Henry Moseley

From Wikipedia, the free encyclopedia

Henry Moseley
Henry G. J. Moseley in the Balliol-Trinity Laboratories, Oxford University (1910).
Born	23 November 1887 Weymouth, Dorset, England
Died	10 August 1915 (aged 27) Gallipoli, Turkey
Nationality	English
Citizenship	British
Education	Trinity College, University of Oxford University of Manchester
Known for	Atomic Number, Moseley's Law
Awards	Matteucci Medal (1919)
Scientific career
Fields	Physics, chemistry
Influences	Ernest Rutherford

Henry Gwyn Jeffreys Moseley (23 November 1887 – 10 August 1915) was an English physicist, whose contribution to the science of physics was the justification from physical laws of the previous empirical and chemical concept of the atomic number. This stemmed from his development of Moseley's law in X-ray spectra.

Moseley's law advanced atomic physics, nuclear physics and quantum physics by providing the first experimental evidence in favour of Niels Bohr's theory, aside from the hydrogen atom spectrum which the Bohr theory was designed to reproduce. That theory refined Ernest Rutherford's and Antonius van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table.^[1][2] This remains the accepted model today.

When World War I broke out in Western Europe, Moseley left his research work at the University of Oxford behind to volunteer for the Royal Engineers of the British Army. Moseley was assigned to the force of British Empire soldiers that invaded the region of Gallipoli, Turkey, in April 1915, as a telecommunications officer. Moseley was shot and killed during the Battle of Gallipoli on 10 August 1915, at the age of 27. Experts have speculated that Moseley could have been awarded the Nobel Prize in Physics in 1916, had he not been killed.^[3][4] As a consequence, the British government instituted new policies for eligibility for combat duty.^[5]

Biography

Henry G. J. Moseley, known to his friends as Harry,^[6] was born in Weymouth in Dorset in 1887. His father Henry Nottidge Moseley (1844–91), who died when Henry Moseley was quite young, was a biologist and also a professor of anatomy and physiology at the University of Oxford, who had been a member of the Challenger Expedition.^[7] Moseley's mother was Amabel Gwyn Jeffreys Moseley, the daughter of the Welsh biologist and conchologist John Gwyn Jeffreys.^[a]

Henry Moseley had been a very promising schoolboy at Summer Fields School (where one of the four 'leagues' is named after him), and he was awarded a King's scholarship to attend Eton College.^[8] In 1906 he won the chemistry and physics prizes at Eton.^[9] In 1906, Moseley entered Trinity College of the University of Oxford, where he earned his bachelor's degree. Immediately after graduation from Oxford in 1910, Moseley became a demonstrator in physics at the University of Manchester under the supervision of Sir Ernest Rutherford.^[10] During Moseley's first year at Manchester, he had a teaching load as a graduate teaching assistant, but following that first year, he was reassigned from his teaching duties to work as a graduate research assistant. He declined a fellowship offered by Rutherford, preferring to move back to Oxford, in November 1913, where he was given laboratory facilities but no support.^[11]

Scientific work

Experimenting with the energy of beta particles in 1912, Moseley showed that high potentials were attainable from a radioactive source of radium, thereby inventing the first atomic battery, though he was unable to produce the 1MeV necessary to stop the particles.^[12]

In 1913, Moseley observed and measured the X-ray spectra of various chemical elements (mostly metals) that were found by the method of diffraction through crystals.^[13] This was a pioneering use of the method of X-ray spectroscopy in physics, using Bragg's diffraction law to determine the X-ray wavelengths. Moseley discovered a systematic mathematical relationship between the wavelengths of the X-rays produced and the atomic numbers of the metals that were used as the targets in X-ray tubes. This has become known as Moseley's law.

Before Moseley's discovery, the atomic numbers (or elemental number) of an element had been thought of as a semi-arbitrary sequential number, based on the sequence of atomic masses, but modified somewhat where chemists found this modification to be desirable, such as by the Russian chemist, Dmitri Ivanovich Mendeleev. In his invention of the Periodic Table of the Elements, Mendeleev had interchanged the orders of a few pairs of elements in order to put them in more appropriate places in this table of the elements. For example, the metals cobalt and nickel had been assigned the atomic numbers 27 and 28, respectively, based on their known chemical and physical properties, even though they have nearly the same atomic masses. In fact, the atomic mass of cobalt is slightly larger than that of nickel, which would have placed them in backwards order if they had been placed in the Periodic Table blindly according to atomic mass. Moseley's experiments in X-ray spectroscopy showed directly from their physics that cobalt and nickel have the different atomic numbers, 27 and 28, and that they are placed in the Periodic Table correctly by Moseley's objective measurements of their atomic numbers. Hence, Moseley's discovery demonstrated that the atomic numbers of elements are not just rather arbitrary numbers based on chemistry and the intuition of chemists, but rather, they have a firm experimental basis from the physics of their X-ray spectra.

In addition, Moseley showed that there were gaps in the atomic number sequence at numbers 43, 61, 72, and 75. These spaces are now known, respectively, to be the places of the radioactive synthetic elements technetium and promethium, and also the last two quite rare naturally occurring stable elements hafnium (discovered 1923) and rhenium (discovered 1925). Nothing was known about these four elements in Moseley's lifetime, not even their very existence. Based on the intuition of a very experienced chemist, Dmitri Mendeleev had predicted the existence of a missing element in the Periodic Table, which was later found to be filled by technetium, and Bohuslav Brauner had predicted the existence of another missing element in this Table, which was later found to be filled by promethium. Henry Moseley's experiments confirmed these predictions, by showing exactly what the missing atomic numbers were, 43 and 61. In addition, Moseley predicted the existence of two more undiscovered elements, those with the atomic numbers 72 and 75, and gave very strong evidence that there were no other gaps in the Periodic Table between the elements aluminium (atomic number 13) and gold (atomic number 79).

This latter question about the possibility of more undiscovered ("missing") elements had been a standing problem among the chemists of the world, particularly given the existence of the large family of the lanthanide series of rare earth elements. Moseley was able to demonstrate that these lanthanide elements, i.e. lanthanum through lutetium, must have exactly 15 members – no more and no less. The number of elements in the lanthanides had been a question that was very far from being settled by the chemists of the early 20th Century. They could not yet produce pure samples of all the rare-earth elements, even in the form of their salts, and in some cases they were unable to distinguish between mixtures of two very similar (adjacent) rare-earth elements from the nearby pure metals in the Periodic Table. For example, there was a so-called "element" that was even given the chemical name of "didymium". "Didymium" was found some years later to be simply a mixture of two genuine rare-earth elements, and these were given the names neodymium and praseodymium, meaning "new twin" and "green twin". Also, the method of separating the rare-earth elements by the method of ion exchange had not been invented yet in Moseley's time.

Moseley's method in early X-ray spectroscopy was able to sort out the above chemical problems promptly, some of which had occupied chemists for a number of years. Moseley also predicted the existence of element 61, a lanthanide whose existence was previously unsuspected. Quite a few years later, this element 61 was created artificially in nuclear reactors and was named promethium.^[14]

Contribution to understanding of the atom

Before Moseley and his law, atomic numbers had been thought of as a semi-arbitrary ordering number, vaguely increasing with atomic weight but not strictly defined by it. Moseley's discovery showed that atomic numbers were not arbitrarily assigned, but rather, they have a definite physical basis. Moseley postulated that each successive element has a nuclear charge exactly one unit greater than its predecessor. Moseley redefined the idea of atomic numbers from its previous status as an ad hoc numerical tag to help sorting the elements into an exact sequence of ascending atomic numbers that made the Periodic Table exact. (This was later to be the basis of the Aufbau principle in atomic studies.) As noted by Bohr, Moseley's law provided a reasonably complete experimental set of data that supported the (new from 1911) conception by Ernest Rutherford and Antonius van den Broek of the atom, with a positively charged nucleus surrounded by negatively charged electrons in which the atomic number is understood to be the exact physical number of positive charges (later discovered and called protons) in the central atomic nuclei of the elements. Moseley mentioned the two scientists above in his research paper, but he did not actually mention Bohr, who was rather new on the scene then. Simple modification of Rydberg's and Bohr's formulas were found to give theoretical justification for Moseley's empirically derived law for determining atomic numbers.

