOT 2 4 [Ar]4s 3d Cu (Copper) [Ar]4s13d10 NOT [Ar]4s23d9 Electron configuration can be written in the “arrows in boxes” method (each direction of the arrow shows a different spin.two electrons cannot have all the same quantum numbers (and hence a maximum of two electrons in the same sub-orbital (same m l). with an exception: in neutral atoms. the 4s is more stable than the 3d and filled up first. Cations are usually done the same way except removing the last added electrons. This follows two rules: Pauli exclusion principle . the reverse is true. The aufbau (building up) principle assembles atoms by adding one electron for every proton (and usually neutron) into the lowest energy orbital free. the 4s is listed before the 3d. A different method uses locations on the periodic table. and this can be remembered by the filing from the top right (first arrow. but in transition metal cations. but different ml) electrons distribute one electron in each orbital alignment (the first spin quantum number) before they go back and fill it up the remaining orbital alignments with the other quantum number o the only exception is when you can get a half-filled instead of a nearly filled as that is more stable. orbitals fill up from lowest energy to highest. and the valence part is given by counting from the left of the table to the element and filling in shells as you go (staying aware of the Cr and Cu anomalies). or by number (which could be replaced by a noble gas configuration followed by valence electrons): Oxygen 1s 22s22p4 [He]2p 4 Once you get to the point where 4s is before the 3d due to less shielding (greater penetration to the nucleus). where the core part of the configuration is given by the noble gas from the period above. Anion ground-state electron configuration is simply adds the number of required electrons to the next available positions. having two different ms) Hund’s rule . and so on). then second.When determining electron configuration (a particular arrangement of electrons).in a subshell of orbitals (same l or orbital symbol. basically not magnetic). resulting in a stronger pull on each electron. whilst still maintaining the nuclear charge. The first ionisation energy is the energy required to remove the least tightly bound electron from a gaseous atom (atom (g) → cation+ (g)+ e. but similar to. nuclear charge increases. Unpaired electrons are attracted more strongly into the field. and are diamagnetic (dia = going apart. whilst the second ionisation energy is the energy required to remove the least tightly bound electron from the gaseous 1+ ion (cation + (g) → cation2+ (g) +e. outermost (n) s. the order of electron removal is outermost (n) p. Paired electrons (two electrons in the same orbital alignment with different spins) are repelled very weakly from a magnetic field. Page 8 Oliver Bogdanovski . dialysis. Anions are always larger than their parent atoms as there is greater shielding (electron-electron repulsions).(g)). extra shells are added and atoms get bigger. If atoms packing into a solid. Small variations occur due to new orbitals being used. but going across from left to right.(g)). Fe [Ar]4s23d6 Fe+ [Ar]3d7 ← note how the other ‘s’ electron moved to ‘d’ Fe2+ [Ar]3d6 Fe3+ [Ar]3d5 In general. causing the 90% density surface to shrink as there is less shielding. and they each have less share of the nuclear charge as there are more electrons. An element’s 2nd IE is always great than the 1st as the nuclear charge per electron will have increased. allowing them to move further away.the d orbitals and it is these that are removed whilst the d remain filled. then the atomic radius is considered half that of the internuclear separation. Going down the periodic table. Paralympics). however these are not significant due to shielding. Successive IEs continue to increase. However they are generally still smaller than cations from the same period due to the larger nuclear charge (they have more protons). then (n-1) d. Size is often measured in picometres (one-thousandth of a nanometre). If an atom contains at least one lone electron (one without an opposite spin) then the paramagnetic effect (attraction) of just one electron is stronger than the total diamagnetism (repulsion) of many electrons. and are paramagnetic (para = distinct from. with a stark increase when the noble gas configuration is forced to ionise. Cations are always smaller than their parent atoms as they form by loss of electrons. and so on. pulling in outer electrons. being the energy change when a gaseous atom gains an electron to form a gaseous anion (atom (g) + e.7 → polar covalent <0. A special case of covalent bonding is metallic bonding. Electron affinity is the opposite of ionisation energy. it is an ionic bond (although this never completely happens.7 → ionic 0.Elements with low 1st IEs usually lose electrons to form cations.4 → mostly covalent (or simply covalent) 0 → non-polar covalent (or simply covalent) In polar bonds. they can be combined to give an overall molecular dipole moment. whilst those with high 1st IEs gain electrons to become anions.(g)). bond polarity can be shown with a dipole arrow (pointing from the positive to the negative (sometimes with a small vertical line at the positive end to make a + shape). lower energy required). being located at the top right of the periodic table. and hence larger negative values are favoured (unlike IE).4-1. however whenever a subshell has reached a filled or half-filled state. IEs decrease down groups (shielding pushes electrons out.represented as zero on the graph as positive values can only be estimated through calculations. EAs are negative as the system loses energy (energy is released. Group II elements have the greatest electron affinity (being large and positive . If main electron density of the bonding electrons moves to a region between the atoms. Some binary polar-covalent compounds don’t Page 9 Oliver Bogdanovski . it is a polar covalent bond (ionic bonds can be thought of as extreme versions of these. where if there difference in the electronegativity of two atoms is: >1. and if it is intermediate (electrons generally closer to one atom than the other). exothermic). Electronegativity is a means to predict which of these a compound is. and is very weakly covalent). it is a covalent bond. The attractive forces between molecules (van der Waals forces) are weak and take little energy to break in melting/boiling processes. As these are vectors. more unstable orbital. Bonding Theory and States of Matter When complete transfer of one or more electrons occurs from one atom to another. and hence the more ionic a substance the higher its melting/boiling point. where the valence electrons are not localised but instead move freely through the metal body. there will be a small jump.(g) → anion. but increase across a period from left to right (greater nuclear charge). not measured) as this would result in starting a new. SiO2) and hence have higher melting/boiling points. of valence electrons . leaving an unpaired free radical electron (e. summing the formal charges gives the overall charge. but instead 3 (AX3) Trigonal they jump from the atom to Planar being bonded and back. bond=1. and this is called resonance. where each atom is represented by its atomic symbol. where lone pair=2. valence electrons are represented as dots around it. Some molecules are stable with an odd number of electrons. Assign the remaining valence electrons to the central atom 5.g. In contrast. we Equatorial d use Valence Shell Electron =blue Page 10 6 (AX6) Octahedr Oliver Bogdanovski al . NO2). In reality the bonds do not flip back and worth. Place the least electronegative element in the middle (except H) 2. Minimise formal charges (formal charge = no. positive charges on least electronegative) Elements in the third period and below can have an expanded valence shall due to the availability of d orbitals. and a line between two atoms represents a pair of shared electrons. not having a total of 8 electrons (e. if unable to balance formal charges. and become electron deficient species.form discrete molecules but networks or lattices with all atoms linked (e. Another means of expressing electron configuration is Lewis electron-dot symbols. negative charges go on most electronegative.g. Al) cannot form Lewis octets in certain circumstances. When completing Lewis structures. Assemble a bonding network using single bonds 3. Note no electron pair is jumping all the way around. some elements (B.number assigned in Lewis structure. Be. and each NO bond length is somewhere Tetrahedr 4 (AX4) between a