These diagrams combine information about the composition of the liquid and vapour phases at a given temperature, and how the compositions of the phases change with pressure. They have the general form (where we maintain our convention of A being more volatile than B): The point I indicates the vapour pressure of a liquid phase of composition xA. The point II indicates the […]

## Vapour Pressure Diagrams

These diagrams consider two component systems at a constant temperature. The two remaining variables that affect the stabilities of the phases are the pressure and the composition of the mixture, so a vapour phase diagram represents diagrammatically the compositions and pressures at which the condensed and vapour phases of the mixture are stable. The partial vapour pressures […]

## The Gibbs-Duhem Equation

We have stated on the previous page that the total Gibbs energy of a binary mixture is given by: Since the chemical potentials depend upon the composition of the solution, we might expect that an infinitesimal change in the composition would bring about a change in G that obeyed: (The first two terms on the right express the effects […]

## Partial Molar Gibbs Energy

We have already remarked that, for a pure substance, the chemical potential is just another name for the molar Gibbs energy. For a substance in a mixture, the chemical potential is defined as being the partial molar Gibbs energy: i.e. the chemical potential is the slope of a plot of the Gibbs energy of the mixture […]

## 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 […]

## The One-Dimensional Schrodinger Equation

The Schrodinger equation is an equation for finding the wavefunction of a system. There are two basic forms of the equation, a time-dependent form that gives the time-dependent wavefunction (showing how properties of the system change with position and time), and a time-independent form that gives the time-independent wavefunction, showing how properties of the system depend upon position, but not […]

## Acceptable Forms of the Wavefunction

The Born interpretation means that many wavefunctions which would be acceptable mathematical solutions of the Schrodinger equation are not acceptable because of their implications for the physical properties of the system. For example, the wavefunction must not be infinite over any finite region. If it is, then the integral of the square modulus of the wavefunction is equal to infinity, […]

## 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 […]

## Principles of Quantum Mechanics

Before a detailed study of quantum mechanics, it is worth introducing some of the mathematical terms and concepts that will feature heavily in this area, and may otherwise be new or unfamiliar: The most trivial point to note is that in quantum mechanics, the quantity h/2π is frequently encountered. A purely notational change is to […]

## The Bohr Model of Hydrogenic atoms

This model was created by Nils Bohr to explain the form of the emission spectrum of atomic hydrogen, which consists of series of discrete lines. It had already been noted that the series of lines could all be fitted to an expression of the form: where n1 and n2 are both positive integers, and n2 = n1 + 1, […]