# Phases of Matter

### Phase Transitions

Solid, liquid, and gas are three common states of matter on Earth. A change between these phases is a phase transition. A fourth state of matter, plasma, is less common on Earth because it requires high energies.

States of matter are physical properties, which means they can change without affecting the chemical makeup of the substance. A common physical change is a phase transition, for example, changing from one state of matter to another.

The three familiar states of matter on Earth are solid, liquid, and gas. A gas has neither definite shape nor definite volume. The phase transition from solid to liquid at a constant temperature and pressure is melting. The phase transition from liquid to gas at a constant temperature and pressure is vaporization. The phase transition from gas to liquid at a constant temperature and pressure is condensation. The phase transition from liquid to solid at a constant temperature and pressure is freezing. Occasionally a substance goes from a gas directly to a solid or from a solid directly to a gas without ever going through a liquid state. The phase transition from gas to solid is deposition. The phase transition from solid to gas at a constant temperature and pressure is sublimation.

#### Phase Changes

Any phase change happens because of a change in enthalpy (H), the internal energy of a system plus the work needed to displace the environment to produce the components of the system. Solids have the lowest enthalpy, while liquids have more enthalpy than solids, but less than gases; gases have the greatest enthalpy. To change from a solid, in which the molecules are rigidly packed with very little movement, to a liquid, in which the molecules move freely past one another, energy in the form of heat must be added. Conversely, to move from a liquid to a solid, energy in the form of heat must be removed. Thus any phase change that increases the enthalpy of the phase is endothermic (takes in heat), while any phase change that decreases the enthalpy of the phase is exothermic (gives off heat).

The temperature at which a substance changes from a solid to a liquid at a constant temperature and pressure is its melting point. The temperature at which a substance changes from a liquid to a gas at constant temperature and pressure is its boiling point. Melting points and boiling points for common substances have been empirically determined. The amount of energy required for these changes has also been determined. The amount of energy required for a substance to transition from a solid to a liquid is its enthalpy of fusion ($\Delta {H}_{f}$), given in kilojoules per mole (kJ/mol). The amount of energy required for a substance to transition from a liquid to a gas is its enthalpy of vaporization ($\Delta {H}_{v}$), also given in kJ/mol. In general, the stronger the bonds between molecules of a substance, the more energy required to break those bonds and, thus, the higher enthalpies of fusion and vaporization, which correspond to higher melting and boiling points.

Importantly, the temperature of the substance does not change while the substance is changing phases. Once melting has begun, for example, all energy taken in by the system is used to increase average kinetic energy to break intermolecular forces and allow for volatilization to transition the solid to a liquid rather than to heat the liquid that has already melted. Consider a cooler full of ice—all the water from the melting ice remains at the melting point of water as long as any ice remains in the cooler. If the temperature of a system is held constant at its melting or boiling point, the system can achieve dynamic equilibrium, a state in which the substance moves between phases at a constant rate without net change. The pressure exerted by a vapor in equilibrium with its solid or liquid form in a closed system is its vapor pressure. When vapor pressure is equal to the pressure of the surroundings, the boiling point is reached.

The melting and boiling points of substances depend not only on temperature, but on pressure as well. The melting and boiling points empirically determined are valid only at 1 atmosphere (atm). At higher pressures, enthalpy, in general, decreases because the particles are more restricted in movement, and thus, the temperatures required to transition from phases of lower enthalpies to higher ones increase. This is the reason that cooking instructions vary with altitude. At lower pressures, which occur at a higher altitude, the melting and boiling points of substances are lower.

If the temperatures are high enough, the kinetic energy of the molecules of a gas cannot be overcome for condensation to occur, regardless of pressure. The temperature above which a gas cannot become a liquid is the critical temperature. At critical temperature, the gas can still become liquid, but at any temperature above, it cannot. For water, the critical temperature is 647 K. At 648 K, water cannot become a liquid, regardless of how much pressure is exerted on it. The minimum pressure required for condensation of a gas at its critical temperature is its critical pressure. The critical pressure of water is 22.064 megapascales (MPa); at any pressure greater than that, water cannot be a gas, even at high temperatures.

Sometimes a liquid exists at the temperature and pressure at which it should be a gas. This is a superheated state. Superheating can occur when surface tension inhibits the expansion of bubbles of gas in a liquid. This causes the vapor pressure to exceed atmospheric pressure even though the substance remains liquid. Superheated liquids are very unstable and tend to violently vaporize as soon as the pressure from surface tension is overcome. A common example is when water is heated in a smooth container in a static heating environment, such as a microwave. The environment in the microwave can be unfavorable for the formation of steam bubbles, preventing the water from becoming steam even while its temperature is above boiling temperature. The water is then said to be superheated and can boil suddenly when removed from the microwave or disturbed by adding something to it.

Similarly, a liquid can exist at the temperature and pressure at which it should become a solid. This is a supercooled state. This occurs when the liquid is completely free of nucleation sites, which are points around which crystals can form. Nucleation sites can be impurities or simply deformations in the container holding the liquid, such as scratches or cracks. Supercooling of a liquid can continue as temperature decreases until the point at which the molecules of the liquid themselves act as nucleation points. At this point, the liquid will crystallize fully.