single and double al bond (approximately calculated by averaging the 5 (AX5) lengths in one of the Axial=gree Trigonal resonance structures). written as shown in the No. Put 3 lone pairs of electrons on all outer atoms except H so they each form a Lewis octet (8 valence electrons) 4. BeCl 2 or BeCl3).g. n Bipyrami To find 3D shape. of Geometrical diagram (or in one structure Name Pairs Shape and stating how many other 2 (AX2) Linear structures possible). To draw a Lewis Structure: 1. there may be more than one way to minimise formal charges. Only in repulsion are multiple bonds considered: multiple bonds are shorter and fatter clouds of electrons. Instead of a bond to a new atom. the actual shape of the molecule is different to its geometry (having one or more outer atoms removed). double or triple bonds. or if there are lone pairs (E).3 in NO3-). The general form of a central atom (A) surrounded by other atoms (X) is AX n. measured in coulomb metres: C m overall asymmetric distribution of electron density) only occurs in atoms where the outer atoms are identical and pull in a net direction. a blue or green sphere could also represent a lone pair. AXn-mEm where n is the number of electron pairs (bonded and/or lone). and the values are directly related (but not exactly proportional) to electronegativity difference. In VSEPR. and they take the place furthest from other lone pairs and bonded pairs. m is the number of LP. may cause the angle to widen (and shorten the others). and thus have stronger repulsion than single bonds. which uses Lewis structures and the repulsion of bonded (BP) or lone pairs (LP) of electrons. Dipol Compou Examp e Geometry Shape nd Class le Mome nt trigonal AX2E bent SO2 Yes planar AX3E tetrahedral trigonal pyramidal NH3 Yes AX2E2 tetrahedral bent H2O Yes trigonal seesaw (remove AX4E SF4 Yes bipyramid equatorial) T-shaped trigonal AX3E2 (remove two ClF3 Yes bipyramid equatorials) I3trigonal AX2E3 linear (triiodid No bipyramid e) AX5E octahedral square pyramid ClF5 Yes AX4E2 octahedral square planar XeF4 No A dipole moment (μ. Molecules with a dipole align in an electrical field (as opposites attract). Dipole moments typically span 0-7×10-30C m. however this is not something we particular care about (only the shape part). and these are treated as one bond. and depending on what is surrounding it. or have different electronegative charges (being different atoms) sufficient enough to produce a dipole moment. This geometry is modified due the hierarchy of electron pair repulsions (from strongest to weakest): LP:LP>LP:BP>BP:BP. This means two neighbouring pairs will deflect.Pair Repulsion (VSEPR). Because lone pairs can replace outer atoms. VSEPR makes no distinction between single. resonance should be treated with an average bond order (being 1. but Page 11 Oliver Bogdanovski . That is. VSEPR rules apply to each central atom (each carbon in the case of hydrocarbons). and so an sp2-orbital is made (with one electron within each box. In larger molecules like hydrocarbons. Overall in methane: Outer atoms (that aren’t hydrogen) also hybridise before bonding (e. and orbital interactions are analogous to the superimposition of waves. VSEPR produces quite accurate results. This leads to the equalisation of energies of the valence orbitals (as they become one orbital) and allows for the greatest possible number of unpaired electrons for bonding. This has been for four electron pairs. however in cases like BF3 there are only three bonds to be made as there are only three free valence electrons. and they should be treated independently. and is called hybridisation.when looking at repulsions as an intermediate between a single bond and double bond. whilst when added to a negative (pink) it is destructive. As electrons can be considered waves. The angles in VSEPR do not match up those in the varying orbital alignments (which are often at 90o to each other) and hence a new model formed by Valence Bond Theory (VBT) is required. Note how positive (blue) with positive enhances the final blue (as they are being added. The new orbital is a composite of the old orbital. when two atoms bond and overlap slightly. constructive). the electron density is the sum of the two parts. their orbitals have wave-like properties. CH2Cl2 .g. Also note that the number of orbitals remains the same (in this case three p’s and one s). except for transition metals and some other molecules. as one p-orbital alignment is ignored (say pz) it does not conform to the Page 12 Oliver Bogdanovski . and the notation in that the three p’s become p3. and the composite being an electron from the fluorine).both chlorines hybridise 3s and 3p orbitals to generate sp3-chlorine). however we don’t need to know these. However. construct π-bonding assembly from partially filled unhybridised p-orbitals We can extend the VBT model to account for double or triple bonds using the unused p-orbitals. Sets of Unused Hybridisa Electrons p-orbitals Geomet Diagram tion (each gold (blue+pin ry lobe) k) sp 2 2 linear sp2 3 1 trigonal planar sp3 4 0 tetrahed ral Sets of electrons is the number of lone pairs plus the number of atoms it is bonded to (so multiple bonds count as much as single bonds). To use VBT we: 1.new energy orbital and remains empty at a slightly higher energy state. d orbitals come necessary to form sp3d and so on. Similarly in BeCl2. apply VSEPR to determine shape 3. as only two orbitals are required. sp2. draw Lewis dot structure 2. For example. the 2s and 2px hybridise to form sp and leaving a vacant 2p y and 2pz (note how because hybridisation occurs in the valence shell there is no number outside of the hybrid orbital). This atomic pz orbital remains vacant. sp3) 4. In elements below the 2nd period. choose the hybridisation model that fits (sp. in ethene: Page 13 Oliver Bogdanovski . and these two adjacent orbitals form a π-bond. However this cannot be explained by VBT. CH2=CH-CH=CH2. and the apparent paramagnetism of some simple molecules like O 2. Extended π-bonding or extended π-orbital overlap occurs when two sets of π-bonds are close to each other (as in butadiene. Being waves. Normal. where alternating double bonds result in extended π-bonds). and into d-orbitals.The electron in the second bond of the double bond sits in the 2pz orbital. and hence we use another new model.and p-orbitals. which simply tell us the side the electron is on. a larger π-cloud of electrons). and hence one s orbital. or grapheme. π-bonds have poorer orbital overlap and hence weaker bonding. In a triple bond. when combining they can be constructive when in phase (called bonding . in addition to the structure of molecules like diborane (in diagram). three p orbitals and two d orbitals are used to make sp3d2. and hence they are different). In larger molecules such as PCl 5 (trigonal bipyramid) and SF 6 (octahedral) hybridisation can go beyond s. in SF6. and they lie around the σ-bond.when two like signs combine) or Page 14 Oliver Bogdanovski . direct single bonds (called σ-bond) have far greater orbital overlap. In resonance structures these are called delocalised π-bonds. For example. and as they are waves have positive and negative amplitude. Atomic orbitals (AOs) are mathematical probability for regions of electron density (determined by squaring the wavefunction). there are two π-bonds (in addition to the σ-bond) which occur at 90 o to each other. the closer the energies between the bonds the stronger the σ-bond. when it is predicted they should be diamagnetic. which accounts for the second bond. MO Theory is based upon the overlap of atomic orbitals. the sulfur must be able to present 6 free places to bond with. In MO Theory. Molecular Orbital (MO) Theory is used to account for this. and hence are stronger. In addition. allowing it to conduct electricity due to the delocalisation of electrons (that is. every two atomic valence orbitals that combine form another two orbitals (unlike VBT where only one was formed. when two opposite signs combine. however if it was period 2 you would use 2pz. two equal-energy orbitals (1s) can produce either a bond (which has a lower energy. Note how the number of nodes is the same before and afterwards in constructive. it is filled from the bottom first. whilst px and py are used for vertical πbonds. VBT does not account for antibonding. 2 2 Page 15 Oliver Bogdanovski . σ*2p. These can be calculated for H2 by the equations: ψbond = (ψ(1s)A + ψ(1s)B) ψantibond = (ψ(1s)A . It cannot be <0 (as bonding electrons always fill first). As there are only two electrons. there is no bond (as can be seen in the case of He2 below. For formality’s sake.