0.3: Chemistry

Particles

Due to the extremely small size of protons and neutrons, scientists created a new unit of measurement, the atomic mass unit (amu). One atomic mass unit is defined as 1/12 of the mass of one atom of carbon. Table \(\PageIndex{1}\) lists the properties of these particles including their mass in amu and grams. The mass of any of these particles in grams is a very small number, about 10^-24.

A proton has a mass of 1.00727 amu and a charge of +1. A neutron is a slightly heavier particle with a mass of 1.00866 amu and a charge of zero because it is neutral. The electron has a charge of -1 and is a much lighter particle with a mass of about 0.00055 amu. It would take about 1800 electrons to equal the mass of one proton. The protons and neutrons are in the nucleus, while the electrons are outside of the nucleus.

Ionization

Atoms are electrically neutral if they contain the same number of positively charged protons and negatively charged electrons. Because the electrons of an atom are in contact with the outside world, it is possible for one or more electrons to be lost, or some new ones to be added in a process called ionization. The resulting electrically-charged atom is called an ion. The charge of an atom is calculated by subtracting the number of electrons from the number of protons. An atom can become completely ionized, losing all of its electrons. A hydrogen atom, having only one electron to lose, can be ionized only once while a helium atom can be ionized twice, and an oxygen atom can be ionized up to eight times.

An atom that has become positively ionized has lost a negative charge—the missing electron—and thus is left with a net positive charge. It therefore exerts a strong attraction on any free electron. Eventually, one or more electrons will be captured and the atom will become neutral (or ionized to one less degree) again. During the electron-capture process, the atom emits one or more photons. Which photons are emitted depends on whether the electron is captured at once to the lowest energy level of the atom or stops at one or more intermediate levels on its way to the lowest available level.

Isotopes

The number of neutrons is not necessarily the same for all atoms of a given element. For example, most hydrogen atoms contain no neutrons at all. There are, however, hydrogen atoms that contain one proton and one neutron, and others that contain one proton and two neutrons. The various types of hydrogen nuclei with different numbers of neutrons are called isotopes of hydrogen, Figure \(\PageIndex{4}\). All other elements have isotopes as well. The isotopes of hydrogen are often referred to using common names and accompanying symbols. Hydrogen-2, symbolized ²H, is also called deuterium and sometimes symbolized D. Hydrogen-3, symbolized ³H, is also called tritium and sometimes symbolized T.

The symbol for a specific isotope of any element is written by placing the mass number as a superscript to the left of the element symbol. The element symbol of magnesium is Mg. The atomic number is sometimes written as a subscript preceding the symbol, but since this number defines the element’s identity, as does its symbol, it is often omitted. For example, magnesium exists as a mixture of three isotopes, each with an atomic number of 12 and with mass numbers of 24, 25, and 26, respectively. These isotopes can be symbolized as ²⁴Mg, ²⁵Mg, and ²⁶Mg. These isotope symbols are read as element, mass number. For instance, ²⁴Mg is read as magnesium 24, and can be written as magnesium-24 or Mg-24. All magnesium atoms have 12 protons in their nucleus. The isotopes differ only because a ²⁴Mg atom has 12 neutrons in its nucleus, a ²⁵Mg atom has 13 neutrons, and a ²⁶Mg has 14 neutrons.

The Periodic Table

As early chemists worked to purify ores and discovered more elements, they realized that various elements could be grouped together by their similar chemical behaviors. Many elements differ dramatically in their chemical and physical properties, but some elements are similar in their behaviors. For example, many elements appear shiny, are malleable, ductile, and conduct heat and electricity well. Other elements are not shiny, malleable, or ductile, and are poor conductors of heat and electricity. Chemists studied materials and attempted to organize them in a chart to group them by their chemical properties.

A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column, Figure \(\PageIndex{5}\). Each box represents an element and contains its atomic number, symbol, average atomic mass, and name. The elements are arranged in seven horizontal rows, called periods or series, and 18 vertical columns, called groups. Groups are labeled at the top of each column. For the table to fit on a single page, parts of two of the rows, a total of 14 columns, are usually written below the main body of the table.

Cosmic Abundances

Hydrogen, helium, and a few other very light elements were formed within about three minutes of the Big Bang. The next 23 elements, through iron, are formed mostly by nuclear fusion processes within stars, in which lighter nuclei combine into successively heavier elements. Elements heavier than iron cannot be formed in this way, and are produced only during the catastrophic collapse of massive stars called supernova explosions. Most of the atoms in the universe still consist of hydrogen, with helium being a distant second. On Earth, oxygen, silicon, and aluminum are most abundant. These profiles serve as useful guides for constructing models for the formation of Earth and other planetary bodies.

