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: