The Three States and Phase Changes
~13 min read · Tier toggle changes depth (T1 plain · T2 standard · T3 rigour)
You should be comfortable with basic SI units (kelvin, pascal, kilogram) and the concept of a system versus its surroundings. No prior knowledge of thermodynamics or statistical mechanics is required for this orientation lecture.
Why this matters
Understanding how matter transitions between solid, liquid, and gas states is the foundation for all physical chemistry.
Before we can apply the ideal gas law or calculate enthalpy changes, we must understand the microscopic differences that define the three classical states of matter. This lecture establishes the qualitative framework: how intermolecular forces and kinetic energy compete to determine the macroscopic properties of a substance. We will define the states, describe the energy changes associated with phase transitions, and introduce the concept of latent heat. This conceptual groundwork is essential because the quantitative laws of gases and thermodynamics rely on these definitions. Without a clear distinction between sensible heat (which changes temperature) and latent heat (which changes phase), subsequent calculations regarding energy transfer will be physically meaningless. We will also clarify the common misconception that temperature is a measure of total energy, distinguishing it clearly from internal energy and enthalpy.
The Microscopic Picture: Order vs. Motion
At a fundamental level, the state of matter is determined by the balance between two opposing factors: the attractive forces between particles (intermolecular forces) and the kinetic energy of those particles. In a solid, the attractive forces are strong enough to hold particles in fixed, regular positions. The particles are not stationary; they vibrate about their equilibrium positions. This rigid structure gives solids a definite shape and volume, and typically a high density. The particles are closely packed, often in a crystalline lattice, which minimises the potential energy of the system. Because the particles are locked in place, solids do not flow. In a liquid, the situation is different. The particles possess enough kinetic energy to overcome the rigid constraints of the solid lattice, but not enough to escape the attractive forces of the bulk liquid entirely. Consequently, liquid particles are still close together, maintaining a definite volume, but they are free to move past one another. This mobility allows liquids to flow and take the shape of their container. The intermolecular forces in a liquid are still significant, which is why liquids are generally much denser than gases and resist compression. The arrangement is disordered compared to a solid, but the proximity of particles means that the potential energy is still relatively low. In a gas, the kinetic energy of the particles vastly exceeds the strength of the intermolecular attractive forces. The particles are far apart relative to their size, moving randomly at high speeds. They collide elastically with each other and with the walls of the container. Because the forces between gas particles are negligible over most of their trajectory, gases have neither a definite shape nor a definite volume; they expand to fill whatever container they occupy. The density of a gas is low because the volume occupied by the particles themselves is a tiny fraction of the total volume. This state is highly sensitive to temperature and pressure, as changes in these variables directly affect the kinetic energy and the spacing between particles. Phase changes occur when energy is added to or removed from a system, tipping the balance between kinetic energy and intermolecular forces. Melting, for instance, involves adding energy to a solid to overcome the lattice energy, allowing particles to move freely while remaining close together. Vaporisation requires even more energy to completely separate the particles, overcoming all significant intermolecular attractions. These transitions are not instantaneous; they occur at specific temperatures (for pure substances at a given pressure) where the added energy goes entirely into changing the potential energy of the system rather than increasing the kinetic energy. This is why the temperature remains constant during a phase change, even though heat is being continuously supplied. This distinction is crucial for understanding energy diagrams and calorimetry in later lectures.
Intermolecular Forces and Phase Stability
The strength of intermolecular forces (IMFs) dictates the temperature at which phase changes occur. Substances with strong IMFs, such as hydrogen bonding in water or dipole-dipole interactions in polar molecules, require more energy to separate their particles. Therefore, they have higher melting and boiling points compared to non-polar substances of similar molar mass. For example, water (\(\mathrm{H_2O}\)) has a boiling point of \(373.15\ \mathrm{K}\), whereas methane (\(\mathrm{CH_4}\)), which has a similar molar mass but only weak London dispersion forces, boils at \(111.65\ \mathrm{K}\). This difference arises because the hydrogen bonds in water are significantly stronger than the instantaneous dipole-induced dipole forces in methane. When a substance is heated, the average kinetic energy of its particles increases. In the solid phase, this increased kinetic energy manifests as more vigorous vibrations. Once the temperature reaches the melting point, the vibrations become strong enough to disrupt the long-range order of the crystal lattice. The added energy is used to break the bonds holding the lattice together, increasing the potential energy of the system. This energy is known as the latent heat of fusion. It is important to note that during this process, the temperature does not rise. All the thermal energy supplied is converted into potential energy as the particles move further apart and the rigid structure collapses. Similarly, when a liquid is heated to its boiling point, the added energy is used to overcome the remaining intermolecular attractions that keep the particles in the liquid phase. This energy is the latent heat of vaporisation. It is typically much larger than the latent heat of fusion because vaporisation requires the complete separation of particles, whereas fusion only requires the loosening of the lattice. For water, the latent heat of fusion is approximately \(334\ \mathrm{J\,g^{-1}}\), while the latent heat of vaporisation is approximately \(2260\ \mathrm{J\,g^{-1}}\). This large difference reflects the significant work required to expand the volume from liquid to gas against the external pressure and to overcome the cohesive forces entirely. The stability of a phase is also influenced by pressure. Increasing the pressure on a liquid generally increases its boiling point, as the gas phase must generate a higher vapour pressure to equal the external pressure. Conversely, for most substances, increasing pressure favours the phase with the smaller volume, which is usually the solid or liquid. However, water is an exception: ice is less dense than liquid water, so increasing pressure favours the liquid phase, lowering the melting point. This anomalous behaviour is due to the open hexagonal structure of ice, which is stabilised by hydrogen bonding. Understanding these relationships is critical for predicting the behaviour of substances under varying environmental conditions.