Use of X-ray spectrometer

X-ray spectrometers are the foundation-stones of X-ray crystallography. The X-ray spectrometers as Moseley knew them worked as follows. A glass-bulb electron tube was used, similar to that held by Moseley in the photo at the top of this article. Inside the evacuated tube, electrons were fired at a metallic substance (i.e. a sample of pure element in Moseley's work), causing the ionization of electrons from the inner electron shells of the element. The rebound of electrons into these holes in the inner shells next causes the emission of X-ray photons that were led out of the tube in a semi-beam, through an opening in the external X-ray shielding. These are next diffracted by a standardized salt crystal, with angular results read out as photographic lines by the exposure of an X-ray film fixed at the outside the vacuum tube at a known distance. Application of Bragg's law (after some initial guesswork of the mean distances between atoms in the metallic crystal, based on its density) next allowed the wavelength of the emitted -rays to be calculated.

Moseley participated in the design and development of early X-ray spectrometry equipment, learning some techniques from William Henry Bragg and William Lawrence Bragg at the University of Leeds, and developing others himself. Many of the techniques of X-ray spectroscopy were inspired by the methods that are used with visible light spectroscopes and spectrograms, by substituting crystals, ionization chambers, and photographic plates for their analogs in light spectroscopy. In some cases, Moseley found it necessary to modify his equipment to detect particularly soft [lower frequency] X-rays that could not penetrate either air or paper, by working with his instruments in a vacuum chamber.

Death and aftermath

Sometime in the first half of 1914, Moseley resigned from his position at Manchester, with plans to return to Oxford and continue his physics research there. However, World War I broke out in August 1914, and Moseley turned down this job offer to instead enlist with the Royal Engineers of the British Army. His family and friends tried to persuade him not to join, but he thought it was his duty.^[15] Moseley served as a technical officer in communications during the Battle of Gallipoli, in Turkey, beginning in April 1915, where he was killed in action on 10 August 1915. Moseley was shot in the head by a Turkish sniper while in the act of telephoning a military order.

Blue plaque erected by the Royal Society of Chemistry on the Townsend Building of the Clarendon Laboratory at Oxford in 2007, commemorating Moseley's early 20th-century research work on X-rays emitted by elements.

Only twenty-seven years old at the time of his death, Moseley could, in the opinion of some scientists, have contributed much to the knowledge of atomic structure had he survived. Niels Bohr said in 1962 that the Rutherford's work "was not taken seriously at all" and that the "great change came from Moseley."^[16]

Robert Millikan wrote, "In a research which is destined to rank as one of the dozen most brilliant in conception, skillful in execution, and illuminating in results in the history of science, a young man twenty-six years old threw open the windows through which we can glimpse the sub-atomic world with a definiteness and certainty never dreamed of before. Had the European War had no other result than the snuffing out of this young life, that alone would make it one of the most hideous and most irreparable crimes in history."^[17]

Isaac Asimov wrote, "In view of what he [Moseley] might still have accomplished … his death might well have been the most costly single death of the War to mankind generally."^[18] Because of Moseley's death in World War I, and after much lobbying by Ernest Rutherford,^[19] the British government instituted a policy of no longer allowing its prominent and promising scientists to enlist for combat duty in the armed forces of the Crown.^[5]