Nearly 100 different kinds of elements exist in nature. Most of them are rare, and only a handful account for more than 99% of everything with which we come in contact. The most abundant elements in the cosmos today are listed in Table Table \(\PageIndex{2}\). The list includes the four elements most common in life on Earth: hydrogen, carbon, nitrogen, and oxygen. To represent the abundance of elements, this table lists the number of elements present in the universe compared to 1 million hydrogen atoms. In the table, there are 80,000 helium atoms for every 1,000,000 hydrogen atoms, or for every 8 helium atoms, there are 100 hydrogen atoms. In this table, the least abundant element is sulfur with just 19 atoms per 1,000,000 hydrogen atoms, but all of the elements are rare compared to hydrogen and helium.

Footnotes

• 1This list of elements is arranged in order of the atomic number, which is the number of protons in each nucleus.

Atomic Theory of Matter

The definition of an element given above is an operational one; a certain result (or in this case, a non-result!) of a procedure that might lead to the decomposition of a substance into lighter units will tentatively place that substance into one of the categories: element or compound. Because this operation is carried out on bulk matter, the concept of the element is also a macroscopic one. The atom, by contrast, is a microscopic concept which in modern chemistry relates the unique character of every chemical element to an actual physical particle.

The idea of the atom as the smallest particle of matter had its origins in Greek philosophy around 400 BCE but was controversial from the start (both Plato and Aristotle maintained that matter was infinitely divisible.) It was not until 1803 that John Dalton proposed a rational atomic theory to explain the facts of chemical combination as they were then known, thus being the first to employ macroscopic evidence to illuminate the microscopic world. It wasn't until the 1900s that the atomic theory became universally accepted. In the 1920's it became possible to measure the sizes and masses of atoms, and in the 1970's techniques were developed that produced images of individual atoms.

Throughout most of history the idea that matter is composed of minute particles had languished as a philosophical abstraction known as atomism, and no clear relation between these "atoms" and the chemical "elements" had been established. This began to change in the early 1800's when the development of balances that permitted reasonably precise measurements of the weight changes associated with chemical reactions ushered in a new and fruitful era of experimental chemistry. This resulted in the recognition of several laws of chemical change that laid the groundwork for the atomic theory of matter.

The parallel concepts of the element and the atom constitute the very foundations of chemical science. As such, the concept of the element is a macroscopic one that relates to the world that we can observe with our senses. The atom is the microscopic realization of this concept; that is, it is the actual physical particle that is unique to each chemical element. Their very small size has long prevented atoms from being observable by direct means, so their existence was not universally accepted until the late 19^th Century. The fact that we still hear the mention of the "atomic theory of matter" should not imply that there is now any doubt about the existence of atoms. Few theories in the history of science have been as thoroughly validated and are as well understood.

Although the word atom usually refers to a specific kind of particle (an "atom of magnesium", for example), our everyday use of element tends to be more general, referring not only to a substance composed of a particular type of atom ("bromine is one of the few elements that are liquids at room temperature"), but also to atoms in a collective sense ("magnesium is one of the elements having two electrons in its outer shell").

The underlying concept of atoms as the basic building blocks of matter has been around for a long time. As early as 600 BCE, the Gujarati (Indian) philosopher Acharya Kanad wrote that "Every object of creation is made of atoms which in turn connect with each other to form molecules". A couple of centuries later in 460 BCE, the Greek philosopher Democritus reasoned that if you keep breaking a piece of matter into smaller and smaller fragments, there will be some point at which the pieces cannot be made any smaller. He called these "basic matter particles"— in other words, atoms. But this was just philosophy; it would not become science until 1800 when John Dalton showed how the atomic concept followed naturally from the results of quantitative experiments based on weight measurements.

Bohr's Model

Niels Bohr was a brilliant Danish physicist who came to dominate the world of atomic and nuclear physics during the first half of the twentieth century. Bohr suggested that the planetary model could be saved if one new assumption were made: certain "special states of motion" of the electron, corresponding to different orbital radii, would not result in radiation, and could therefore persist indefinitely without the electron falling into the nucleus. Specifically, Bohr postulated that the angular momentum of the electron, mvr (the mass and angular velocity of the electron and in an orbit of radius \(r\)) is restricted to values that are integral multiples of \(h/2\pi\). The radius of one of these allowed Bohr orbits is given by

\[r=\dfrac{nh}{2\pi m u} \nonumber \]

in which h is Planck's constant, m is the mass of the electron, v is the orbital velocity, and n can have only the integer values 1, 2, 3, etc. The most revolutionary aspect of this assumption was its use of the variable integer n; this was the first application of the concept of the quantum number to matter. The larger the value of n, the larger the radius of the electron orbit, and the greater the potential energy of the electron.

