Inorganic and Physical Chemistry - WordPress.com
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Inorganic and Physical Chemistry
Electrochemistry
Introduction The study of the interchange of chemical and electrical energy. An idealised chemical cell is shown
below:
Cell Diagram
Cell Potential The cell potential is the potential difference between the anode and the cathode. It represents the
energy level on the electrons - a larger cell potential will lead to a larger electron driving force. Cell
potentials are always measured at standard conditions: 25 C, 1M concentrations of solute species,
and 1atm pressure. Specifically, the cell potential measures the amount of energy that one coloumb
of charge moving from the anode to the cathode would lose.
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Standard Reduction Potential It is more useful to know the half-cell potential (i.e. for each half of the reaction separately),
however only full-cell potential differences can actually be measured experimentally. To get around
this, the cell potential is measured for a wide range of different half-cells, each connected to a
standard hydrogen cell at standard conditions. By arbitrarily defining the potential of the hydrogen
cell as zero, the cell potential of the other half-cell can thereby be determined.
The resulting measurement is referred to as the standard reduction potential. The higher the
standard reduction potential of a given reaction, the more energy it would lose when undergoing
reduction, and hence the more likely it is to undergo reduction.
The overall cell potential is given by the reduction potential of the reduction reaction minus the
reduction potential of the oxidation reaction (the lower one on the table).
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Nernst Equation It is important to note that the rate of electrochemical reactions and the cell potential depends upon
the concentration of the reducing and oxidising agents. Moreover, this concentration dependence is
non-linear. We can model this effect using the Nernst equation.
An electrochemical reaction will continue spontaneously until it reaches equilibrium, which will
occur when and .
Concentration Cells It is also possible to produce an electrochemical current with two half cells of the same chemical
species, but of different concentrations. Such a setup is referred to as a concentration cell.
The work done by a galvanic cell is given by:
Where the amount of charge is:
Where is the number of moles of electrons, and is Faraday's constant.
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Batteries Primary batteries: cannot be recharged
Secondary batteries: can be repeatedly discharged and recharged
Fuel cells: reactants are continuously replenished so reaction can continue
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Corrosion Corrosion refers to the oxidation of metals, converting the pure metal form (or an alloy) into a metal
oxide which often crumbles or is dissolved away, thereby weakening the structure of which it forms
a part.
Methods of corrosion prevention include coating with paint or metal (so oxygen cannot access the
metal to react), use of alloys to change to reduction potential of the main metal, and use if sacrificial
anodes (placing metals of higher reduction potential nearby so these will corrode first).
Electrolysis Electrolysis is the forcing of a current through a cell to produce a chemical change when the cell
potential is negative. One prominent example of this is the electrolysis of water, which inverts the
operation of a fuel cell to separate water into hydrogen and oxygen.
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Transition Metal Chemistry
Defining Transition Metals Transition metals are those metals found in the 'middle' of the periodic table, which exhibit
incomplete d-orbitals. Transition metals find extensive application in industry and in biological
systems.
Characteristic Properties There are a number of properties shared by the transition elements that are not found in other
elements, which results from the partially filled d shell. These include:
the formation of compounds whose colour is due to d–d electronic transitions
the formation of compounds in many oxidation states, due to the relatively low reactivity of
unpaired d electrons
the formation of many paramagnetic compounds due to the unpaired d electrons
Transition Metal Ores Most transition metals are very readily oxidised, and so they tend to be found in nature with positive
oxidation numbers, bound to oxygen atoms or other highly electronegative elements. To convert
them into pure form, the ores need to first be physically separated and purified (to remove rock and
other contaminants), and then reduced to remove the oxygen and leave a pure metal. A common
reducing agent used to purify metals is coke, which is a form of carbon which undergoes oxidation
when heated.