Isaac Asimov also speculated that, in the event that he had not been killed while in the service of the British Empire, Moseley might very well have been awarded the 1916 Nobel Prize in Physics, which, along with the prize for chemistry, was not awarded to anyone that year. Additional credence is given to this idea by noting the recipients of the Nobel Prize in Physics in the two preceding years, 1914 and 1915, and in the following year, 1917. In 1914, Max von Laue of Germany won the Nobel Prize in Physics for his discovery of the diffraction of X-rays by crystals, which was a crucial step towards the invention of X-ray spectroscopy. Then, in 1915, William Henry Bragg and William Lawrence Bragg, a British father-son pair, shared this Nobel Prize for their discoveries in the reverse problem — determining the structure of crystals using X-rays (Robert Charles Bragg, William Henry Bragg's other son, had also been killed at Gallipoli, on 2 September 1915^[20]). Next, Moseley used the diffraction of X-rays by known crystals in measuring the X-ray spectra of metals. This was the first use of X-ray spectroscopy and also one more step towards the creation of X-ray crystallography. In addition, Moseley's methods and analyses substantially supported the concept of atomic number, placing it on a firm, physics-based foundation. Moreover, Charles Barkla of Great Britain was awarded the Nobel Prize in 1917 for his experimental work in using X-ray spectroscopy in discovering the characteristic X-ray frequencies emitted by the various elements, especially the metals. "Siegbahn, who carried on Moseley's work, received one [the 1924 Nobel Prize in Physics]."^[21] Moseley's discoveries were thus of the same scope as those of his peers, and in addition, Moseley made the larger step of demonstrating the actual foundation of atomic numbers. Ernest Rutherford commented that Moseley's work, "Allowed him to complete during two years at the outset of his career a set of researches that would surely have brought him a Nobel prize".^[22]

Memorial plaques to Moseley were installed at Manchester and Eton, and a Royal Society scholarship, established by his will, had as its second recipient the physicist P. M. S. Blackett, who later became president of the Society.^[23]

Atomic number

From Wikipedia, the free encyclopedia

An explanation of the superscripts and subscripts seen in atomic number notation. Atomic number is the number of protons, and therefore also the total positive charge, in the atomic nucleus.

The Rutherford–Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1). In this model it is an essential feature that the photon energy (or frequency) of the electromagnetic radiation emitted (shown) when an electron jumps from one orbital to another, be proportional to the mathematical square of atomic charge (Z²). Experimental measurement by Henry Moseley of this radiation for many elements (from Z = 13 to 92) showed the results as predicted by Bohr. Both the concept of atomic number and the Bohr model were thereby given scientific credence.

The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of an atom. It is identical to the charge number of the nucleus. The atomic number uniquely identifies a chemical element. In an uncharged atom, the atomic number is also equal to the number of electrons.

The sum of the atomic number Z and the number of neutrons, N, gives the mass number A of an atom. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.

Atoms with the same atomic number Z but different neutron numbers N, and hence different atomic masses, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.

The conventional symbol Z comes from the German word Zahl meaning number, which, prior to the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physical characteristic of atoms, did the word Atomzahl (and its English equivalent atomic number) come into common use in this context.

History

The periodic table and a natural number for each element

Russian chemist Dmitri Mendeleev, creator of the periodic table.

Loosely speaking, the existence or construction of a periodic table of elements creates an ordering of the elements, and so they can be numbered in order.

Dmitri Mendeleev claimed that he arranged his first periodic tables in order of atomic weight ("Atomgewicht").^[1] However, in consideration of the elements' observed chemical properties, he changed the order slightly and placed tellurium (atomic weight 127.6) ahead of iodine (atomic weight 126.9).^[1][2] This placement is consistent with the modern practice of ordering the elements by proton number, Z, but that number was not known or suspected at the time.

A simple numbering based on periodic table position was never entirely satisfactory, however. Besides the case of iodine and tellurium, later several other pairs of elements (such as argon and potassium, cobalt and nickel) were known to have nearly identical or reversed atomic weights, thus requiring their placement in the periodic table to be determined by their chemical properties. However the gradual identification of more and more chemically similar lanthanide elements, whose atomic number was not obvious, led to inconsistency and uncertainty in the periodic numbering of elements at least from lutetium (element 71) onwards (hafnium was not known at this time).

Niels Bohr, creator of the Bohr model.

The Rutherford-Bohr model and van den Broek

In 1911, Ernest Rutherford gave a model of the atom in which a central core held most of the atom's mass and a positive charge which, in units of the electron's charge, was to be approximately equal to half of the atom's atomic weight, expressed in numbers of hydrogen atoms. This central charge would thus be approximately half the atomic weight (though it was almost 25% different from the atomic number of gold (Z = 79, A = 197), the single element from which Rutherford made his guess). Nevertheless, in spite of Rutherford's estimation that gold had a central charge of about 100 (but was element Z = 79 on the periodic table), a month after Rutherford's paper appeared, Antonius van den Broek first formally suggested that the central charge and number of electrons in an atom was exactly equal to its place in the periodic table (also known as element number, atomic number, and symbolized Z). This proved eventually to be the case.