As the electron moves to orbits of increasing radius, it does so in opposition to the restoring force due to the positive nucleus, and its potential energy is thereby raised. This is entirely analogous to the increase in potential energy that occurs when any mechanical system moves against a restoring force— as, for example, when a rubber band is stretched or a weight is lifted.

Thus what Bohr was saying, in effect, is that the atom can exist only in certain discrete energy states: the energy of the atom is quantized. Bohr noted that this quantization nicely explained the observed emission spectrum of the hydrogen atom. The electron is normally in its smallest allowed orbit, corresponding to n = 1; upon excitation in an electrical discharge or by ultraviolet light, the atom absorbs energy and the electron gets promoted to higher quantum levels. These higher excited states of the atom are unstable, so after a very short time (around 10^—9 sec) the electron falls into lower orbits and finally into the innermost one, which corresponds to the atom's ground state. The energy lost on each jump is given off as a photon, and the frequency of this light provides a direct experimental measurement of the difference in the energies of the two states, according to the Planck-Einstein relationship e = hν.

This suggestion, in the words of science historian Abraham Pais, was “one of the most audacious hypotheses ever introduced in physics.” If something equivalent were at work in the everyday world, you might find that, as you went for a walk after astronomy class, nature permitted you to walk two steps per minute, five steps per minute, and 12 steps per minute, but no speeds in between. No matter how you tried to move your legs, only certain walking speeds would be permitted. To make things more bizarre, it would take no effort to walk at any one of the allowed speeds, but it would be difficult to change from one speed to another. Luckily, no such rules apply at the level of human behavior. But at the microscopic level of the atom, experiment after experiment has confirmed the validity of Bohr’s strange idea. Bohr’s suggestions became one of the foundations of the new (and much more sophisticated) model of the subatomic world called quantum mechanics.

In Bohr’s model, if the electron moves from one orbit to another closer to the atomic nucleus, it must give up some energy in the form of electromagnetic radiation. If the electron goes from an inner orbit to one farther from the nucleus, however, it requires some additional energy. One way to obtain the necessary energy is to absorb electromagnetic radiation that may be streaming past the atom from an outside source.

A key feature of Bohr’s model is that each of the permitted electron orbits around a given atom has a certain energy value; we therefore can think of each orbit as an energy level. To move from one orbit to another (which will have its own specific energy value) requires a change in the electron’s energy—a change determined by the difference between the two energy values. If the electron goes to a lower level, the energy difference will be given off; if the electron goes to a higher level, the energy difference must be obtained from somewhere else. Each jump (or transition) to a different level has a fixed and definite energy change associated with it.

A crude analogy for this situation might be life in a tower of luxury apartments where the rent is determined by the quality of the view. Such a building has certain, definite numbered levels or floors on which apartments are located. No one can live on floor 5.37 or 22.5. In addition, the rent gets higher as you go up to higher floors. If you want to exchange an apartment on the twentieth floor for one on the second floor, you will not owe as much rent. However, if you want to move from the third floor to the twenty-fifth floor, your rent will increase. In an atom, too, the “cheapest” place for an electron to live is the lowest possible level, and energy is required to move to a higher level.

Here we have one of the situations where it is easier to think of electromagnetic radiation as particles (photons) rather than as waves. As electrons move from one level to another, they give off or absorb little packets of energy. When an electron moves to a higher level, it absorbs a photon of just the right energy (provided one is available). When it moves to a lower level, it emits a photon with the exact amount of energy it no longer needs in its “lower-cost living situation.”

The photon and wave perspectives must be equivalent: light is light, no matter how we look at it. Thus, each photon carries a certain amount of energy that is proportional to the frequency (f) of the wave it represents. The value of its energy (E) is given by the formula

$$E=$$

where the constant of proportionality, h, is called Planck’s constant.

The constant is named for Max Planck, the German physicist who was one of the originators of the quantum theory (Figure 5.18). If metric units are used (that is, if energy is measured in joules and frequency in hertz), then Planck’s constant has the value h = 6.626 × 10^–34 joule-seconds (J-s). Higher-energy photons correspond to higher-frequency waves (which have a shorter wavelength); lower-energy photons are waves of lower frequency.