ψ(1s)B) This can be shown diagrammatically: Antibonding orbitals (indicated by an asterisk * after the σ) always have one more node than their bonding counterparts. bond order = (2-0)/2 = 1.destructive when out of phase (antibonding . This new electron configuration is written as σ1s . Bond order is also redefined: Bond Order = In the case of H2. and there is one more in destructive. and hence is more stable) or antibond (which has a higher energy and is less stable). positive and negative). however He2+ does exist). pz is used for horizontal σ-bonds. This has all been for elements in the first period. This model can be used to explain the paramagnetism of oxygen as using the aufbau principle (and abiding by Pauli’s Exclusion Principle and Hund’s Rule) we get lone electrons that aren’t paired. but it works much the same in the second period (in the diagram the p-orbitals have been generalised. and as σ1s is more stable it is filled first (labelled as σ1s as there are two electrons). In the bonding of H2. σ2p. If bond order is 0. π2p and π*2p). as there are two bonding electrons and no antibonding electrons. 2py. and hence energies. This is because the 2s and 2p orbitals are similar in radii. or in other words causes them to move further apart in energy. bond energy/enthalpy (the energy required to break the bond) also increases as there are more bonds to break. mixing occurs most where the energies are closest. so as bond order increases.all except Be and Ne as antibonding cancels with bonding). by this theory. C and N have a FLIPPED σ-bonding and π-bonding order. double and triple bonds in more simple bonding theories. 2nd shell. the labels σs and πy are used to show the predominant type. . causing some overlap (particularly in those before and including N) resulting in orbital mixing (or s-p hybridisation) and σ-π crossover. However. so the π-bond is actually filled up first. As the resulting orbitals are not derived from one atomic orbital from each atom in the bond. whilst destabilising the σ2p (from the 2pz orbital). and hence we never think of an “empty” hybridised orbital (whilst MO theory requires unfilled or partially unfilled antibonding orbitals). Li and Be are done normally. As shown in the diagram of energy levels. so valence). however bond length decreases due to electrostatic attraction: Bond Order ↑ Bond Energy ↑ Bond Length ↓ There are two critical factors that determine whether an MO will form and how stable the bonding orbital will be (or how unstable to antibonding orbital is): 1) degree of overlap (more overlap (σ>π-bonds)=greater bonding/antibonding character) 2) similarity in energies of contributing orbitals (a 1s orbital will form a lower energy bonding orbital or even a higher energy anti-bonding orbital with another 1s rather than going with a 2s) nd 2 period elements often exist as homonuclear diatomics (Li2. etc. B2. and there is no MO anti-bonding equivalent in VBT. The bond order in MO is analogous to single. It is important to note that the number of molecular orbitals is Page 16 Oliver Bogdanovski . This stabilises the σ 2s (‘s’ is just the diamond of orbitals. but B. B 2 should be diamagnetic when it shows paramagnetic properties.This is different to VBT as in VBT electrons are involved from the beginning in the hybridisation of orbitals (whilst now they are considered two at a time). occurring in all molecules. it is almost 10× stronger than other intermolecular forces. with a higher SA:V ratio (so more SA) being higher forces as they are more polarisable Dipole-dipole . Intermolecular Forces The state of a substance (the boiling/melting point) depends on the strength and nature of the forces between atoms/molecules of a substance: Dispersion forces . and we label this with δ + and δ. one to create the dipole. molecular shape also determines strength of the force. the other to bond with. Page 17 Oliver Bogdanovski .a molecule with no permanent dipole that can become temporarily polar when collisions induce unsymmetrical electron distributions (distortions of the electron cloud). It follows both Pauli exclusion principle and Hund’s rule. dominating molecular properties (evident in binary compounds as boiling point increases drastically despite smaller molecular size). the greater the chance of orbital mixing (so NO does not have orbital mixing.or an arrow pointing from positive→negative with a perpendicular line through it at the positive end Hydrogen bonding . if both atoms are below nitrogen (as in CN -) there will also be orbital mixing. the more electronegative atom will have lower atomic orbital energies (as energies are negative and it requires more energy to pull out an atom).the strongest intermolecular force is the result of a dipole-dipole interaction between a strongly polarised H (due to high electronegativity of O/N/F-H) and an O. which can be caused by asymmetric structure or peripheral atoms of differing electronegativity. N or F (note: requires two of these high electronegativity atoms. has the form: donor-H⋅⋅⋅acceptor (the donor makes the Hδ+. Additionally. In heteronuclear diatomics. whilst CO does) as the different orbitals (e. the bonding orbitals are lower than the atomic orbitals from which they were formed whilst antibonding is higher. increasing with the number of electrons present (as more electrons means larger molecule which means less electronegative). and they form best when composed of atomic orbitals of like energies. So CO would be the same as N2. Another means of deducing this is by considering what something is isoelectronic (having the same electron configuration) with.two molecules with permanent dipole moments attract each other by the approach of oppositely charged ends. the 1s of one and the 2pz of another) are likely to cross.equal to the number of atomic orbitals that made them. polarisability is the ease of distortion and determines the strength of the force. The bigger the difference in energies (or electronegativity).g. and hence has orbital mixing. larger b means larger molecules. stopping the volume from becoming any smaller until the ratio begins to increase (as pressure is still increasing but volume isn’t decreasing as much) so it surpasses 1. less available valence electrons in N 2 and CH4 compared to halogens). we use the van der Waals equation: The pressure correction term (first bracket) takes into account the intermolecular forces (note: a = strength of intermolecular forces. added as pressure increases). If forces aren’t as strong (for example. then the dip down is not as strong. The volume correction (second bracket) accounts for the molecular volume (note: b = volume of gas molecules. In noble gases. larger a means stronger.and the acceptor has a lone pair of electrons for attraction) Non-Ideal Gases The ideal gas laws make two assumptions: there is no attractive force between atoms/molecules the volume of the atoms/molecules is negligible In a compressibility isotherm (graph). subtracted as free volume decreases). as volume of the total gas decreases the volume of each particle becomes significant. Page 18 Oliver Bogdanovski . we can plot the gas equation ratio (which should always be 1 in an ideal gas) against pressure. At 0 pressure. there are so few intermolecular forces (as molecules are monatomic and hence dispersion forces small). and hence the ratio. however as it increases it deviates below 1 as intermolecular forces play a role. then the effects of volume push up the ratio faster as they come into play with a larger effect sooner. attracting the molecules and reducing volume. If the volume of the molecules is larger. so they don’t really dip down. the ratio is 1. less free volume. To correct for this. However. having both covalent bonding and dispersion forces (that only exist at the delocalised electrons that form π-bonds between the planes) between planes (giving it actually a slightly higher melting point of 3652oC vs. They are brittle as any distortion results in electrostatic repulsion between ions.. after which electrons begin filling antibonding orbitals and weaken the bonds) and the cationic radius of the metal (smaller=closer=stronger). Diamond is an sp3-hybridised 3D network with only covalent bonding. and depends on the charge of the anions and cations (being greater when the number is bigger) and the size of the cations and anions (decreasing size leads to a higher charge density and hence higher melting point. and their melting point is dependent on these forces (although it is generally low). larger intermolecular forces producing higher points. They are electrical and thermal conductors. and the melting point is dependent upon the number of valence electrons (more means greater forces. Despite lack of covalency. dipole forces and/or hydrogen bonding. Atomic solids are held together by just dispersion forces. and malleable/ductile as the cations can be arranged anywhere in the electron cloud. Page 19 Oliver Bogdanovski . Molecular or atomic solids are made of covalently bonded atoms or free atoms. or irregularly to give an amorphous solid (disorder) like glass. up until after the middle of the d-block. Ionic solids have electrostatically attraction cations and anions that drive it to become electrically neutral. Condensed Phases of Matter Solids have fixed shape. the kinetic energy energies of the molecules are at a point where solidification and liquidation are equally possible (also with a normal melting point). held together by dispersion forces. At the melting point. and if this occurs at P=1. 