better to use the fraction reacted, a, instead of concentration, and for a simple
(first order) reaction the rate may be written in terms of a:da/dt =k(1 − a) (1)where k is the rate constant at the experimental temperature and (1 − a) is the
amount of sample remaining. It should be pointed out that many solid state
reactions follow very complex kinetic mechanisms, and their rate equations are
much more complex than this.
Any chemical change speeds up as the temperature is raised. This is most
simply represented by the Arrhenius equation:k =A exp(−E/RT) (2)where A is called the pre-exponential factor,E is the activation energy, Ris the
molar gas constant and Tthe thermodynamic temperature in Kelvin.
This expression shows that as the temperature increases, the rate constant
also increases exponentially. Combining the effects of equations (1) and (2), the
result is that a solid state reaction will start very slowly at low temperature,
speed up as the temperature is raised, and then slow down again as the reactant
is used up. This produces a sigmoid curve as shown in Figure 1. It also means
that it is difficult to quote with accuracy a single decomposition temperature.It
is probably better to give the range of temperature over which a reaction occurs
or even to quote the temperature at which only a small fraction, say 0.05%, has
decomposed.
If only a single mass loss occurs, for example, when the amount of moisture
in a soil or a polymer is measured, then the evaluation is simple. A mass loss of
1.5% when a sample of nylon was heated from room temperature to 130°C at
10 °C min−^1 measures the percentage moisture in the nylon, assuming that the
loss is due only to moisture, not to any other solvent or other volatile material.306 Section G – Thermal methods
Table 1. Principal thermal analysis techniques
Technique Property Uses
Thermogravimetry (TG) Mass Decompositions
(thermogravimetric analysis, TGA) Oxidation
Differential thermal analysis (DTA) Temperature Phase changes
difference Reactions
Differential scanning calorimetry (DSC) Heat flow Heat capacity
Phase changes
Reactions
Thermomechanical analysis (TMA) Deformations Softening
Expansion
Dynamic mechanical analysis (DMA) Moduli Phase changes
Polymer cure
Dielectric thermal analysis (DETA) Electrical Phase changes
Polymer cure
Evolved gas analysis (EGA) Gases Decompositions
Thermoptometry Optical Phase changes
Surface reactions