IR of alkanes

C-H stretch: For saturated carbons, this always occurs under 3000, with the rare exception of cyclopropane due to its ring strain. It can go higher than 3000 in unsaturated carbons.

As a general rule, ring strain and s character increases the frequency of a vibration, moving the peak to the left.

CH₂ bending: Occurs around 1465

CH₃ bending; Occurs around 1375 

Long-chain bending: This is a rocking motion which occurs with four or more CH₂ in an open chain. It is around 720

C-C stretch: This has many weak peaks, so it is not considered useful.

Below is the spectra of cyclohexane, notice how the CH₃ bend and the long-chain bend disappear:

IR spectroscopy 1

In A-level chemistry, questions requiring you to interpret IR spectra have a list of wavenumbers and the bonds they represent. Many undergraduate exams will not provide this, and will expect you to recognize the main absorptions from memory.

The most important absorption to memorise is the carbonyl stretch around 1715 cm^-1. You should also recognize the C-H stretch, which is just below 3000 cm^-1.

Unfortunately the carbonyl stretch can dip into the 1600s, and the 1600s is where the C=C stretch is located. But there is a difference - the carbonyl stretch is much more intense:

Another important stretch is the broad O-H peak at 3400:

The broadness is caused by hydrogen bonds. So the O-H stretch becomes a sharp peak if the spectrum is done on gaseous alcohol.

The N-H stretch can also be found in this region, at similar intensity. However, the N-H stretch is shaper, and for primary amines it is split into two peaks:

Index of hydrogen deficiency

Each time a ring or π bond is added to an alkane, the number of hydrogens decrease by two.

The index of hydrogen deficiency (IHD), sometimes called the unsaturation index, is the amount of rings or π bonds which a molecule contains. When working out a molecule's structure, this is generally calculated before considering other spectral data. It is calculated by taking the difference between a molecular formula and the general formula for an acyclic alkane, then dividing that difference by two.

Take C₄H₆ for example. Compared to the general formula C_nH_2n+2, there is a difference of four hydrogens. Dividing four by two gives us an unsaturation index of 2.

If other elements are contained in the molecular formula, there are three simple rules to account for them:

1. For group V atom in the molecular formula (N, P, As, Sb, Bi), add one hydrogen to the general formula.

2. For group VI atoms in the molecular formula (O, S, Se, Te), leave the general formula unchanged.

3. For group VII atoms in the molecular formula (F, Cl, Br, I), subtract one hydrogen from the general formula.

These rules are also simple enough to visualize intuitively. Remember that double bonds on these elements count in the unsaturation index. Below are two examples where the rules are applied.

C₇H₁₄O₂:

1. Compared to the general formula C_nH_2n+2 (where n = 7), there is a difference of two hydrogens.

2. The oxygen atoms have no effect on the general formula.

3. The unsaturation index therefore equals one.

The molecule could, for example, be an ester:

C₁₀H₁₄N₂:

1. The general formula for n = 10 is C₁₀H₂₂

2. Since there are two group V atoms, we add two hydrogens to the general formula to give C₁₀H₂₄

3. There is a difference of 10 hydrogens, giving an unsaturation index of 5.

So the structure has 5 rings, 5 double bonds, or a mixture of both. One possibility is nicotine:

C₅H₇O₂Cl

1. The general formula for C₅ is C₅H₁₂

2. Oxygen atoms have no effect

3. There is one halogen atom, so we subtract one hydrogen from the general formular to give C₅ is C₅H₁₁

There is a difference of 4 hydrogens, so there is a IHD of 2.

One possibility is 2-Chloro-1-methylcyclopropanecarboxylic acid:

Determination of molecular mass

In the example in the previous post, we were able to work out the moles of H, O, and C in the sample. But that doesn't tell us the moles of the sample. For example, 14 moles of C could be contained in one mole of C₁₄H₂₈O₄ or could be contained in two moles of C₇H₁₄O₂. In this example we can only derive the empirical formula, while we need the molecular mass to derive the molecular formula.

In a modern lab, the molecular mass is determined using a mass spectrometer. But the oldschool methods are also good to know:

Titration: This can be used if the sample is an acid. Since we know the moles used in the titrant, and we know the ratio of the reaction, we therefore know the number of moles of the sample. Dividing the sample mass by the moles gives us the molecular weight.

Vapor density method: This can be used if the sample is a gas. One mole of an ideal gas will occupy 24000 cm³ at standard pressure/temperature, so we can use the volume to determine the number of moles in a given mass of gas.

Many gases deviate from ideal, but determining the molecular weight can be done with rough numbers. For example, if we had the empirical formula H₂O, we know that the molecular weight has to be 18, 36, 54, 72... So an inaccurate experimental value of 22 is still good enough to tell us that the molecular weight is 18 and the molecular formula is therefore H₂O.

Cryoscopic method: This measures the freezing point depression when a known quantity of solid is dissolved in a liquid - which is a function of the solid's molecular weight.

Vapor pressure osmometry: This measures the change in the vapour pressure of a liquid when a known amount of solid is dissolved it - which is a function of the solid's molecular weight.