44 oC. increasing charge density similarly). At the boiling point of a substance.013×10 5 Pa (1atm) it is the normal boiling point. The atoms may pack in a crystalline solid (long range order) like silica/quartz. whilst graphite is an sp2-hybridised 2D network. 3550oC). melting points are quite high. Networked/covalent solids have far higher melting points (like silicon. In metals. also important is if they are a similar size it tessellates better. there is a sea of mobile valence electrons about a regular array of metal cations.Both melting and boiling point can be used as measures of intermolecular forces. They are hard and non-malleable (held in position). despite both being sp3-hybridised) as there are many more bonds to break. Thus they can have a wide range of melting points. 1410oC) than molecular solids (like phosphorus. high density and low compressibility due to the strong bonding between the atoms. the intermolecular attractive forces balance with the kinetic energy of the substance. Thus the rates of escape and capture from a phase depends on the kinetic energy and intermolecular forces. and if this occurs at 1atm this is the normal boiling point. as increasing kinetic energies allows greater movement by overcoming intermolecular forces All substances have a kinetic energy distribution.dependent on strength of intermolecular forces (slows it down) and molecular shape (more surface area means more places to have forces or to bump into each other).Liquids are one of the rarest phases. however eventually an equilibrium is reached where the number of molecules that leave the liquid is the same as the number of gas molecules that collide with and are recaptured by the liquid. so even in a liquid phase some will continuously vaporise to become gaseous. The temperature at which the vapour pressure of a substance in an open container reaches the external pressure is called the boiling point. Phase Changes Phase changes depend on intermolecular and bonding (intramolecular) forces. leads to meniscus Viscosity .resistance of a liquid to increase its surface area due to cohesion from the intermolecular forces between the molecules. They have three important properties: Surface Tension . being the narrow phases where kinetic energy means the substance cannot remain independent but it higher enough to ensure free movement. The partial pressure of a liquid in a closed container gradually increases once the system has been sealed as some gas molecules are released. Phase changes require energy. They have a specific volume like solids. with surface molecules being pulled back into the main body Capillary Action . but are fluid like gases.adhesive (with cohesion) that leads water to climb through small-diameter tubes. The partial pressure of the gas above the liquid at equilibrium is called the vapour pressure of the liquid. and hence as heat is added at particular changes of phase the energy is not added as temperature but used as kinetic energy to overcome the intermolecular forces. Page 20 Oliver Bogdanovski . Vapour pressure is approximately proportional to the “a” constant from the van der Waals equation. Hence temperature does not increase at these phases. also dependent upon temperature. only limited by gravity. at which point it becomes a saturated solution. the solute dissolves in the solvent (if soluble) until no more solute can be dissolved. it becomes a supercritical liquid.013×105 Pa 5) Draw lines linking the points (starting at (0. As temperature increases. In a liquid. After the critical temperature (at the critical point. decaffeinating coffee beans and fat-reduced potato chips. and hence is used for extracting essential oils from plants. hence increasing its density. having the higher levels of diffraction of a liquid (although not entirely) but no line distinguishing gas from liquid. Solutions could also be gas-gas or solid-solid (alloy) combinations (however we’ll only study liquids).Phase diagrams describe the most stable phase behaviour of a substance across T and P. This looks like a cross between a liquid and gas. Don’t forget to learn transitions between phases. Properties of Solutions A solution is a homogenous mixture of two or more pure substances. liquid and gas is the triple point. as ice takes up more volume and hence increasing pressure (decreasing volume) would convert from solid to liquid at constant temperature). When the density of the liquid and gas is the same. Example: supercritical CO2 diffuses rapidly (even through solids) and transports material quickly due to its low viscosity (plus disposal is easy). the gas will not condense into a liquid at any pressure. Lines represent phase boundaries (states occur at equilibrium). the critical temperature is determined by the strength of the intermolecular forces). The point of equilibrium between solid. At a given point. There are two main thermodynamic factors that determine solubility: Bond energies Entropy (disorder/chaos) Page 21 Oliver Bogdanovski .0)) to the extremes (except stopping at the critical point) If temperature is high enough (past the critical temperature). at constant pressure adding heat will not change the temperature of the substance until it has been completely converted to the new phase (as seen in the diagram on the previous page. no amount of compression can cause liquefaction/condensation. The line between solid and liquid is near vertical as it is almost independent of pressure (however note this would go the other way in water. pesticides from meat for analysis. the density of the liquid becomes smaller whilst more molecules are added to the gas. To sketch a phase diagram: 1) Draw P and T axes 2) Place triple point in lower left quadrant 3) Place critical point (if given) in upper right quadrant 4) Plot melting and boiling points at P=1. solute-solvent. Raoult’s Law states that if the solution is sufficiently dilute. As the total vapour pressure is the sum of the partial pressures of each species (which can be expressed diagrammatically): Ptotal = XAPA + BBPB Page 22 Oliver Bogdanovski . however in solutions we cannot made this assumption as density is higher and intermolecular forces are highly influential. preferably both). so there is a substantial energy cost when “hydrating” a solute. the vapour contains molecules of each species. and we can calculate the vapour pressure of a mixture by assuming the solution is ideal. An ideal solution is one where all intermolecular forces (solute-solute. hydrogen bonding is strong. and the substance will only dissolve if that energy is repaid. The properties of gases can be modelled under the ideal has law. In aqueous solutions.The process of a solid dissolving in a solvent is scarcely favoured by entropy. However water also already contains open holes in its network of loose hydrogen bonds at room temperature. Solutes can dissolve if they are ionic (strong ion-dipole bonds) or ionise in water. Bond energies are therefore the determining factor. Instead solution composition and the properties of the parent species are the best guides for prediction. form hydrogen bonds (having either H-bond donor or acceptors. we can say Psolution=Psolvent-(Xsolute)(Psolvent) or: ΔP = (Xsolute)(Psolvent) When two or more components are volatile. Non-polar solvents dissolves solute predominantly through dispersion forces. solvent-solvent) are equivalent. making the influence of temperature and pressure hard to predict. their energy overall is lowered and hence excess energy is produced. Using Xsolvent=1-Xsolute. or a polar to make strong dipole-dipole bonds (remember: like dissolves with like). and hence requires very little