Atomic and Molecular Spectra Some of the most impressive evidence for non-classical behaviour comes from the spectra of atoms and molecules. Rather than showing emission or absorption of radiation at all frequencies, nonzero intensities are only observed at discrete frequency values: This diagram is a schematic representation of a typical atomic emission spectrum. Note the […]

## Wave-Particle Duality

A fundamental distinction was drawn in classical physics between waves and particles. This was refuted by experimental evidence that showed waves demonstrating particle-like character and vice versa. Evidence for the particle-like character of electromagnetic radiation was given by the photoelectric effect. This is the name given to the phenomenon whereby electrons are ejected from a sample of metal […]

## Black body radiation and the Planck distribution

In the late nineteenth and early twentieth centuries, a great deal of experimental evidence began to accumulate for which classical mechanics could provide no explanation. It was the consideration and explanation of these data which led to the development of quantum mechanics. One of the most significant failures of classical mechanics was its inability to […]

## Properties of the Gibbs Energy – Temperature dependence

On the previous page, we derived an expression which gives us a relationship between the Gibbs energy and temperature: This relation tells us that, since everything has a positive entropy, G always decreases when the temperature is raised at constant pressure and composition. Gases have much greater entropies than liquids, which in turn have somewhat larger entropies than […]

## Properties of the Gibbs Energy – Pressure dependence

We start with the definition of the Gibbs energy, G = H – TS . When the system undergoes a change of state, we may write, for any general change: Since H = U + pV (by definition) we can write dH = dU + pdV + Vdp. Now, the First Law of Thermodynamics states that dU = dw + […]

## Comments on the Gibbs Energy

The criterion for spontaneous change dG £ 0 may be very simply expressed in words as a tendency of the Gibbs energy to tend to a minimum value. i.e. reactions are only spontaneous in the direction of decreasing Gibbs energy. Thus, if we wish to know whether a reaction is spontaneous under conditions of constant pressure and temperature, we consider the […]

## The Gibbs Energy

Entropy is the fundamental basis for assigning the direction of spontaneous change, but to use it we must consider the entropy changes of both the system and the surroundings, which is somewhat inconvenient. It is possible to devise a method which relates the entropy change of the surroundings to properties of the system, thus allowing us to focus solely on the […]

## Partial pressure and Daltons Law

If we consider a mixture of gases in a container, then they each exert a pressure on the walls of that container. ie: one gas provides a component of the total pressure, and another gas provides another component. The component that any one gas provides is called the partial pressure and is measured in Pascals (or other […]

## The Van der Waals Equation

How can deviations from ideal behaviour be compensated for in our model of the situation? Recall that our model produced p.Vm = RT (ideal gas equation) One assumption was that the molecules had no size. This is clearly not true (but is a reasonable approximation at low pressures when the size of the molecules is very small compared to […]

## Boyles Law and pressure/volume relationships

Boyles Law states that, for any sample of gas, its pressure multiplied by the volume it occupies is a constant providing the temperature remains constant. (ie pV = constant). This is always true for perfect gases, for which pV = nRT by definition. Real gases behave most like perfect gases at high temperatures and low pressures (as […]