Energy Changes During Phase Transitions
Phase changes are isothermal processes for pure substances at a constant pressure. This means that the temperature remains constant throughout the transition, even though heat is being transferred. This follows from energy bookkeeping (the first law) once we split the internal energy into kinetic and potential parts. The internal energy \(U\) of a system is the sum of the kinetic energy of the particles and their potential energy. Temperature is a measure of the average kinetic energy. During a phase change, the added heat \(q\) does not increase the kinetic energy (and thus not the temperature) but instead increases the potential energy by separating the particles. The amount of heat required for a phase change is proportional to the amount of substance. This relationship is expressed using the molar enthalpy of phase change. For melting, the enthalpy change is the molar enthalpy of fusion, \(\Delta H_\mathrm{fus}\). For vaporisation, it is the molar enthalpy of vaporisation, \(\Delta H_\mathrm{vap}\). The heat \(q\) absorbed or released is given by the equation: \[ q = n \Delta H_\mathrm{phase} \] where \(n\) is the number of moles of the substance. These enthalpy values are positive for endothermic processes (melting, vaporisation) and negative for exothermic processes (freezing, condensation). For example, to melt \(1.00\ \mathrm{mol}\) of ice at \(273.15\ \mathrm{K}\), one must supply \(6.01\ \mathrm{kJ}\) of energy. This energy is stored in the liquid water as increased potential energy, allowing the molecules to move freely. It is crucial to distinguish between sensible heat and latent heat. Sensible heat is the heat transfer that results in a temperature change, calculated using the specific heat capacity \(c\) or molar heat capacity \(C\): \[ q = m c \Delta T \] Latent heat, on the other hand, is the heat transfer that results in a phase change at constant temperature. In a heating curve, the temperature rises linearly with heat input in the single-phase regions (solid, liquid, gas), but remains constant during the phase transitions. The slope of the temperature vs. heat input graph is steeper in the solid phase than in the liquid phase for most substances, reflecting the lower heat capacity of the solid. The horizontal segments represent the phase changes, where the length of the segment is proportional to the latent heat. The energy required for vaporisation is particularly significant in biological and industrial contexts. The high latent heat of vaporisation of water allows it to act as an effective coolant. When sweat evaporates from the skin, each gram carries away about 2.4 kJ, so a modest amount of evaporation cools the body substantially. This principle is also used in refrigeration cycles, where a refrigerant vaporises in an evaporator coil, absorbing heat from the surroundings, and then condenses in a condenser coil, releasing that heat. Understanding the magnitude of these energy changes is essential for designing efficient thermal systems and understanding climate dynamics.
Equilibrium and Vapour Pressure
Phase changes are reversible processes. In a closed system, a dynamic equilibrium is established between the phases. For example, in a closed container containing liquid water, molecules are constantly escaping from the liquid surface into the gas phase (evaporation) and molecules from the gas phase are returning to the liquid surface (condensation). Initially, the rate of evaporation exceeds the rate of condensation. As the concentration of water vapour in the gas phase increases, the rate of condensation increases until it equals the rate of evaporation. At this point, the system is in dynamic equilibrium. The pressure exerted by the vapour in this equilibrium state is called the vapour pressure. The vapour pressure is a function of temperature only; it is independent of the amount of liquid present, provided some liquid remains. As the temperature increases, the average kinetic energy of the liquid molecules increases, allowing more molecules to overcome the intermolecular forces and enter the gas phase. Consequently, the vapour pressure increases with temperature. The boiling point of a liquid is defined as the temperature at which its vapour pressure equals the external atmospheric pressure. At standard atmospheric pressure (\(101.325\ \mathrm{kPa}\)), water boils at \(373.15\ \mathrm{K}\). At lower pressures, such as at high altitudes, the boiling point is lower because the vapour pressure reaches the external pressure at a lower temperature. The relationship between vapour pressure and temperature is often described by the Clausius-Clapeyron equation, which relates the natural logarithm of the vapour pressure to the inverse of the absolute temperature: \[ \ln P = -\frac{\Delta H_\mathrm{vap}}{R} \frac{1}{T} + C \] where \(P\) is the vapour pressure, \(\Delta H_\mathrm{vap}\) is the molar enthalpy of vaporisation, \(R\) is the gas constant, \(T\) is the absolute temperature, and \(C\) is a constant. This equation shows that a plot of \(\ln P\) versus \(1/T\) should yield a straight line with a slope of \(-\Delta H_\mathrm{vap}/R\). This linear relationship allows for the determination of the enthalpy of vaporisation from experimental vapour pressure data. It also explains why small changes in temperature can lead to significant changes in vapour pressure, which is critical for understanding weather patterns and the behaviour of volatile liquids. Understanding vapour pressure is also key to the concept of the triple point, where the solid, liquid, and gas phases coexist in equilibrium. For water, this occurs at \(273.16\ \mathrm{K}\) and \(611.657\ \mathrm{Pa}\). The triple point is a fixed property of a substance; the triple point of water was used to define the kelvin until 2019, when the kelvin was redefined by fixing the Boltzmann constant. The phase diagram of a substance maps the regions of stability for each phase as a function of temperature and pressure. The boundaries between these regions represent the conditions under which phase changes occur. The slope of the solid-liquid boundary indicates whether the solid or liquid is denser. For most substances, this slope is positive, meaning the solid is denser. For water, the slope is negative, reflecting the anomalous density of ice. This detailed understanding of phase equilibria is fundamental to physical chemistry and materials science.