To take a specific example, consider a calcium atom inside the Sun’s atmosphere in which an electron jumps from a lower level to a higher level. To do this, it needs about $5\times {10}^{-19}$ joules of energy, which it can conveniently obtain by absorbing a passing photon of that energy coming from deeper inside the Sun. This photon is equivalent to a wave of light whose frequency is about $7.5\times {10}^{14}$ hertz and whose wavelength is about $3.9\times {10}^{-7}$ meters (393 nanometers), in the deep violet part of the visible light spectrum. Although it may seem strange at first to switch from picturing light as a photon (or energy packet) to picturing it as a wave, such switching has become second nature to astronomers and can be a handy tool for doing calculations about spectra.

Particles

Due to the extremely small size of protons and neutrons, scientists created a new unit of measurement, the atomic mass unit (amu). One atomic mass unit is defined as 1/12 of the mass of one atom of carbon-12. Table \(\PageIndex{2}\) lists the properties of these particles including their mass in amu and grams. The mass of any of these particles in grams is a very small number, about 10^-24. 

A proton has a mass of 1.00727 amu and a charge of 1+. A neutron is a slightly heavier particle with a mass 1.00866 amu and a charge of zero because it is neutral. The electron has a charge of 1− and is a much lighter particle with a mass of about 0.00055 amu. It would take about 1800 electrons to equal the mass of one proton. The sum of an atom’s subatomic particles does not equal the atom’s actual mass. The total mass of six protons, six neutrons, and six electrons is 12.0993 amu, slightly larger than 12.00 amu. This missing mass is known as the mass defect.

Ionization

Atoms are electrically neutral if they contain the same number of positively charged protons and negatively charged electrons. Because the electrons of an atom are in contact with the outside world, it is possible for one or more electrons to be lost, or some new ones to be added in a process called ionization. The resulting electrically-charged atom is called an ion. The charge of an atom is calculated by subtracting the number of electrons from the number or protons. An atom can become completely ionized, losing all of its electrons. A hydrogen atom, having only one electron to lose, can be ionized only once while a helium atom can be ionized twice. and an oxygen atom up can be ionized up to eight times.

An atom that has become positively ionized has lost a negative charge—the missing electron—and thus is left with a net positive charge. It therefore exerts a strong attraction on any free electron. Eventually, one or more electrons will be captured and the atom will become neutral (or ionized to one less degree) again. During the electron-capture process, the atom emits one or more photons. Which photons are emitted depends on whether the electron is captured at once to the lowest energy level of the atom or stops at one or more intermediate levels on its way to the lowest available level.

Isotopes

The number of neutrons is not necessarily the same for all atoms of a given element. For example, most hydrogen atoms contain no neutrons at all. There are, however, hydrogen atoms that contain one proton and one neutron, and others that contain one proton and two neutrons. The various types of hydrogen nuclei with different numbers of neutrons are called isotopes of hydrogen, Figure \(\PageIndex{x}\). All other elements have isotopes as well. The isotopes of hydrogen are often referred to using common names and accompanying symbols. Hydrogen-2, symbolized ²H, is also called deuterium and sometimes symbolized D. Hydrogen-3, symbolized ³H, is also called tritium and sometimes symbolized T. 

The symbol for a specific isotope of any element is written by placing the mass number as a superscript to the left of the element symbol. The element symbol of magnesium is Mg. The atomic number is sometimes written as a subscript preceding the symbol, but since this number defines the element’s identity, as does its symbol, it is often omitted. For example, magnesium exists as a mixture of three isotopes, each with an atomic number of 12 and with mass numbers of 24, 25, and 26, respectively. These isotopes can be symbolized as ²⁴Mg, ²⁵Mg, and ²⁶Mg. These isotope symbols are read as element, mass number. For instance, ²⁴Mg is read as magnesium 24, and can be written as magnesium-24 or Mg-24. All magnesium atoms have 12 protons in their nucleus. The isotopes differ only because a ²⁴Mg atom has 12 neutrons in its nucleus, a ²⁵Mg atom has 13 neutrons, and a ²⁶Mg has 14 neutrons.