energy. however it also releases energy as once solute-solvent bonds are formed. the vapour pressure of the pure solution multiplied by its mole fraction is equivalent to the vapour pressure of the solvent (and hence total solution): Psolution = (Xsolvent)(Psolvent) Adding a non-volatile solute to a volatile solvent increases the boiling point of the solvent (as boiling point is the temperature at which the vapour pressure of the substance is equal to the atmospheric pressure). It consumes energy to separate the solute-solute affinities by overcoming them (so the solids can slot in). The composition of a vapour above a mixture of solvents is usually different from the solution (as it is richer in more volatile species). which in the general equation aA + bB ⇌ cC + dD is given by: Π is like Σ. it is like multiplying by -1. and hence we can use distillation to separate solutions. When adding two sequential reactions (like equilibriums that lead into each other or redox reactions) you Page 23 Oliver Bogdanovski . the reverse of dissociation). This is how crude oil is separated into petroleum. like the 2NO2 (brown) ⇌ N2O4 (colourless) in the atmosphere (dimerisation. the binding of O2 to iron within haemoglobin. K is dimensionless and has no units. and the dissolving of CO2 into oceans. We can plot concentration as a function of time to observe equilibrium. resulting in a positive deviation. the concentration of the products and reactants is constant. If you multiply the stoichiometry by n. except means product of rather than sum of. more will be stored in solution and there will be a lower vapour pressure (negative deviation). if they are stronger. then the vapour pressure will be higher than expected (as less is being stored as the solution). but the rate of the forward reaction is equal to the rate of the reverse reaction. so a fractionation column is used. however this does not mean the reaction has stopped. Equilibrium There are many natural instances of equilibrium. Conversely. where the high surface area means there are many mini evaporation-condensation cycles.If the A:B intermolecular forces are weaker than A:A and B:B. Hence the equilibrium constant must be associated with a specific stoichiometric chemical equation. Once a dynamic equilibrium has been reached. gasoline and other constituents. If you reverse the chemical equation. The equilibrium constant (K) is used to define the ratios of concentrations at which equilibrium will exist. you change K by the power of n (so multiplying by a half means K is square rooted). and they do not depend on which side of the reaction you begin with. so you take the inverse (flip) K. It is not practical to do repeated distillations to achieve a complete separation. then adding or subtracting a multiple of x that reflects the stochiometry of that substance in the equation) 3) Equilibrium = Initial + Change (gives concentrations at equilibrium) 4) Using these values as your concentrations. To calculate concentrations from the equilibrium constant use ICE by writing out the chemical reaction and then underneath write the: 1) Initial concentrations 2) Change in concentrations (by working out which way the reaction will go. To convert between them. A small K means the equilibrium favours the reactants. letting x=0 when subtracting from larger numbers (rule of thumb is when x<5% of this larger number). find which value is impossible . Likewise. 10-8). Therefore. let it equal your K value. whilst a large K means the equilibrium favours the products. The above formula can also be done in terms of pressure for a has (as pressure is proportional to concentration as PV=nRT and we can divide by V to get P=cRT). giving us K p (note this number will be different to Kc but works similarly). varying amounts will render the same pressure and concentration. as the equilibrium is independent of the amount of solids present.a negative value means the reaction goes the other way and may be impossible. The reaction quotient (Q) is calculated in exactly the same as K. If Kc is small (e. then it is likely it will be small on the top. or values bigger than the amount of what you are subtracting from are impossible too) 5) Substitute in x to find final concentrations To avoid having to solve complex calculations. Page 24 Oliver Bogdanovski . then simplify. then solve for x (if you have a quadratic. sub into the equilibrium constant expression. In heterogeneous equilibria (where the reactants are not all in the same phase). except it uses the current concentrations rather than the concentrations at equilibrium. the amount of product produced (x) is small compared to the amount of reactants left. which can be used to show (although you can just do this first principles): Kp = Kc (RT)Δng where Δng = total mol(products) . if pure solids or liquids are present they are not included in the equilibrium constant expressions (as they have a concentration of 1). so we can approximate it to 0 on the denominator.g. that is. we can use small x approximations.total mol(reactants) Note that the units of R change with the units used. if K c is large. sub in the alternate value (from P=cRT) into the equilibrium constant expression (the bit K equals) above.MULTIPLY the K values together. it will shift to the right (this can also be used to predict which way a reaction will go) Pressure . if Q<K. like the production of ammonia for fertiliser (Pt catalyst).changing the concentration of the reactants or products changes the value of Q. removing NO in vehicle exhaust (Pd oxide). it has no effect on the partial pressures of each species. and cracking petroleum (zeolite). then treat heat as part of the reaction by adding it to the appropriate side (endothermic is release. related by the van’t Hoff equation which can be integrated (this can be used to calculate a new K. the position of the equilibrium will shift in a direction that tends to reduce that change. increasing temperature will make a smaller K): Adding a catalyst will greatly accelerate a reaction without being consumed. however they do not appear in the final overall reaction and therefore cannot affect the equilibrium position of the reaction. only the rate of the reaction.note three effects (works similarly to concentration) o adding/removing gas or product (same effect as doing so in terms of concentration as P ∝ c) o changing the volume of the container (note in diagram NO2 diminishes twice as fast as N2O4) o adding an inert gas (NO EFFECT as whilst it changes total pressure of the system.Le Chatelier’s Principle states: If a change is imposed on a system at equilibrium. They do this by providing an alternate reaction path/mechanism with a lower activation energy. This is important for all modern chemical products. and they are important in biology. disturbing equilibrium by changing temperature is fundamentally different as it changes the equilibrium constant. more products need to be formed and the reaction will shift to the right. whilst if Q>K.determine if reaction is endothermic or exothermic (ΔH<0 → exothermic). We can induce this in three different ways: Concentration . doesn’t increase number of collisions) Temperature . so add to products). note in an exothermic reaction. Page 25 Oliver Bogdanovski . whilst a base contains an OH that ionises in water to give an OH . Equilibrium constant values vary from 10-20 to 1030. Hence: pH = -log[H3O+] (or [H3O+] = 10-pH) pOH = -log[OH-] pKa = -logKa From this we can show that because [H3O+][OH-] = 10-14: pH + pOH = 14 Strong acids and bases dissociate completely in water (use arrow. acting as both acid and base. At 25oC. Brønsted-Lowry’s definition is that an acid is a proton donor. and thus the products are also conjugate acids and bases themselves (as the species are in equilibrium). and hence have the equilibrium constants: (acidity constant) Page 26 Oliver Bogdanovski . Water is unique as it is amphiprotic/amphoteric.ion. and hence their conjugate species do not react to any measureable extent with water. but it is solvated by surrounding water (all the exact nature of it is still the subject of research) and forms hydrogen bonds with the oxygen from other water/hydronium molecules. we use the log scale (and apply a negative to make the small values we commonly deal with positive). not equilibrium). the equilibrium constant (also called the autoprotolysis constant for water due to its self-ionisation) for pure water is: Kw = [H3O+][OH-] = 10-14 + H as a bare proton doesn’t really exist. however this didn’t explain NH3 being basic.Acids and Bases Arrhenius’s definition of an acid was that