Calculating percentage composition from combustion data

I hope this subject isn't too obvious to include. Combustion analysis is a way to determine the percentage composition of elements in an organic molecule. The process is time-consuming and hence rarely done in research labs, unless it is a specialist lab which the sample has been sent to. Non-specialist labs typically just put a sample straight into modern spectrometers.

The logic used here is that moles of the product CO₂ equals the moles of C in the sample, while moles of product H₂O equals half the moles of H in the sample.

The moles of oxygen in the sample is what is left - assuming there are no other elements to take into account. In the above example, you can work out the moles of C and H in the sample, convert to weight, and subtract their weights from 9.83 mg. Convert the remaining weight to moles to get the moles of oxygen. 

With the moles of all three elements, you can convert into percentage composition.

The original process involved trapping the produced water in a hygroscopic agent, and the carbon dioxide in a strong base. Since carbon dioxide produces carbonic acid in water, the formation of an insoluble carbonate salt will, via Le Chatelier's principle, encourage the solvation of CO₂.

Structure of carbonic acid

Modern methods will separate the products via gas chromatography. Gas chromatography is a modern and complex way of separating and analysing compounds which can be vaporised without decomposition. I look forward to learning how they work.

Autoprotolysis constant

If you consider the equilibrium constant of water protonating itself, and once again assume the solution is dilute enough to ignore [H₂O], you get the autoprotolysis constant K_w.

The experiment value of K_w at room temperature is 1 x 10^-14. We know that pure water has a ph of 7; a pH of 7 corresponds to a H₃O⁺ concentration of 1 x 10^-7. Since with pure water [H₃O⁺] = [OH^-], then we can get K_w by multiplying [H⁺] and [OH^-], which is 1 x 10-7 x 1x-10-7 = 1 x10^-14.

What makes the autoprotolysis constant really useful is that it remains constant even when adding acid or base in dilute quantities, and nearly all acid or base used in a lab can be called dilute. So because K_w = [H⁺][OH^-] , doubling the concentration of hydrogen ions will half the concentration of OH^-. Unfortunately I have never been able to grasp why intuitively. But the equation works.

We can also express [H⁺] and [OH^-] as an acidity and basicity constant respectively, and substitute them into the autoprotolysis equation:

Or in log format:

The K_a is the strength of the acid (ability to give a proton to water), the K_b is the strength of the conjugate base (the ability to receive a proton from water). So the stronger the acid, the weaker its conjugate base. The stronger a base, the weaker its conjugate acid. We already knew that of course, but the equations both confirm this fact and gives a more precise relationship.

pK_w = 14. Similar expressions apply to other solvents, with pK_w replaced by the autoprotolysis constant of the solvent, pK_sol.

Basicity constant

The basicity constant (K_b) is similar to the acidity constant. It is the equilibrium constant for a base absorbing a proton from water to produce OH^-, while assuming enough dilution to ignore [H₂O].

Like the K_a, the basicity constant is often written in -log form:

Acidity constant

The equilibrium constant for the disassociation of a Bronsted acid:

This constant can be used as a way of comparing acidity. To make comparing acidity simpler, the concentration of water can be assumed to be constant in dilute solutions and removed, because constants won't affect relative sizes. This produces the K_a, called the acidity constant:

Remember [H₃O⁺ is equivalent to [H⁺].

K_a is often expressed in a negative log form as the pK_a:

Note the similarity with the formula for pH (-log[H⁺]), in general the p sign takes the -log of something.

Both the pH and pK_a decrease with the strength of an acid. pH is related to concentration of H⁺ while pK_a is related to an equilibrium constant, so only pH will change with concentration. I suggest to avoid trying to understand them intuitively and to just focus on being able to relate them in equations.

Example: Calculate the pKa of 0.145M CH₃COOH (acetic acid) with a pH of 2.80

First we convert pH to the concentration of hydrogen ions.

Then we substitute this into the equation for K_a

We know that the concentration of [H⁺] is the same as the concentration of the conjugate base. So [H₃O⁺]=[X^-]. Subtracting that concentration from the initial concentration of acetic acid gives us of the concentration of the disassociated molecules, or [HX].

Taking the negative log of the answer gives a pK_a of 4.75

Laboratory equipment

Many guides just state the names of these without explaining why they exist, but I will include examples. This helps to understand things such as why we have differently-shaped containers of the same volume:

Volumetric flask:

This the most accurate flask for measuring volume. This is because the main source of inaccuracy in volume is judging whether the miniscus is touching the volume-marking:

The error range of this increases as the width of the container increases. That's why a container with a thin neck is useful for accuracy. A volumetric can also be sealed with a stopper.

Beaker:

These are not so good at measuring volume, but are much safer to use when pouring out chemicals from a large storage container:

Typically you will want to pour them into a beaker first, then into a measuring cylinder or flask. Using the beaker as an intermediate will greatly reduce risk of spillage.

Erlenmeyer/conical flask:

This flask can used for titrations, where the neck is big enough to fit the end of a burrette into, yet the shape prevents splashing. Likewise for using a magnetic stirrer, or if you want to gently swirl the container without spillage.