Late transition metals (Cu, ZN, Ni, to the right of the periodic table), have larger nuclei and therefore
have a stronger attractive force for electrons. This makes them easier to reduce, hence explaining
why these were the first metals humans began to use. Mid transition metals (Fe, Mn) are somewhat
harder to reduce, and so came later, while early transition metals (Ti, V, Cr), are much harder to
reduce, and so were not widely used until modern times, as very high temperatures are required.
Kroll Process The Kroll process is an industrial process used to produce metallic titanium from titanium dioxide.
The first stage involves converting the raw ore to an intermediate TiCl4. This is done at very high
temperatures (1000 degrees), and by adding chlorine gas:
Impurities are separated by fractionation, and following that the is reduced using magnesium
as a strong reducing agent:
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Mond Process The Mond process is a technique created by Ludwig Mond in 1890 to extract and purify nickel. This
process has three steps:
First, nickel oxide is reacted with hydrogen gas at 200°C to remove oxygen, leaving impure nickel.
Impurities include iron and cobalt.
Next, the impure nickel is reacted with excess carbon monoxide at 50–60°C to form the gas nickel
carbonyl, leaving the impurities as solids.
Finally, the nickel carbonyl is heated to 250°C, causing the nickel tetracarbonyl to decompose into
pure nickel. This works because only nickel will react with CO to form a gas.
Coordination Complexes Transition metals tend to form structures called coordination complexes, in which the central metal
atom binds with one or more other chemical species called ligands. In general, the metal acts as a
lewis acid, accepting a lone pair of electrons from the ligands, which act as a lewis base. These bonds
are referred to as coordinate bonds or dative bonds. A coordination compound consists of a complex
ion, which itself is comprised of the transition metal plus its coordinated ligands, and one or more
associated counter ions, which ensure that the entire complex has a neutral charge.
Coordination Number Atoms in the ligands that directly bind to the transition metal (i.e. the atoms that actually give up the
lone electron pairs) are referred to as donor atoms. The total number of donor atoms bound to the
central metal atom is called the coordination number of that metal ion.
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Denticity A single ligand can sometimes coordinate with the metal ion via more than one donor atom. The
number of donor atoms with which a single ligand is bound to the metal ion is refered to as the
denticity of that ligand. Monotendate ligands have only a single donor atom, while bidendate ligands
have to donor atoms. Unlike polydentate ligands, ambidentate ligands can attach to the central
atom in two places, but not both at the same time. A good example of this is thiocyanate, SCN−,
which can attach at either the sulfur atom or the nitrogen atom.
Nomenclature The cation is always named before the anion
The ligands are listed before the metal, in alphabetical order (ignoring the prefix)
Usually the name of the neutral molecule is used, with the following exceptions:
When there is more than one of a given type of ligand, the following prefixes are used
The suffix -ate is appended to the end of the name of the metal, unless the name ends in
'ium' or 'ese', in which case this suffix is dropped and replaced with 'ate'. Certain metals also
receive special Latin names:
The oxidation state of the metal is written in Roman numerals in parentheses after the name
of the metal
The number of counter ions is never specified, as this can be inferred from the oxidation
number of the metal
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Coordination Geometries The shape of a coordination complex is determined by its coordination number. There is generally
no way to predict which of the two possible geometries for 2- and 4-coordinate complexes will occur.
Chelation Chelation involves the formation of two or more separate coordinate bonds between a polydentate
(multiple bonded) ligand and a single central metal atom. Usually these ligands are organic
compounds, and are called chelating agents or sequestering agents. The chelate effect describes the
enhanced affinity of chelating ligands for a metal ion compared to the affinity of a collection of
similar nonchelating (monodentate) ligands for the same metal. This occurs because in order to
disassociate, monodentate ligands need only break one ligand bond, whereas polydendate ligands
need to break several at the same time, which is far less likely.
Siderophores are small, high-affinity iron chelating compounds secreted by microorganisms such as
bacteria, fungi and grasses. Siderophores are amongst the strongest soluble Fe3+ binding agents
known. One important siderophore is called enterobactin, found in certain bacteria. Enterobactin is
such a strong chelating agent that it can even extract iron from the air. Blue arrows are donor atoms.