The energy required to change a system from one phase to another can be calculated only if the mass of the substance and its starting and ending temperatures are known. This can be done using the specific heat of the substance, which is the energy required per unit of mass to raise the temperature by one degree Celsius. The formula for calculating heat energy of the system is $q=mc\Delta T$, where q is the heat energy measured in Joules (J), m is the mass in grams of the substance, c is the specific heat of the substance, and $\Delta T$ is the total change in temperature measured in degrees Celsius. The specific heat differs depending on the state of the mass. Ice and liquid water, for example, have different specific heats. The formula for calculating the heat energy of a phase change between a solid and a liquid is $q=m\Delta {H}_f$, where $\Delta {H}_f$ is the enthalpy of fusion. The formula for calculating the heat energy of a phase change between a liquid and a gas is $q=m\Delta {H}_v$, where $\Delta {H}_v$ is the enthalpy of vaporization of the substance. To calculate the total heat energy of the system, all formulas involved in the phase change must be used and their products added together.

Step-By-Step Example
Heat Energy Calculation
Calculate the heat energy required to warm 10.0 grams of ice at –5.0°C to liquid water at 10.0°C. Assume a specific heat of 2.09 J/g°C for ice, heat of fusion of 334 J/g, and specific heat of 4.18 J/g°C for liquid water.
Step 1
Calculate qice for the ice warming to its melting point.
\begin{aligned} q_{\rm{ice}}&=mc_{\rm{ice}}{\Delta}{T}\\&=\left(10.0\;{\rm{g}}\right)\!(2.09\;{\rm{J}}/{\rm{g}}\,\degree{\rm{C}})(5.0\degree{\rm{C}})\\&=104.5\;{\rm{J}}\end{aligned}
Step 2
Calculate qmelt for melting the entire 10.0 g ice using the specific heat of fusion for water at its freezing point.
\begin{aligned}q_{\rm{melt}}&=m\Delta{ H}_f\\&=(10.0\;{\rm{g}})(334\;{\rm{J}}/{\rm{g}})\\&=3340\;{\rm{J}}\end{aligned}
Step 3
Calculate qwater for warming the liquid water from 0.0°C to 10.0°C.
\begin{aligned} q_{\rm{water}}&=mc\Delta{T}\\&=(10.0\;{\rm{g}})(4.18\;{\rm{J}}/{\rm{g}}\,\degree{\rm{C}})(10.0\,\degree{\rm{C}})\\&=418.0\;{\rm{J}}\end{aligned}
Solution
\begin{aligned}q_{\rm{total}}&=q_{\rm{ice}}+q_{\rm{melt}}+q_{\rm{water}}\\&=104.5\,\rm{J}+3340\,\rm J+418.0\,\rm{J}\\&=3.9\times{10}^3\,\rm{J}\end{aligned}

### Phase Diagrams

A phase diagram is a graphical representation of the relationship between a substance's phases of matter and temperature, as well as pressure.
All elements and compounds can transition between phases of matter under certain conditions of temperature and pressure. The graph showing the relationship between phases of matter and temperature and pressure is a phase diagram.

#### Phase Diagram

A phase diagram shows curves that represent the transitions between solids and gases (the sublimation or deposition curve), solids and liquids (the melting or freezing curve), and liquids and gases (the vaporization or condensation curve). The point at which all these curves intersect is the triple point. At the temperature and pressure represented by the triple point (Ttp and Ptp, respectively), the substance exists in all three phases simultaneously. At the end of the vaporization or condensation curve is the critical point, which represents the critical temperature and critical pressure (Tcp and Pcp, respectively). At this point, the substance cannot be distinguished between a liquid and a gas. Beyond the critical point, a substance will form a supercritical fluid, a substance that has properties of both a liquid and a gas at a temperature and pressure above the critical point. Supercritical fluids can dissolve materials and effuse through solids.

#### Phase Diagram for Carbon Dioxide

A phase diagram can be used to predict the phase for a substance at a given temperature and pressure, as well as to determine the temperature and pressure at which a phase transition will happen for a particular substance. For example, given the phase diagram for carbon dioxide (CO2), the temperature at which the compound vaporizes from a liquid to a gas at 60 atmospheres (atm) can be determined. Examine the phase diagram to see that this change occurs just above 20°C. It is also apparent that CO2 is a supercritical fluid at 40°C and 80 atm. An important phase diagram is water, H2O. Unlike in phase diagrams for other substances, for water, the melting/freezing curve slopes to the left. This indicates that solid water (ice) is less dense than liquid water. This is because of the hydrogen bond, which causes water to form a crystalline structure when frozen. This property of water has important physical and biological implications. Since ice floats in water, life in lakes and ponds is able to survive in frigid temperatures, with the floating ice insulating the water below. Furthermore the triple point of water lies at about 1 atm. This means that water occurs in all three phases—solid, liquid, and gas—quite readily across Earth's surface, where pressure is about 1 atm.