Watch glass:

A watch glass is a circular piece of glass, convex on one side and concave on the other. It can roughly cover an erlenmeyer flask or a beaker, which helps prevent contamination or escape of vapour.

As a clean, dry, and unreactive surface, it can also be used for drying or weighing a solid powder:

Intrinsic and extrinsic semiconductors

An intrinsic semiconductor is the type described in the previous post, where the band gap is small enough for temperature to promote electrons from the valence band to the conduction band:

There is no official rule which decides whether the band gap is small enough to be called an intrinsic semiconductor, or large enough to be called an insulator. It is something you can judge for yourself depending on the situtation.

An extrinsic semiconductor is an insulator which has been doped with impurities. These impurities have their own bands:

Doping to produce extrinsic semiconductors requires remarkably low levels of impurities, such as a one in a billion atoms. There are two types of extrinsic semiconductors:

N-type: These have an electron-filled donor band close in energy to the conductance band of the insulator. Heat promotes electrons to the conductance band which can then move freely, turning the insulator into a semiconductor.

P-type: These have an empty acceptor band close to the filled valance band of the insulator. Heat promotes electrons into the acceptor band. The holes left over in the valance band are then able to move freely, turning the insulator into a semiconductor.

The trick to remember these is that negative electrons carry charge in the n-type semiconductor, while positive hole carry charge in the p-type semiconductor.

Band theory 3

Molecules with partially-filled bands are metals, because an electron can easily be promoted to different molecular orbitals.

Molecules with just a filled band (which doesn't overlap with an empty band) are insulators and semiconductors. The difference between the two just depends on the band-gap between the filled band and the next empty band:

In the semiconductor above, electrons can be promoted from the filled s band to the empty p band. Both the electrons and the "holes" left behind can act as charge carriers. Since electron promotion increases with temperature, conductivity increases with temperature.

The highest-energy band which contains electrons at T = 0 is called the valence band. The next band up is called the conduction band.

Band theory 2

At T = 0, electrons occupy the energy band in accordance with the building up principle. For example, if each atom donates a single s electron, the band will be half filled:

The highest occupied orbital is called the fermi level.

The density of molecular orbitals is not uniform throughout the band. There is only one way of arranging a purely bonding or purely antibonding orbital, but multiple ways of arranging in-between states. The image below shows density on the x axis:

So more MOs are found in the middle of the bands than on the edges.

Band theory

Band theory describes a metal as one large molecular orbital with an infinite number of contributing atoms. For example, consider overlaping multiple 2s orbitals as in lithium:

For small numbers of atoms, you can draw the possible overlaps to understand the patterns of energy levels, as done with allyls in a previous post. But the important result of band theory is that the molecular orbitals are approximated as blending into a continuous line.

The band has finite end points. Electrons are considered free to move inside the band. This stuff is why metals are described in A-level as "a sea of freely moving electrons". The above example is a s-band, but this merging can also be done with p orbitals to make a p-band:

Since p orbitals are higher in energy than s, p-bands are higher in energy than s-bands. These bands can overlap, or they can have a band-gap between them:

You can likewise create d-bands. In fact, orbital overlap in band theory (and MO in general) does not have to happen between orbitals with the same letters. For example, the d orbitals of a metal might overlap with the p orbitals of oxygen.

Conductors

The resistance of a metallic conductor decreases with temperature. The easy way to remember this is to think of electronics which stop working when they overheat.

The resistance of a semiconductor increases with temperature.

Superconductors have 0 resistance below a critical temperature.

It is possible to classify every type of material into these categories. Insulators, when possible to measure, are found to increase in conductivity when heated - so they can also be called semiconductors.

A-level teaches the equation:

Conductivity is the reciprocal of resistivity. A siemen (S) is defined as the reciprocal of an ohm. Using that, you should be able to tell why conductivity can use the units S cm^-1.

Overlap of multiple pi bonds

As mentioned, two orbitals of similar symmetry can overlap in-phase (bonding) and out-of-phase (anti-bonding).

Electrons in opposite phases cancel out. The lower energy of bonds comes from electrons being in between atoms, the higher energy of anti-bonds comes from a lack of electrons in between the atoms.

The method of considering how phases can overlap can be extended, such as by having three pi orbitals next to eachother, as in an allyl anion:

Only adjacent orbitals are considered to overlap. The lowest level has two in-phase overlaps and the highest has two out-of-phase overlaps. The middle MO is non-bonding, since the central carbon can point a pi orbital in either direction and it would still produce one in-phase overlap and one out-of-phase, producing a net bond order of 0.

All three carbons are sp² hybridized, so the lone pair on the carbon is in a p orbital. This means the energy gained from overlaping three p orbitals is greater then the energy gained from having one sp³ carbon and just two pi-bonded carbons. The allyl only adopts the former structure because it is lower in energy.

Notice that the above MO energy levels also predicts the stability of an ally radical or an ally cation, because producing them just means one or two less electrons in a non-bonding orbital. Also, de-localisation of charge or radicals is in itself a stabilisation affect.

Below are two different molecules being homolytically cleaved. The second type requires less energy to cleave because of the extra stability of the product, you should be able to explain why:

The same techique is applied to butadiene below: