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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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