The Particle in a One-Dimensional Box

The heading of this page refers to the hypothetical system that will be considered on it. Though in itself this problem may appear quite a trivial one, it introduces various important concepts, and paves the way for exploration of some slightly more complex and physically relevant systems. It may also itself be used as a first approximation to some … Read more

Partial Molar Volume

The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the overall volume of the solution. However, there is rather more to it than this: When one mole of water is added to a  large volume of water at 25ºC, the volume increases by 18cm3. The molar … Read more

Wavefunctions and the Born Interpretation

The wave-particle duality of matter is dealt with in quantum mechanics by considering that, rather than a particle traveling along a definite path, it is distributed through space like a wave. The classical idea of a trajectory is thus replaced in quantum mechanics by a wave, which is defined by a wavefunctionrepresented by ψ. i.e. the  spatial distribution … Read more

Entropy of Phase Changes

We would expect that a phase change would be accompanied by a change in entropy. For example, when a liquid boils, a compact condensed phase is converted into a widely dispersed vapour phase. Clearly, the molecular disorder in a gas will be greater than that in a liquid, so there must be an entropy increase upon vapourisation. Likewise, … Read more

Electronic Transitions and the d2 Configuration

The magnitude of the ligand field splitting parameter in the octahedral field can be determined from the frequency of maximum absorption in the optical absorption spectrum. This absorption arises from an electronic transition from the t2g level to the eg level. This is the most important form of electronic transition in the transition metal complexes, but others are also observed, and these … Read more