A common misconception is that temperature is a measure of the total thermal energy of a system. In reality, temperature is a measure of the average kinetic energy of the particles. A large cup of warm water has a lower temperature than a small cup of boiling water, but it contains significantly more total thermal energy due to its larger mass. During a phase change, the temperature remains constant, but the total internal energy of the system increases significantly as potential energy is added. Confusing temperature with total energy leads to errors in calorimetry and energy balance calculations. Always distinguish between intensive properties (temperature, pressure) and extensive properties (internal energy, enthalpy) when analysing phase changes. C
Worked example
Problem. Calculate the total heat energy required to convert \(50.0\ \mathrm{g}\) of ice at \(273.15\ \mathrm{K}\) into steam at \(373.15\ \mathrm{K}\). Use the following data: molar mass of water \(18.02\ \mathrm{g\,mol^{-1}}\), specific heat capacity of liquid water \(4.18\ \mathrm{J\,g^{-1}\,K^{-1}}\), molar enthalpy of fusion \(\Delta H_\mathrm{fus} = 6.01\ \mathrm{kJ\,mol^{-1}}\), and molar enthalpy of vaporisation \(\Delta H_\mathrm{vap} = 40.7\ \mathrm{kJ\,mol^{-1}}\).
- Determine the number of moles of water: \(n = \frac{50.0\ \mathrm{g}}{18.02\ \mathrm{g\,mol^{-1}}} = 2.775\ \mathrm{mol}\).
- Calculate the heat required to melt the ice at \(273.15\ \mathrm{K}\): \(q_1 = n \Delta H_\mathrm{fus} = 2.775\ \mathrm{mol} \times 6.01\ \mathrm{kJ\,mol^{-1}} = 16.68\ \mathrm{kJ}\).
- Calculate the heat required to raise the temperature of the liquid water from \(273.15\ \mathrm{K}\) to \(373.15\ \mathrm{K}\): \(\Delta T = 100.0\ \mathrm{K}\), \(q_2 = m c \Delta T = 50.0\ \mathrm{g} \times 4.18\ \mathrm{J\,g^{-1}\,K^{-1}} \times 100.0\ \mathrm{K} = 20900\ \mathrm{J} = 20.90\ \mathrm{kJ}\).
- Calculate the heat required to vaporise the water at \(373.15\ \mathrm{K}\): \(q_3 = n \Delta H_\mathrm{vap} = 2.775\ \mathrm{mol} \times 40.7\ \mathrm{kJ\,mol^{-1}} = 112.94\ \mathrm{kJ}\).
- Sum the heat contributions from all three steps: \(q_\mathrm{total} = q_1 + q_2 + q_3 = 16.68\ \mathrm{kJ} + 20.90\ \mathrm{kJ} + 112.94\ \mathrm{kJ} = 150.52\ \mathrm{kJ}\).
Units check. The final answer is in kilojoules, consistent with the input data for enthalpies and the conversion of joules from the specific heat calculation.
Three quick tests
- Why does the temperature remain constant during the melting of a pure solid?
Answer
The added energy is used to overcome intermolecular forces and increase potential energy, not to increase kinetic energy. - Which phase change requires the most energy per mole for water: fusion or vaporisation?
Answer
Vaporisation, because it requires complete separation of particles, overcoming all significant intermolecular attractions. - How does increasing external pressure affect the boiling point of a liquid?
Answer
It increases the boiling point, as the liquid must reach a higher temperature to generate a vapour pressure equal to the external pressure.
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Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes checked line by line by the editor; every number in the worked example was recomputed.