Moseley's 1913 experiment

Henry Moseley in his lab.

The experimental position improved dramatically after research by Henry Moseley in 1913.^[3] Moseley, after discussions with Bohr who was at the same lab (and who had used Van den Broek's hypothesis in his Bohr model of the atom), decided to test Van den Broek's and Bohr's hypothesis directly, by seeing if spectral lines emitted from excited atoms fitted the Bohr theory's postulation that the frequency of the spectral lines be proportional to the square of Z.

To do this, Moseley measured the wavelengths of the innermost photon transitions (K and L lines) produced by the elements from aluminum (Z = 13) to gold (Z = 79) used as a series of movable anodic targets inside an x-ray tube.^[4] The square root of the frequency of these photons (x-rays) increased from one target to the next in an arithmetic progression. This led to the conclusion (Moseley's law) that the atomic number does closely correspond (with an offset of one unit for K-lines, in Moseley's work) to the calculated electric charge of the nucleus, i.e. the element number Z. Among other things, Moseley demonstrated that the lanthanide series (from lanthanum to lutetium inclusive) must have 15 members—no fewer and no more—which was far from obvious from the chemistry at that time.

(DJS:  Mosely tragically and needlessly died in WWI, during the futile British attack on Gallipoli.)

Missing elements

After Moseley's death in 1915, the atomic numbers of all known elements from hydrogen to uranium (Z = 92) were examined by his method. There were seven elements (with Z < 92) which were not found and therefore identified as still undiscovered, corresponding to atomic numbers 43, 61, 72, 75, 85, 87 and 91.^[5] From 1918 to 1947, all seven of these missing elements were discovered.^[6] By this time the first four transuranium elements had also been discovered, so that the periodic table was complete with no gaps as far as curium (Z = 96).

The proton and the idea of nuclear electrons

In 1915 the reason for nuclear charge being quantized in units of Z, which were now recognized to be the same as the element number, was not understood. An old idea called Prout's hypothesis had postulated that the elements were all made of residues (or "protyles") of the lightest element hydrogen, which in the Bohr-Rutherford model had a single electron and a nuclear charge of one. However, as early as 1907 Rutherford and Thomas Royds had shown that alpha particles, which had a charge of +2, were the nuclei of helium atoms, which had a mass four times that of hydrogen, not two times. If Prout's hypothesis were true, something had to be neutralizing some of the charge of the hydrogen nuclei present in the nuclei of heavier atoms.

In 1917 Rutherford succeeded in generating hydrogen nuclei from a nuclear reaction between alpha particles and nitrogen gas,^[7] and believed he had proven Prout's law. He called the new heavy nuclear particles protons in 1920 (alternate names being proutons and protyles). It had been immediately apparent from the work of Moseley that the nuclei of heavy atoms have more than twice as much mass as would be expected from their being made of hydrogen nuclei, and thus there was required a hypothesis for the neutralization of the extra protons presumed present in all heavy nuclei. A helium nucleus was presumed to be composed of four protons plus two "nuclear electrons" (electrons bound inside the nucleus) to cancel two of the charges. At the other end of the periodic table, a nucleus of gold with a mass 197 times that of hydrogen, was thought to contain 118 nuclear electrons in the nucleus to give it a residual charge of + 79, consistent with its atomic number.

The discovery of the neutron makes Z the proton number

All consideration of nuclear electrons ended with James Chadwick's discovery of the neutron in 1932. An atom of gold now was seen as containing 118 neutrons rather than 118 nuclear electrons, and its positive charge now was realized to come entirely from a content of 79 protons. After 1932, therefore, an element's atomic number Z was also realized to be identical to the proton number of its nuclei.

The symbol of Z

The conventional symbol Z possibly comes from the German word Atomzahl (atomic number).^[8] However, prior to 1915, the word Zahl (simply number) was used for an element's assigned number in the periodic table.

Chemical properties

Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom, which is Z (the atomic number). The configuration of these electrons follows from the principles of quantum mechanics. The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. Hence, it is the atomic number alone that determines the chemical properties of an element; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.