The Periodic Table

As early chemists worked to purify ores and discovered more elements, they realized that various elements could be grouped together by their similar chemical behaviors. Many elements differ dramatically in their chemical and physical properties, but some elements are similar in their behaviors. For example, many elements appear shiny, are malleable, ductile, and conduct heat and electricity well. Other elements are not shiny, malleable, or ductile, and are poor conductors of heat and electricity. Chemists studied materials and attempted to organize them in a chart to group them by their chemical properties.

A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column . Each box represents an element and contains its atomic number, symbol, average atomic mass, and name. The elements are arranged in seven horizontal rows, called periods or series, and 18 vertical columns, called groups. Groups are labeled at the top of each column. For the table to fit on a single page, parts of two of the rows, a total of 14 columns, are usually written below the main body of the table. 

Cosmic Abundances

Hydrogen, helium and a few other very light elements were formed within about three minutes of the Big Bang. The next 23 elements, through iron, are formed mostly by nuclear fusion processes within stars, in which lighter nuclei combine into successively heavier elements. Elements heavier than iron cannot be formed in this way, and are produced only during the catastrophic collapse of massive stars called supernovae explosions.

Quite markedly, and very differently in different bodies in the cosmos. Most of the atoms in the universe still consist of hydrogen, with helium being a distant second. On Earth, oxygen, silicon, and aluminum are most abundant. These profiles serve as useful guides for constructing models for the formation of Earth and other planetary bodies.

Nearly 100 different kinds of elements exist in nature. Most of them are rare, and only a handful account for more than 99% of everything with which we come in contact. The most abundant elements in the cosmos today are listed in Table \(\PageIndex{3}\). The list includes the four elements most common in life on Earth: hydrogen, carbon, nitrogen, and oxygen.

Sublimation

Some solids have such high vapor pressures that heating leads to a substantial amount of direct vaporization even before the melting point is reached. This is the case for solid iodine, for example. I₂ melts at 115°C and boils at 183°C, is easily sublimed at temperatures around 100°C. Even ice has a measurable vapor pressure near its freezing point, as evidenced by the tendency of snow to evaporate in cold dry weather. There are other solids whose vapor pressure overtakes that of the liquid before melting can occur. Such substances sublime without melting; a common example is solid carbon dioxide (“Dry Ice”) at 1 atm (see the CO₂phase diagram below).

We witness and utilize changes of physical state, or phase transitions, in a great number of ways. As one example of global significance, consider the evaporation, condensation, freezing, and melting of water. These changes of state are essential aspects of our earth’s water cycle as well as many other natural phenomena and technological processes of central importance to our lives. In this module, the essential aspects of phase transitions are explored.

Vaporization and Condensation

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally collide with the surface of the condensed phase, and in some cases, these collisions will result in the molecules re-entering the condensed phase. The change from the gas phase to the liquid is called condensation. When the rate of condensation becomes equal to the rate of vaporization, neither the amount of the liquid nor the amount of the vapor in the container changes. The vapor in the container is then said to be in equilibrium with the liquid. Keep in mind that this is not a static situation, as molecules are continually exchanged between the condensed and gaseous phases. Such is an example of a dynamic equilibrium, the status of a system in which reciprocal processes (for example, vaporization and condensation) occur at equal rates. The pressure exerted by the vapor in equilibrium with a liquid in a closed container at a given temperature is called the liquid’s vapor pressure (or equilibrium vapor pressure). The area of the surface of the liquid in contact with a vapor and the size of the vessel have no effect on the vapor pressure, although they do affect the time required for the equilibrium to be reached. We can measure the vapor pressure of a liquid by placing a sample in a closed container, like that illustrated in Figure \(\PageIndex{1}\), and using a manometer to measure the increase in pressure that is due to the vapor in equilibrium with the condensed phase.

The chemical identities of the molecules in a liquid determine the types (and strengths) of intermolecular attractions possible; consequently, different substances will exhibit different equilibrium vapor pressures. Relatively strong intermolecular attractive forces will serve to impede vaporization as well as favoring “recapture” of gas-phase molecules when they collide with the liquid surface, resulting in a relatively low vapor pressure. Weak intermolecular attractions present less of a barrier to vaporization, and a reduced likelihood of gas recapture, yielding relatively high vapor pressures. The following example illustrates this dependence of vapor pressure on intermolecular attractive forces. 

As temperature increases, the vapor pressure of a liquid also increases due to the increased average KE of its molecules. Recall that at any given temperature, the molecules of a substance experience a range of kinetic energies, with a certain fraction of molecules having a sufficient energy to overcome IMF and escape the liquid (vaporize). At a higher temperature, a greater fraction of molecules have enough energy to escape from the liquid, . The escape of more molecules per unit of time and the greater average speed of the molecules that escape both contribute to the higher vapor pressure.