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Isomerism The are four main different types of isomerism present in coordination compounds.
Coordination Isomerism Occurs when a ligand 'swaps' position with a counter ion.
Linkage Isomerism Occurs with ambidentate ligands, which can bind to the metal cation in more than one way.
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Geometric Isomerism Occurs when the atoms are bonded in the same way, but are positioned differently relative to some
rigid ring or bond.
Square planar complexes will display geometric isomerism when exactly two of the ligands
are the same. There will be two isomers in this case: a cis- version (when the two identical
ligands are on the same side of the plane), and a trans- version (when they are on opposite
sides).
Octahedral complexes can also exhibit geometric isomerism. In this case the two possible
arrangements are facial and meridional.
Optical Isomerism Occur when a complex has a non-superimposable mirror image of itself. The name comes from the
face that the two optical isomers will differ in the direction with which they rotate plane-polarised
light. Optical isomerism can also result from multiple bonding of polydentate ligands.
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Crystal Field Theory Crystal field theory describes the breaking of degeneracies of electronic orbital states, usually d or f
orbitals, due to a static electric field produced by a surrounding charge distribution. It can be used to
explain the spectroscopic properties, magnetic properties, and colour of transition metal
coordination complexes.
CFT makes several simplifications, including that ligands can be approximated by negative point
charges, and that all bonding is entirely ionic.
The d orbitals are shown below:
In an octahedral complex the orbitals align as shown below:
As is evident from the diagram, the and orbitals point directly at a ligand, whereas the
other three orbitals point into the space between ligands. This means that the electrons in these two
orbitals are closer to other electrons, and hence have a higher energy level than the other three
orbitals, hence causing a degeneracy. This effect is known as crystal field splitting.
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The energy level splitting for a tetrahedral complex is actually the inverse of the octahedral
arrangement.
The average energy level of the orbitals cannot be changed by field splitting; only the relative levels
of the different orbitals. The average energy level will simply be equal to the level that would prevail
if the ligands were distributed spherically about the complex.
This means that for an octahedral complex, the first three electrons will be more stable than average,
and the second two will be less stable than average.
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This degeneracy of energy levels has implications for the atomic radius:
Field Theory and Colour The colour of a material is determined by the photon wavelengths that it is capable of absorbing. If it
can absorb a particular wavelength, then it will not reflect the colour that corresponds to that
wavelength. The wavelengths that a material is able to absorb, in turn, depend upon the difference
in energy levels between adjacent orbitals.
This energy difference will vary according to the geometry of the coordination complex in question,
and the number and identity of the ligands. In particular, some ligands split the energy levels in
octahedral complexes more than others - this needs to be determined experimentally. Usually the
energy splitting is not greatly influenced by the metal's oxidation state.
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Magnetic Properties The magnetic moment of a coordination complex is given by the formula:
Where is the number of unpaired electrons in the complex. The number of unpaired electrons will
of course depend upon the valency of the metal cation, and also on the size of the energy gap.
Strong field complexes tend to have fewer unpaired electrons, while weak field complexes tend to
have more unpaired electrons, as the energy gap is sufficiently small such that being an unpaired
electron in the higher orbital becomes energetically favourable to being a paired electron in the
lower orbital.
Transition Metals in Biology Transition metals are essential, in relatively small amounts, to many biological enzymes. Transition
metals also play an important role in facilitating redox reactions (owing to their ability to cycle
between oxidation states).
A haem is a chemical compound of a type known as a prosthetic group consisting of an Fe2+ ion
contained in the centre of a large heterocyclic organic ring called a porphyrin, made up of four
pyrrolic groups joined together. Not all porphyrins contain iron, but a substantial fraction of
porphyrin-containing metalloproteins have heme as their prosthetic group; these are known as
hemoproteins.
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Myoglobin is an iron- and oxygen-binding protein found in the muscle tissue of vertebrates.
Haemoglobin is the iron-containing oxygen-transport metalloprotein in the red blood cells of all
vertebrates. The protein molecule is an assembly of four globular protein subunits, for example
myoglobin in mammals. Each subunit in turn is composed of a protein chain tightly associated with a
non-protein heme group.
One oxygen molecule reversibly binds in the polar position to the iron atom in each heme group,
thus each hemoglobin molecule carries four oxygen molecules.
Deoxygenated hemoglobin is the form of hemoglobin without the bound oxygen. The absorption
spectra of oxyhemoglobin and deoxyhemoglobin differ, owing to the fact that the energy gap is
larger for oxygenated hemoglobin than for deoxygenated.
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Reaction Kinetics
Reaction Rates The rate at which a reactant is consumed or a product is formed is defined as the rate of change
of the concentration of either the reactant or the product (both reported as positive values).
As different species in a chemical reaction will be formed at different rates, it is often useful to
define the rate of reaction as follows:
Rate Laws Reaction rates generally decrease over time as the reaction comes closer to completion. An equation
with gives this relationship between the concentration of the reactant(s) and the rate of reaction is
known as a rate law.
The constant is known as the rate constant for the reaction, while is the order of the reaction.
The values of and can only be found experimentally. It is not determined by the stoichiometry of
the chemical equation.
Rate laws can be more complicated, involving the concentrations of multiple reactants and/or
products. For example:
Order of reaction . Orders of rates of reaction can be negative, zero, or fractional.
Pseudo-1st order reactions occur when the real order of reaction is greater than one, however the
concentration of all but one species changes very little, so they can be taken as being roughly
constant.
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Integrated Rate Laws Integrates rate laws express concentration as a function of time.
Zeroth-Order:
First-Order:
Second-Order:
Reaction Half-Life The half-life of a reactant is the time required for the concentration of that reactant to fall to half of
its initial value. The half-life for a given reaction can be found by simply substituting
into the integrated rate law, and solving for .
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Zeroth-Order:
First-Order:
Second-Order:
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Collision Theory Collision theory states that when suitable particles of the reactant hit each other, only a certain
percentage of the collisions cause any noticeable or significant chemical change; these successful
changes are called successful collisions. Five separate factors determine the number and
effectiveness of collision between two reactant species:
Concentration : higher concentration means more particles and hence more collisions
Particle velocity : higher velocity means higher energy per collision. Particle velocity
increases with temperature , and also depends on the viscosity of the medium
Collisional area : the area around a particle in which the centre of another particle must
be found for a collision to occur. Larger radii and make collisions more frequent
Molecular orientation : also known as the steric factor, representing the probability of
particles colliding in the correct orientation for the reaction to occur
Activation energy : the energy required to form the unstable transition state. Higher
activation energies are harder to attain, and hence slow the rate of reaction. The proportion
of particles with energies above the activation energy is given by the Boltzmann distribution
The Arrhenius Equation Arrhenius' equation is a formula for the temperature dependence of reaction rates. It incorporates
all of the factors from collision theory into a single equation.
The full rate equation from collision theory can be written as:
Substituting in the following equations:
We find the full expression:
The Arrhenius equation is actually a simplified version of this full equation:
Where is called the pre-exponential factor. Note that as per the full equation, is actually a
function of temperature, however often treating it as a constant yields sufficient accuracy. This
equation is often written as a linear relationship between and .
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Catalysis A catalyst is a substance added to a chemical reaction in order to increase the rate of reaction.
Catalysts are not consumed in the reaction process, so they are neither reactants nor products.
Catalysts open up a new potental reaction pathway with lower activation energy, thereby allowing
the same reaction to occur with less energy, and hence increasing the rate above that for the
corresponding uncatalyzed reaction at the same temperature.
