Calorimetry

Determining the amount of energy within a reaction is an area of science known as calorimetry. Within calorimetry, a reaction is performed under known conditions. The enthalpy change will invoke an increase or decrease in the temperature of the environment (see Figure 7.4.1).

There are two types of calorimeters commonly used: constant pressure and constant volume, although they are more commonly referred to by less scientific names! “Coffee cup” calorimeters (constant pressure) involve the use of an insulated container to create a closed system. This can be easily achieved in science classrooms by stacking two polystyrene cups (see Figure 7.4.2). By filling the cup with a medium (commonly water), a reaction or process can then be facilitated, with the energy released or absorbed quantifiable through a change in temperature. In the case of sodium chloride salt being dissolved in water, the “enthalpy of dissolution” is positive – indicating an endothermic reaction. The temperature should, therefore, decrease. Due to the overall crudeness of this setup, energy readings will involve a degree of inaccuracy as energy seeps out from the container. Commercial options are available to alleviate these issues alongside providing more accurate electrical thermometers.

Bomb calorimeters (constant volume; see Figure 7.4.3) allow for the measurement of violent and energetic combustion reactions. A sealed “bomb” is loaded with the substance under investigation, with a source of ignition, generally an electrical spark, into an insulated container. The generated explosion will heat the water surrounding the bomb unit, allowing for energy release to be calculated. Bomb calorimeters are more accurate than their coffee cup counterparts but require calibration before use. Explosions are always exothermic processes, and so bomb calorimeters are generally useful in detecting increases in temperature.

Specific Heat Capacity

While it is easy for us to measure the temperature change of a substance, converting that figure demands that we know how much energy it takes to heat a given mass of a substance. Specific heat capacity is the amount of energy needed to heat 1 gram of a substance by one degree Celsius or Kelvin^[1]. It is used in the following equation:\[
q=mc\Delta T
\]

Where, [latex]q[/latex] is the energy exerted or emitted [latex]\left(\textrm{J}\right)[/latex]
[latex]m[/latex] is the mass of the substance [latex]\left(\textrm{g}\right)[/latex]
[latex]c[/latex] is the specific heat capacity of the substance [latex]\left(\textrm{J}\textrm{K}^{-1}\textrm{g}^{-1}\right)[/latex] or [latex]\left(\textrm{J}\textrm{°C}^{-1}\textrm{g}^{-1}\right)[/latex]
[latex]\Delta T[/latex] is the temperature change of the substance [latex]\left(\textrm{K}\right)[/latex] or [latex]\left(\textrm{°C}\right)[/latex]

While different substances will have different heat capacities — commonly utilised environmental mediums have been well-documented in scientific literature. Water is the most common substance, thanks to its availability and relatively high specific heat capacity (owing to its strong hydrogen bonding). It is recommended to learn the heat capacity of water by memory. For any other substances, capacities will be given within the question.

Latent Heat Capacity

Whereas specific heat details the amount of energy needed to heat a substance, latent heat capacity quantifies the amount of energy needed to induce a state change within a substance. It utilises the following equation:

\[
q=mL
\]

Where, [latex]q[/latex] is the energy exerted or emitted [latex]\left(\textrm{J}\right)[/latex]
[latex]m[/latex] is the mass of the substance [latex]\left(\textrm{g}\right)[/latex]
[latex]L[/latex] is the latent heat capacity of the substance of the transformation taking place [latex]\left(\textrm{J}\textrm{g}^{-1}\right)[/latex] or [latex]\left(\textrm{J}\textrm{g}^{-1}\right)[/latex]

The type of latent heat described depends on the transformation taking place:

• Latent heat of fusion — the amount of energy required or released during solid/liquid conversion.
• Latent heat of vaporisation — the amount of energy required or released during liquid/gas conversion.
• Latent heat of sublimation — the amount of energy required or released during solid/gas conversion.

Figure 7.4.4 shows the change in temperature of a substance as heat is applied. Note that during a change in state, such as in the freezing or melting process, the temperature doesn’t change — energy is focused into overcoming intermolecular forces holding molecules together. Additionally, the gradients between the state changes may also be different, as the different states of matter within a substance will have different specific heat capacities.