Boiling Points

When the vapor pressure increases enough to equal the external atmospheric pressure, the liquid reaches its boiling point. The boiling point of a liquid is the temperature at which its equilibrium vapor pressure is equal to the pressure exerted on the liquid by its gaseous surroundings. For liquids in open containers, this pressure is that due to the earth’s atmosphere. The normal boiling point of a liquid is defined as its boiling point when surrounding pressure is equal to 1 atm (101.3 kPa). Figure \(\PageIndex{3}\) shows the variation in vapor pressure with temperature for several different substances. Considering the definition of boiling point, these curves may be seen as depicting the dependence of a liquid’s boiling point on surrounding pressure.

The quantitative relation between a substance’s vapor pressure and its temperature is described by the Clausius-Clapeyron equation:

\[P=A e^{-\Delta H_{\text {vap }} / R T} \nonumber \]

where ΔH_vap is the enthalpy of vaporization for the liquid, R is the gas constant, and A is a constant whose value depends on the chemical identity of the substance. Temperature T must be in Kelvin in this equation. This equation is often rearranged into logarithmic form to yield the linear equation:

\[\ln P=-\frac{\Delta H_{ vap }}{R T}+\ln A \nonumber \]

This linear equation may be expressed in a two-point format that is convenient for use in various computations, as demonstrated in the example exercises that follow. If at temperature T₁, the vapor pressure is P₁, and at temperature T₂, the vapor pressure is P₂, the corresponding linear equations are:

\[\ln P_1=-\frac{\Delta H_{ vap }}{R T_1}+\ln A \nonumber \]

and

\[\ln P_2=-\frac{\Delta H_{ vap }}{R T_2}+\ln A \nonumber \]

Since the constant, A, is the same, these two equations may be rearranged to isolate ln A and then set them equal to one another:

\[\ln P_1+\frac{\Delta H_{\text {vap }}}{R T_1}=\ln P_2+\frac{\Delta H_{\text {vap }}}{R T_2} \nonumber \]

which can be combined into:

\[\ln \left(\frac{P_2}{P_1}\right)=\frac{\Delta H_{\text {vap }}}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) \nonumber \] 

Enthalpy of Vaporization

Vaporization is an endothermic process. The cooling effect can be evident when you leave a swimming pool or a shower. When the water on your skin evaporates, it removes heat from your skin and causes you to feel cold. The energy change associated with the vaporization process is the enthalpy of vaporization, ΔH_vap. For example, the vaporization of water at standard temperature is represented by:

\[\ce{H2O (l) -> H2O (g)} \quad \quad \Delta H_{ vap }=44.01 kJ / mol \nonumber \]

As described in the chapter on thermochemistry, the reverse of an endothermic process is exothermic. And so, the condensation of a gas releases heat:

\[\ce{H2O (g) -> H2O(l)} \quad \quad \Delta H_{\text {con }}=-\Delta H_{\text {vap }}=-44.01 kJ / mol \nonumber \] 

Melting and Freezing

When we heat a crystalline solid, we increase the average energy of its atoms, molecules, or ions and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state, or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is melted. Only after all of the solid has melted will continued heating increase the temperature of the liquid.

If we stop heating during melting and place the mixture of solid and liquid in a perfectly insulated container so no heat can enter or escape, the solid and liquid phases remain in equilibrium. This is almost the situation with a mixture of ice and water in a very good thermos bottle; almost no heat gets in or out, and the mixture of solid ice and liquid water remains for hours. In a mixture of solid and liquid at equilibrium, the reciprocal processes of melting and freezing occur at equal rates, and the quantities of solid and liquid therefore remain constant. The temperature at which the solid and liquid phases of a given substance are in equilibrium is called the melting point of the solid or the freezing point of the liquid. Use of one term or the other is normally dictated by the direction of the phase transition being considered, for example, solid to liquid (melting) or liquid to solid (freezing).

The enthalpy of fusion and the melting point of a crystalline solid depend on the strength of the attractive forces between the units present in the crystal. Molecules with weak attractive forces form crystals with low melting points. Crystals consisting of particles with stronger attractive forces melt at higher temperatures.