Homogeneous catalysts function in the same phase as the reactants, whereas heterogenous
catalysts are in a different phase.
There are four steps to a heterogenous catalysis reaction:
1) Adsorption of the reactants to the surface of the catalyst
2) Migration of the adsorbed reactants about the surface
3) Reaction between adsorbed reactants
4) Desorption of the products from the catalyst surface
Reaction Mechanisms A reaction mechanism is the step by step sequence of elementary reactions by which an overall
chemical reaction occurs. An elementary step is distinguished from an ordinary reaction in that we
can always write its rate law directly using the stoichiometric constants.
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Reaction mechanisms are seldom directly observable. Hence, for any proposed mechanism we can
only deduce its correctness by the extent to which it agrees with observation. In particular, the sum
of elementary steps must yield the overall reaction (obviously), and the proposed mechanism rate
law must agree with the experimentally-determined rate law.
The slowest step in any reaction mechanism is called the rate determining step, and it is the step
which determines the rate of the overall reaction.
Steady-State Approximation A reaction intermediate is a molecular entity that is formed from the reactants (or preceding
intermediates) and reacts further to give the directly observed products of a chemical reaction. Most
chemical reactions are stepwise, that is they take more than one elementary step to complete. An
intermediate is the reaction product of each of these steps, except for the last one, which forms the
final product. Reactive intermediates are usually short lived and are very seldom isolated, so they
are difficult to observe.
This causes a problem when the rate-limiting stage of the reaction is determined by the
concentration of intermediates, as such a rate law will not be directly measurable.
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The steady-state approximation states that the concentration of intermediates is small, and
approximately constant for the duration of the experiment. This can be expressed as:
Using this approximation, we can write an expression for the concentration of the intermediate in
terms of observable quantities:
Solving for the concentration of the intermediate we find:
Substituting this into the rate equation:
If this derived rate law fits experimental evidence, then the proposed mechanism may be correct.
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Pre-Equilibrium Another method for determining the rate of reaction in the presence of intermediates is possible
when the first elementary step of a reaction happens very fast, and can thus reach equilibrium even
before the reaction as a whole has proceeded very far.
For example, consider the decomposition of ozone to oxygen:
Since step 2 is the rate-determining step:
Use the pre-equilibrium of step 1 to derive an expression for :
Substitute this into the overall reaction equation:
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Chain Reactions A chain reaction is a sequence of reactions where a reactive product or intermediate causes
additional reactions to take place. In a chain reaction, intermediates are called chain carriers.
Consider as a second example the pryolysis of acetaldehyde:
Applying the steady-state approximation:
Hence we know that:
Combining these equations:
From equation 2 the overall reaction equation is given by:
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Substituting in the derived expression for the intermediate :
Quantum Mechanics
Energy and Wavelength
Heisenberg's Uncertainty Principle
Rydberg formula
Where is the Rydberg constant, equal to
Pauli Exclusion Principle In an atom, no two electrons can have the same four quantum numbers
Hund's Rule The lowest energy configuration for an atom is that in which there is the maximum number of
unpaired electrons permitted by the Pauli Exclusion Principle.
Aufbau Principle As an atom is 'built up', each additional electron assumes the lowest energy configuration with
respect to the electrons already present.
Orbital Penetration and Shielding Penetration describes the proximity of electrons in an orbital to the nucleus. Electrons which
experience greater penetration experience less shielding and therefore experience a larger Effective
Nuclear Charge but shield other electrons more effectively. Electrons in different orbitals have
different wavefunctions and therefore different distributions around the nucleus. Shielding reduces
the ionisation energy of shielded electrons.
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Note that although s orbitals get closer to the nucleus than p or d orbitals, their average position is
actually slightly further away from the nucleus.
The main consequence of orbital penetration and shielding is to break the degeneracy of the energy
levels of the outer shell electrons.
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Quantum Numbers
Atomic Orbital Visualisation
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