Valence-Bond Description of the Hydrogen Molecule

There are two main approaches to the description of bonding in molecules, valence bond (VB) theory and molecular orbital (MO) theory. Though molecular orbital orbital theory is considered a more satisfactory explanation and has largely superseded valence bond theory, it is still worth briefly considering VB theory, as it provides a reasonable explanation of the structure of many molecules. From … Read more

A summary of Activity

It is important not to lose track of the basic principles of activity amongst all the detailed derivations of the equations. Thus it is appropriate to provide here a brief summary of the salient points of the previous two pages: Activities are an adjusted form of the mole fraction (or molality or concentration) of a species in a solution, be it … Read more

Molality and Activity

Molalities are an alternative way of expressing the composition of a mixture, rather than mole fractions. The molality of a dissolved substance is expressed as the number of moles of the substance present per kilogram of solution. We may thus introduce an another definition of activity (which follows on from those we have considered thus far) which will prove … Read more

Activities of solvents and solutes

We have derived an expression for the general form of the chemical potential of any solvent: Recall that pA* is the vapour pressure of the pure liquid, and pA is the vapour pressure of the substance when it is a component of a solution. For an ideal solution, the solvent obeys Raoult’s Law at all concentrations, so it satisfies this … Read more

Henry’s Law and the Ideal Dilute Solution

In an ideal solution of two liquids, both components obey Raoult’s Law. However, it has been experimentally observed that, for real solutions at low concentrations, although the solvent (the major component of the solution) usually obeys Raoult’s Law, the solute (the minor component of the solution) does not. The vapour pressure of the solute is proportional to its mole fraction, but the constant of proportionality is … Read more

Raoult’s Law and Ideal Solutions

To discuss the thermodynamic properties of liquid mixtures, it is necessary to establish how the chemical potential of a liquid varies with its composition. To calculate the value of the chemical potential of the liquid we use the fact that at equilibrium the chemical potentials of a substance in its liquid and vapour phases are identical. It … Read more

Rotation in Three Dimensions

We can extend the two dimensional model of the particle on a ring to three dimensions by considering a particle that is constrained to move on the surface of a sphere of radius r. (Clearly this will be useful when it comes to modelling the behaviour of electrons in atoms.) We have two boundary conditions in this situation … Read more

Polar Coordinates

Before proceeding any further, it is useful to introduce a new coordinate system that is particularly suited to the problems we shall encounter. In two dimensions, the normal Cartesian system sets an origin and then specifies the position of a point as its distance from this origin in two perpendicular directions, the x, and y directions. In the polar coordinate system, … Read more

Vibrational Motion

A particle performs harmonic motion if it experiences a restoring force proportional to its displacement, x,  from a given point. i.e. F = -k x. k is called the force constant. Since the force, F, is related to the potential energy, V, by the expression F = -dV/dx, we may write the following expression for the potential energy of a particle undergoing … Read more

Heisenberg’s Uncertainty Principle

This is a fundamental principle of Quantum mechanics. Loosely speaking, it states that: It is impossible to specify precisely both the linear momentum and the position of a particle at a single moment in time. We can illustrate this principle by a consideration of some wavefunctions. We have established that the wavefunction for a particle in free … Read more