it contains an H that ionises in water to give an H + ion. and due to its large breadth. and thus a base is a proton acceptor. Weak acids and bases react with water but dissociate incompletely as an equilibrium is established. As the protons may have different bond strengths. it is acidic). This means it has both an acidic and a basic end. we can only make a small x approximation for [HA] when the initial [HA] is 400×Ka. consider the anion and cation differently. When looking at the pH of salts. the pK a for removing the first is different to the second (as the molecule is now slightly negative and has a tighter control on its H +). and hence will Page 27 Oliver Bogdanovski . and rather than using the initial [H3O+] or [OH-] of water as 0 (as we have been approximating). and thus making it a strong acid). if the concentration of the acid or base is less than 10-5. and so on. converting to Ka and Kb. then the autoprotolysis of water must be considered. they become amphiprotic (becoming either H 2A or A2-). Those attached to more electronegative atoms (like oxygen) will have a lower pKa and hence dissociate more (as the Ocan then H-bond with H3O+/H2O. Note that when solving equilibriums with acids and bases. they will be extremely weak conjugates. However if both ions are weak. the anion or cation (respectively).+ H2O ⇌ HA + OHKb + 2H2O ⇌ H3O + OH Ka × Kb = Kw = 10-14 Therefore: pKa + pKb = pKw = 14 Many acids (particularly organic ones) have more than one proton that can react with water. Even when there are identical protons. the amino acid glycine). they have different values for pKa. Weak acids and bases have moderate-strong conjugates. If they form part of a strong acid or base.+ H3O+ Ka A. making it overall neutral (e. base with conjugate acid . pKa (2). For an acid and its conjugate base (or this could be written vice versa. Whilst in the form HA . These are written as pKa (1). the equilibrium will shift left to minimise the change.g. and similarly bases are stronger with a higher K b and lower pKb.pKa (1)). and hence not react with water nor alter pH. if Ka > Kb. filling in this space and limiting the ability of an H+ to come back and bond. If we were the add CH3COONa. be Le Chatelier’s principle. and then the larger equilibrium constant will win out (as it produces more of those products). Consider CH3COOH (aq) + H2O (l) ⇌ H3O+ (aq) + CH3COO.(losing a proton in a diprotic acid).same thing): HA + H2O ⇌ A. then we need to consider their K’s (NOT pK). we must now use 10-7. and hence are polyprotic. Zwitterions are molecules that contain both positive and negative charges (that do not combine). which can raise or lower the pH.(aq). and the one with the greater equilibrium constant will produce more product and hence determine if it is acidic or basic (that is. determining if it is an acid or base. and you can determine whether they will go acidic or basic by looking at the pKa (2) and pKb (14 .(basicity constant) Acids are stronger (easier to remove protons) with a higher K a but lower pKa. Also. move away from disassociation and always tend towards neutral.2-7. meaning pH=pKa and hence it is a buffer.6 is symptomatic. Page 28 Oliver Bogdanovski .9. There are many important buffers in nature.or H3O+ (depending on what you are titrating) as the amount of acid or base (respectively) that you had initially.): pH = pKa + log = pKa + log The common ion effect also provides the basis of buffers. Any mixture of weak acid and conjugate base (or vice versa) will produce a buffer. in weak acidstrong base titrations it is >7. and amino acids (which act as an acid. Thus from the Henderson-Hasselbalch equation. pH=pKa. but takes longer).4). Consider: HA + H2O ⇌ A. The equivalence point is the point at which you have the same number of moles of added OH .9-7. for example the blood buffer between carbonic acid and hydrogen carbonate (pKa=6. [base] = 10×[acid] (so pH is correct for HendersonHasselbalch equation). the current [acid]=[base] (as half of the acid has been reacted into its conjugate base). however the capacity of the solution to resist a pH change depends on the relative concentrations. In strong acid-strong base/strong base-strong acid titrations it is 7. Titrations are used to determine the concentration of an unknown solution by reacting a known volume with a standard solution (known concentration) of a reactant.2). Rearranging our equilibrium constant expression for K a in terms of H3O+ and taking the -log of both sides we get the Henderson-Hasselbalch equation which tells use directly the pH (useful for common ion effect. Halfway to the equivalence point. and fatal outside of 6. pKa≈7 as various). The pH of a buffer can be calculated using the Henderson-Hasselbalch equation (or ICE. To get within these ranges. and thus minimising the disturbance of the acid or base. Blood outside the range 7. This is shift in equilibrium is called the common ion effect. uses initial conc.+ H2O ⇌ HA + OHAdding a small amount of base (OH -) or acid (H3O+) will result in the equilibrium shifting in the other direction (however H2O concentration increasing is irrelevant as it is a liquid and hence its concentration is always 1). Usually the standard solution is in the burette and titrates a known volume that has been pipetted into a conical flask. hydrogen phosphate and dihydrogen phosphate (pKa=7. The buffer is most stable the weak acid and conjugate base are added in equal concentrations as deviations on either side (adding either one) will be equal.+ H3O+ A. whilst in weak base-strong acid titrations it is <7. whilst isolated systems cannot pass either mass or energy) Surroundings . heat) flows across There are four thermodynamic state functions (only depend on current state.the place where the energy (e.g. whilst 1 Calorie=1000 calories. only ΔU (in the cases shown due to bond energies) Page 29 Oliver Bogdanovski .system + surroundings Boundary . which helps us understand the direction of chemical change (including how to approach equilibrium) and how much energy it takes to drive a chemical reaction.Acid-base indicators are weak acids or bases that change colour with pH. System . electronic. like heat and work. absolute U cannot be measured. whilst a Lewis base is an electron-pair donor (inverse of proton acceptor). For example.sum of nuclear. different materials will yield different temperatures for the same energy.everything else (we only worry about this if affected by the system. Similarly. whilst closed systems can pass energy but not mass. The pK In or endpoint should be close to the equivalence point in a titration. A Lewis acid is an electron-pair acceptor (inverse of proton donor). vibrational. They react with water (or the solution) to gain or lose protons and hence change colour. like in thermal contact) Universe . not the pathway taken. Heat is the amount of energy transferred between two objects. not affected by how it cam to be or will be. hence the change in each is only dependent on final-initial. as opposed to path functions that depend on the pathway taken. heating two differently sized bodies of water with the same amount of energy will result in a higher temperature in the smaller one.the reaction (or thing) we are interested in (open systems can pass energy/mass across boundaries into surroundings. phenolphthalein has a pKa of 9.g. as some method may require more of one or the other): Internal Energy (U) . whilst absolute/thermodynamic temperature is what can actually be measured (in K).184J (the energy required to heat 1g of H 2O by 1oC). generally occurring at pH = pKa (indicator) ± 1 (e. and as little indicator used as possible is better to avoid changing the pH. Thermochemistry Thermochemistry is the study of energy change in a chemical reaction. rotational. translational and interaction energies of all the individual particles in a sample of matter.4). however the strengths of these acids and bases aren’t as readily quantified as Brønsted–Lowry counterparts. Note 1 calorie = 4. it will expand to atmospheric pressure and move the piston up. Alternatively. not ΔU.measure of the number of ways energy is distributed throughout a chemical system (related to enthalpy) Gibbs free energy (G) . In pistons. Hence work is dependent upon the change in volume of the pistons and the opposing pressure. and hence is used in the form of heat or movement. determined by measured temperature change under constant pressure Entropy (S) . simply transferred.related to the heat absorbed or produced in a chemical system.relates enthalpy and entropy The First Law of Thermodynamics states: ΔU = q + w where q = heat absorbed by the system (J) w = work done by the system (J) Work is the energy required to move something against a force.pΔV gives us the enthalpy or heat of reaction: ΔH (=q) = ΔU (or ΔE) + PΔV Many chemical reactions occur under constant pressure (not constant volume) like laboratory experiments in open containers. atmospheric reactions and combustion reactions that aren’t in closed systems. spring energy or piston energy (the main focus of thermochemistry). to measure ΔH by having constant pressure. biological reactions in living systems. light. This comes from the conservation of energy. given by: w = -pΔV (don’t think we need to use this). Calorimetry can a bomb calorimeter to measure ΔU (usually for combustion reactions) by having a thermally insulated constant volume from the rest of the universe and a known heat capacity (and hence we can predict the effect of the surroundings). This energy can be electrical. we can use a “coffeePage 30 Oliver Bogdanovski . Enthalpy (H) . as energy cannot be lost or gained. if a compressed gas is placed under a piston. Heat can be determined from temperature by: q = cΔT where c = heat capacity (dependent upon both the type and amount of substance present). so measuring the heat change would give ΔH. For pure substances: q = mcΔT q = nCΔT where c = specific heat capacity (J/K/g) C = molar heat capacity (J/K/mol) Rearranging ΔU = q . occurring at 1 bar (105 Pa). Atomisation enthalpies can be found by summing all the individual bond enthalpies. For an element in its standard state (e. and enthalpy of atomisation (ΔHatom>0 as you have to put in energy to break the bonds) is splitting a substance into each individual atom (not even into H 2. whilst a non-spontaneous reaction must constantly have energy applied for it to run. Now we use enthalpy/heat of formation (ΔfHo). The other criterion is entropy. or their standard state. However in this case it is only approximate as bond energies depend on the entire molecule. In any chemical reaction (assuming states remain the same). we look at the energy required to make the products and subtract the energy required to make the reactants: ΔrH = Σ ΔfH (products) .g. such as combustion. and this is denoted by a o (e. So instead of using bond enthalpies (which are hard to measure as isolated atoms in the gas are difficult to measure experimentally). This is Hess’s Law: if you add up chemical equations to form a new overall equation. ΔfHo = 0. not just the two atoms involved. O2 (g). then the overall enthalpy is the sum of the individual enthalpies. Fe (s)). Page 31 Oliver Bogdanovski . and the more exothermic the more vigorous). we can approximate the enthalpy by finding the atomisation enthalpy and then adding the negative values of the product’s bond enthalpies (basically final-initial but using an alternate pathway). The thermite reaction is used to weld railroad tracks (when there is no electricity). 298K and 1M. enthalpy of combustion (ΔHc<0 as you are releasing energy by forming new bonds) is burning in oxygen. but in actuality the bond energies are lower).g. ΔH is not the only criterion for spontaneity (despite most exothermic reactions (ΔH<0) being spontaneous. and usually used for liquids in heat of dissolution. for example the thermite reaction (Fe 2O3 + 2Al) is highly exothermic so we know the safety precautions to use.cup” calorimeter that is also thermally insulted. heat capacity of solids and aqueous reactions. A spontaneous reaction means once it has started it will continue on its own. In this. and the values on tables are mere averages (for example we would predict CHClBr 2 wouldn’t decompose in the stratosphere as bond energies appear higher than the energy of the light there. we use atoms in the state they are most commonly found in. and a variant is used as an igniter for rocket fuel.Σ ΔfH (reactants) We can use this to predict the properties of different substances. but 2H). as endothermic reactions like that between barium hydroxide and ammonium nitrate can also be spontaneous. or otherwise it will stop. ΔHo). We can have enthalpy of vaporisation (ΔHvap>0 as you have to overcome intermolecular forces) is the energy required to go from liquid to gas (in J/mol). this makes sense as G will only decrease. ΔSuniverse > 0. like diffusion). and hence if a reaction will be spontaneous at 298K.If we look at H2O (s) ⇌ H2O (l). as the molecules can spread further apart.02kJ/mol (hence endothermic. add heat to left). ΔH=6. This is because energy (heat) is flowing from the surroundings to the system (or vice versa). and this energy flow is key to understanding spontaneous change.TΔSsystem < 0 This is called Gibbs Free Energy. it can be shown that for a spontaneous process: ΔG = ΔHsystem . we can deduce whether the ΔS of a reaction will be positive or negative (by doing final-initial). At T>273K. Knowing which is greater. and that minimum occurs at equilibrium. For ALL chemical reactions. Using data from tables (having ΔfH0 in kJ/mol and S0 in J/K/mol . we can then determine the difference between reactants and products. Entropy is the tendency for energy to spread out as far as possible (so having a hot object next to a cold one will result in energy moving from the hot to the cold until they are equal . As ΔG<0 for any spontaneous reaction. it will shift to the right. Therefore entropy is greater in: gas > solid particles spread further solution > solid + liquidenergy localised in solid spreads gas + liquid > solution energy spreads even further in gas C2H6 > CH4 more bonds to spread energy across 3mol > 2mol entropy ∝ amount (spreads across more molecules) 20K>10K more kinetic energy=collisions.REMEMBER UNITS). or the energy is spread across more molecules. The energy can spread out in two main ways: the molecules themselves move further apart. and using q=ΔH. We can find entropy by: ΔS = The propensity for energy to spread out is known in the 2nd Law of Themodynamics: ΔSuniverse = ΔSsystem + ΔSsurroundings For any spontaneous process. spreads energy Note that phase (position entropy) tends to dominate molecular complexity. whilst below this it will shift left. Standard entropies (S0) are the entropy change from T=0K (where S=0) to T=298K (25oC). Using the above value of ΔS for surroundings. a measure of the spontaneity of a process and the useful energy available from it.a result of random probability. If the system does not form an Page 32 Oliver Bogdanovski . a graph of ΔG against the mole fraction of a reactant/product will have a minimum. Group 2 always +2 3. only used for convenience). If less raised. K<1. Galvanic Cells The concept of oxidation from reactions with oxygen. The relationship between ΔGo and the equilibrium constant (K) is: ΔGo = -RT ln(K) where R = universal gas constant (J/mol/K . and therefore have oxidation numbers of 0. down. but the parts within those molecules and ions are equivalent to the ionic charge (or charge it would be if ionic). If basic.to cancel H+ (cancel any additional H2O) Page 33 Oliver Bogdanovski . it “raises” the graph and the equilibrium shifts towards the reactants (as more energy is required to shift towards the raised end). As we can see in this case of the equilibrium. and always below both sides. in which the metal was oxidised to form an ionic compound (although originally thought to be equal sharing of electrons. Then follow the rules in this order: 1. or horizontal like water going between solid and liquid at 0oC. F is always -1 2. the oxidation number decreases. Note that the reducing agent reduces the other species and it itself is oxidised (and vice versa). when one side has a higher value of ΔG0 than the other. Multiply each half-reaction by an integer for the same number of e4. Free elements are neutral. O is usually -2 (except in peroxides where it is -1) 4. Balance atoms other than O and H b. Balance charge by adding e3. Group 1 is always +1. and the reactants are favoured. deducing properties and identifying redox reactions. H is -1 with metals and +1 with non-metals To balance redox reactions we: 1. Oxidation numbers are used for naming compounds. Oxidation is loss. check balanced a. add OH.equilibrium. the equilibrium will be more centred. Add half-reactions (including states). Balance O by adding H2O c. reduction is gain (of electrons).make sure G uses same units) When ΔrGo>0. it will just be a straight line from the reactant to product (and depending on which direction it goes it could be diagonally up. as do neutral molecules. Balance atoms and charges a. including the sign. whilst in reduction the oxidation number decreases (oxidation numbers are also used for covalent substances but are not ionic charge. Halogens are usually -1 5. In oxidation. Determine half-reactions 2. Balance H by adding H+ d. cancel excess. however we now know electron density is higher on the oxygen). shown in the graphs. The activity series shows the order of most likely to be oxidised (or more correctly. so it was initially replace with a normal and then saturated calomel electrode. regardless if active or inactive. the strongest reducing agents). the middle salt bridge ): Using a table of cell potentials (E 0 (V or J/C . Generally their reactions involve a gas or another ion. The shorthand nomenclature for standard cell notation is (note it shows the direction of reactions/flow of electrons. Electrodes are always placed on outside of the shorthand notation. Note that unlike the equilibrium constant. The tables provided are for reduction potentials (not oxidation). so now we use a silver/silver chloride standard electrode. and if it shifts to the right the cell potential Page 34 Oliver Bogdanovski . When the electrodes themselves are part of the chemical reaction. We can also use inert materials like graphite (often used for halogen gases) or platinum. we use a standard concentration in E0. The opposite occurs at the anode. A spontaneous reaction always has E0>0. Initially a standard hydrogen electrode was used to make measurements off. electrons are transferred from one element to another.the number of joules transported by 1 amp in 1 second)). where E0=0. we can add the cell potentials together to find the overall potential of the reaction by determining their direction. In redox reactions. and we can harness these electrons by separating the half-reactions in a galvanic cell. The higher species on the reactivity series determines the direction of the spontaneous reaction. being 1M. this does not depend on the stoichiometry. Using a number line. As electrons are gained (reduction) through the circuitry in the cathode. and knowing which reaction is more positive. called inactive electrodes.22V. we can deduce the other electrode’s standard potential. They conduct electrons. balancing electrons and summing. but do not partake in the reaction. and hence multiplying by a specific number does not change the cell potential. so everything will be backwards and upside down from HSC. however this is difficult to replicate accurately (as concentration may vary with the gas). Varying the concentration will involve Le Chatelier’s principle. cations in the solution bump into these electrons and become part of the solid. however this contained mercury. As concentration affects cell potential. they are called active electrodes. × ln(Q) where Ecell = the maximum potential a cell can generate (V) E0 = cell potential if c=1M R = 8. We can also use this to determine the concentration of a cell by measuring it against a cell of known concentration (usually 1M) and measuring the cell potential. Concentration cells are also used in nerve signalling. the anode is now the other electrode which is becoming positive (as it is now losing electrons). the cell potential is constantly lowering (as less reaction is happening). and Ecell=0. so a larger E0 is produced): E0 = ln(Kc) Using the relationship ΔG = -RT lnK: ΔG = -nFE0 Using the relationship between E0 and concentration from the Nernst equation. This is quantified in the Nernst Equation: Ecell = E0 .will increase. Forcing the electrons in the opposite direction (that is. A similar thing can be done with other ions for ion selective electrodes (to measure the concentration of particular ions). where the halfreaction in each cell is identical but they consist of different concentrations. The values are proportional to a log scale. against the spontaneous reaction) is called electrolysis. so plotting Q=10x along the bottom will produce a decreasing line. whilst shifting to the left it will decrease. E cell<E0. This is how pH meters work (comparing 2H+ (aq. we can build concentration cells. forming an electrolytic cell.note units) T = temperature (K) n = number of electrons transferred per mole of reagent F = Faraday constant = 96485C/mol (on data sheet) = charge of 1 mol(e-) Q = reaction quotient (current ratio of [products]/[reactants] Alternatively. Therefore (this makes sense as a larger K favours products. 1M) + 2e. Page 35 Oliver Bogdanovski . until it stops. the anode was already negative.× log10(Q) If Q>1 (more product than reactants). at standard conditions (T=25oC): Ecell = E0 . and the converse is true. As the reaction approaches equilibrium. In a galvanic cell.→ H2 (g) or more commonly a silver/silver chloride reference to an unknown solution and measuring current can be used to calculate concentration and hence pH). and electrons flowed from it to the cathode.314 J/K/mol (universal gas constant . As oxidation always occurs at the anode. and energy production and storage in cells. ion pumps across cell membranes. which can be used to deduce the number of moles of a substance being reduced or oxidised. We can divide this q (C) by Faraday’s constant (C/mol) to find the number of moles of electrons.carbon cathode coated in MnO2 (with graphite powder for conductivity). OHelectrolyte.non-reversible (can’t charge) o Dry Cell .reversible and rechargeable o Lead-Acid . NiO(OH) anode. t in seconds).44V Page 36 Oliver Bogdanovski . It consists of two sets of reactions: Anode 2Fe → 2Fe2+ + 4eE0=+0. with graphite electrodes surrounded by platinum catalysts The oxidation of a metal to its oxide is often spontaneous (as they are generally exothermic).light with high cell potential (meaning little is needed) with Li anode and MNO2 cathode Fuel Cells .uses alkaline environment (KOH electrolyte) to prevent build up of gas and preserves the zinc electrode Secondary Batteries . and Zn as active anode.→ H2O). a paste of NH4Cl and ZnCl2 as an electrolyte. ammonium gradually turns to ammonia which evaporates away o Alkaline Battery . in grams) liberated at an electrode during electrolysis is proportional to the quantity of charge (q.Faraday’s First Law of Electrolysis states that the mass of a substance (m. Oxidation occurs through an active anode (the Fe) to form a pit.Cd anode.which travels through the metal. There are three main classes of batteries: Primary Batteries . in Coulombs) passing through the electrolyte: m ∝ q Faraday’s Second Law of Electrolysis states the number of Coulombs needed to liberate one mole of different products occurs in whole number ratios: q = It (I in amps. same cell potential as primary batteries so can be used interchangeably o Lithium . The most economically important corrosion is that of steel (more specifically. or structural supports like bridges).fuels/chemicals can constantly be passed into the battery o reactants are burnt (overall like combustion). the iron inside) as it results in loss of structural strength (rust holes in cars. CH4. cathode: O2 + 4H+ + 4e.alternating Pb and PbO2 plates that provide large surface area to H 2SO4 electrolyte (delivers large currents) o Nickel-Cadmium . however the two half reactions (anode: H2. and yielding e. at which point Fe located elsewhere acts as an inactive cathode to reduce O 2 to OH-.. etc. preventing oxygen from reaching the metal. Page 37 Oliver Bogdanovski . and iron rusts more quickly at the seaside (more salt=more conductivity for salt bridge). Electro-refining is the principle method of obtaining Cu of a high purity.→ H2O E0=+1. and hence less easily reduced metals remain in solution.23V Overall 2Fe2+ (aq) + ½O2 (g) + 2H+ (aq) → 2Fe3+ (aq) + 0 H2O (l) E =+0.Cathode O2 + 4H+ + 4e.23V Overall 2Fe (s) + O2 (g) + 4H+ (aq) → 2Fe2+ (aq) + 2H2O (l) E0=+1.greasing (oiling the surface) or allowing a thin metal oxide film to form (often done with sodium chromate to form Cr2O3). takes a route with a lower energy requirement).46V Iron(III) then forms a very insoluble oxide which is deposited at the edge. rusting does not occur in oxygen-free water like ocean depths (no oxygen=no oxidant).77V Cathode ½O2 + 4H+ + 4e. it must be a catalyst.→ H2O E0=+1. iron rusts more quickly in acidic environments (as H+ is a catalyst.67V Anode 2Fe2+ → 2Fe3+ + 2e0 E =-0. 2He3+ (aq) + (3+n) H2O (l) → Fe2O3 •nH2O (s) + 6H+ (aq) OVERALL 2Fe (s) + 3/2O2 (g) + nH2O (l) → Fe2O3•nH2O As H+ is cancelled out of the reaction. and noble metals (those less reactive than Cu) are not oxidised and fall to the bottom as mud. Features include: rusting doesn’t occur in dry air (no water=no salt bridge). To protect against rusting we can use anodic inhibition . as pure Cu is less easily oxidised.