The amount of heat required to change one mole of a substance from the solid state to the liquid state is the enthalpy of fusion, ΔH_fus of the substance. The enthalpy of fusion of ice is 6.0 kJ/mol at 0 °C. Fusion (melting) is an endothermic process:

\[\ce{H2O (s) -> H2O(l)} \quad \Delta H_{\text {fus }}=6.01 kJ / mol \nonumber \]

The reciprocal process, freezing, is an exothermic process whose enthalpy change is −6.0 kJ/mol at 0 °C:

\[\ce{H2O(l) -> H2O(s)} \quad \Delta H_{\text {frz }}=-\Delta H_{\text {fus }}=-6.01 kJ / mol \nonumber \]

Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid \(\ce{CO2}\)) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublime at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes and a vivid purple vapor forms (Figure \(\PageIndex{6}\)). The reverse of sublimation is called deposition, a process in which gaseous substances condense directly into the solid state, bypassing the liquid state. The formation of frost is an example of deposition.

Like vaporization, the process of sublimation requires an input of energy to overcome intermolecular attractions. The enthalpy of sublimation, ΔH_sub, is the energy required to convert one mole of a substance from the solid to the gaseous state. For example, the sublimation of carbon dioxide is represented by:

\[\ce{CO2(s)  -> CO_2(g)} \quad \quad \Delta H_{\text {sub }}=26.1 kJ / mol \nonumber \]

Likewise, the enthalpy change for the reverse process of deposition is equal in magnitude but opposite in sign to that for sublimation:

\[\ce{CO_2(g) -> CO_2(s)} \quad \quad \Delta H_{\text {dep }}=-\Delta H_{\text {sub }}=-26.1 kJ / mol \nonumber \]

Consider the extent to which intermolecular attractions must be overcome to achieve a given phase transition. Converting a solid into a liquid requires that these attractions be only partially overcome; transition to the gaseous state requires that they be completely overcome. As a result, the enthalpy of fusion for a substance is less than its enthalpy of vaporization. This same logic can be used to derive an approximate relation between the enthalpies of all phase changes for a given substance. Though not an entirely accurate description, sublimation may be conveniently modeled as a sequential two-step process of melting followed by vaporization in order to apply Hess’s Law. Viewed in this manner, the enthalpy of sublimation for a substance may be estimated as the sum of its enthalpies of fusion and vaporization, as illustrated in Figure \(\PageIndex{7}\). For example:

\[\begin{array}{lc}
\text { solid } \longrightarrow \text { liquid } & \Delta H_{\text {fus }} \\
\text { liquid } \longrightarrow \text { gas } & \Delta H_{\text {vap }} \\
\hline \text { solid } \longrightarrow \text { gas } & \Delta H_{\text {sub }}=\Delta H_{\text {fus }}+\Delta H_{\text {vap }}
\end{array} \nonumber \]

Phase Diagrams

In the previous module, the variation of a liquid’s equilibrium vapor pressure with temperature was described. Considering the definition of boiling point, plots of vapor pressure versus temperature represent how the boiling point of the liquid varies with pressure. Also described was the use of heating and cooling curves to determine a substance’s melting (or freezing) point. Making such measurements over a wide range of pressures yields data that may be presented graphically as a phase diagram. A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature, and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points).. 

To illustrate the utility of these plots, consider the phase diagram for water shown in Figure \(\PageIndex{2}\).

We can use the phase diagram to identify the physical state of a sample of water under specified conditions of pressure and temperature. For example, a pressure of 50 kPa and a temperature of −10 °C correspond to the region of the diagram labeled “ice.” Under these conditions, water exists only as a solid (ice). A pressure of 50 kPa and a temperature of 50 °C correspond to the “water” region—here, water exists only as a liquid. At 25 kPa and 200 °C, water exists only in the gaseous state. Note that on the H₂O phase diagram, the pressure and temperature axes are not drawn to a constant scale in order to permit the illustration of several important features as described here.

The curve BC in Figure \(\PageIndex{2}\) is the plot of vapor pressure versus temperature as described in the previous module of this chapter. This “liquid-vapor” curve separates the liquid and gaseous regions of the phase diagram and provides the boiling point for water at any pressure. For example, at 1 atm, the boiling point is 100 °C. Notice that the liquid-vapor curve terminates at a temperature of 374 °C and a pressure of 218 atm, indicating that water cannot exist as a liquid above this temperature, regardless of the pressure. The physical properties of water under these conditions are intermediate between those of its liquid and gaseous phases. This unique state of matter is called a supercritical fluid, a topic that will be described in the next section of this module.

The solid-vapor curve, labeled AB in Figure \(\PageIndex{2}\), indicates the temperatures and pressures at which ice and water vapor are in equilibrium. These temperature-pressure data pairs correspond to the sublimation, or deposition, points for water. If we could zoom in on the solid-gas line in Figure \(\PageIndex{2}\), we would see that ice has a vapor pressure of about 0.20 kPa at −10 °C. Thus, if we place a frozen sample in a vacuum with a pressure less than 0.20 kPa, ice will sublime. This is the basis for the “freeze-drying” process often used to preserve foods, such as the ice cream. 

Consider the phase diagram for carbon dioxide . The solid-liquid curve exhibits a positive slope, indicating that the melting point for CO₂ increases with pressure as it does for most substances (water being a notable exception as described previously). Notice that the triple point is well above 1 atm, indicating that carbon dioxide cannot exist as a liquid under ambient pressure conditions. Instead, cooling gaseous carbon dioxide at 1 atm results in its deposition into the solid state. Likewise, solid carbon dioxide does not melt at 1 atm pressure but instead sublimes to yield gaseous CO₂. Finally, notice that the critical point for carbon dioxide is observed at a relatively modest temperature and pressure in comparison to water.

The temperatures and pressures at which a given phase of a substance is stable (that is, from which the molecules have the lowest escaping tendency) is an important property of any substance. Because both the temperature and pressure are factors, it is customary to plot the regions of stability of the various phases in P - T coordinates, as in this generic phase diagram for a hypothetical substance.

Because pressures and temperatures can vary over very wide ranges, it is common practice to draw phase diagrams with non-linear or distorted coordinates. This enables us to express a lot of information in a compact way and to visualize changes that could not be represented on a linearly-scaled plot. It is important that you be able to interpret a phase diagram, or alternatively, construct a rough one when given the appropriate data. Take special note of the following points:

1. The three colored regions on the diagram are the ranges of pressure and temperature at which the corresponding phase is the only stable one.
2. The three lines that bound these regions define all values of (P,T) at which two phases can coexist (i.e., be in equilibrium). Notice that one of these lines is the vapor pressure curve of the liquid as described above. The "sublimation curve" is just a vapor pressure curve of the solid. The slope of the line depends on the difference in density of the two phases.
3. In order to depict the important features of a phase diagram over the very wide range of pressures and temperatures they encompass, the axes are not usually drawn to scale, and are usually highly distorted. This is the reason that the "melting curve" looks like a straight line in most of these diagrams.
4. Where the three named curves intersect, all three phases can coexist. This condition can only occur at a unique value of (P,T ) known as the triple point. Since all three phases are in equilibrium at the triple point, their vapor pressures will be identical at this temperature.
5. The line that separates the liquid and vapor regions ends at the critical point. At temperatures and pressures greater than the critical temperature and pressure, no separate liquid phase exists. We refer to this state simply as a fluid, although the term supercritical liquid is also commonly used.

The best way of making sure you understand a phase diagram is to imagine that you are starting at a certain temperature and pressure, and then change just one of these parameters, keeping the other constant. You will be traversing a horizontal or vertical path on the phase diagram, and there will be a change in state every time your path crosses a line. Of special importance is the horizontal path (shown by the blue line on the diagram above) corresponding to a pressure of 1 atmosphere; this line defines the normal melting and boiling temperatures of a substance.

Notice the following features for the phase diagram of water (Figure \(\PageIndex{11}\)):

Dry ice, solid carbon dioxide, is widely used as a refrigerant and the phase diagram in Figure \(\PageIndex{12}\) shows why it is “dry”. The triple point pressure is at 5.11 atm, so below this pressure, liquid CO₂ cannot exist; the solid can only sublime directly to vapor. Gaseous carbon dioxide at a partial pressure of 1 atm is in equilibrium with the solid at 195K (−79 °C, 1); this is the normal sublimation temperature of carbon dioxide. The surface temperature of dry ice will be slightly less than this, since the partial pressure of CO₂ in contact with the solid will usually be less than 1 atm. Notice also that the critical temperature of CO₂ is only 31°C. This means that on a very warm day, the CO₂ in a fire extinguisher will be entirely vaporized; the vessel must therefore be strong enough to withstand a pressure of 73 atm.

This view of the carbon dioxide phase diagram employs a logarithmic pressure scale and thus encompasses a much wider range of pressures, revealing the upper boundary of the fluid phase (liquid and supercritical). Supercritical carbon dioxide (CO₂ above its critical temperature) possesses the solvent properties of a liquid and the penetrating properties of a gas; one major use is to remove caffeine from coffee beans.