New elements

The quest for new elements is usually described using atomic numbers. As of 2010, all elements with atomic numbers 1 to 118 have been observed. Synthesis of new elements is accomplished by bombarding target atoms of heavy elements with ions, such that the sum of the atomic numbers of the target and ion elements equals the atomic number of the element being created. In general, the half-life becomes shorter as atomic number increases, though an "island of stability" may exist for undiscovered isotopes with certain numbers of protons and neutrons.

Chemical thermodynamics

From Wikipedia, the free encyclopedia

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.^[1]

History

J. Willard Gibbs - founder of chemical thermodynamics

In 1865, the German physicist Rudolf Clausius, in his Mechanical Theory of Heat, suggested that the principles of thermochemistry, e.g. the heat evolved in combustion reactions, could be applied to the principles of thermodynamics.^[2] Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published a series of three papers, the most famous one being the paper On the Equilibrium of Heterogeneous Substances. In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both the thermodynamic equilibrium of chemical reactions as well as their tendencies to occur or proceed. Gibbs’ collection of papers provided the first unified body of thermodynamic theorems from the principles developed by others, such as Clausius and Sadi Carnot.

During the early 20th century, two major publications successfully applied the principles developed by Gibbs to chemical processes, and thus established the foundation of the science of chemical thermodynamics. The first was the 1923 textbook Thermodynamics and the Free Energy of Chemical Substances by Gilbert N. Lewis and Merle Randall. This book was responsible for supplanting the chemical affinity with the term free energy in the English-speaking world. The second was the 1933 book Modern Thermodynamics by the methods of Willard Gibbs written by E. A. Guggenheim. In this manner, Lewis, Randall, and Guggenheim are considered as the founders of modern chemical thermodynamics because of the major contribution of these two books in unifying the application of thermodynamics to chemistry.^[1]

Overview

The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation.^[3] In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:

1. Chemical reactions
2. Phase changes
3. The formation of solutions

The following state functions are of primary concern in chemical thermodynamics:

• Internal energy (U)
• Enthalpy (H)
• Entropy (S)
• Gibbs free energy (G)

Most identities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.

The 3 laws of thermodynamics:

1. The energy of the universe is constant.
2. In any spontaneous process, there is always an increase in entropy of the universe (DJS -- in the universe!  Many errors are made here by forgetting that.)
3. The entropy of a perfect crystal(well ordered) at 0 Kelvin is zero

Chemical energy

Chemical energy is the potential of a chemical substance to undergo a transformation through a chemical reaction or to transform other chemical substances. Breaking or making of chemical bonds involves energy or heat, which may be either absorbed or evolved from a chemical system.

Energy that can be released (or absorbed) because of a reaction between a set of chemical substances is equal to the difference between the energy content of the products and the reactants. This change in energy is called the change in internal energy of a chemical reaction. Where ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}$ is the internal energy of formation of the reactant molecules that can be calculated from the bond energies of the various chemical bonds of the molecules under consideration and ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}$ is the internal energy of formation of the product molecules. The change in internal energy is a process which is equal to the heat change if it is measured under conditions of constant volume (at STP condition), as in a closed rigid container such as a bomb calorimeter. However, under conditions of constant pressure, as in reactions in vessels open to the atmosphere, the measured heat change is not always equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called the enthalpy change; in this case the enthalpy of formation).

Another useful term is the heat of combustion, which is the energy released due to a combustion reaction and often applied in the study of fuels. Food is similar to hydrocarbon fuel and carbohydrate fuels, and when it is oxidized, its caloric content is similar (though not assessed in the same way as a hydrocarbon fuel — see food energy).

In chemical thermodynamics the term used for the chemical potential energy is chemical potential, and for chemical transformation an equation most often used is the Gibbs-Duhem equation.

Chemical reactions

In most cases of interest in chemical thermodynamics there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which always create entropy unless they are at equilibrium, or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such as pistons or electrodes, to deliver and receive external work. Even for homogeneous "bulk" materials, the free energy functions depend on the composition, as do all the extensive thermodynamic potentials, including the internal energy. If the quantities { N_i }, the number of chemical species, are omitted from the formulae, it is impossible to describe compositional changes.

Gibbs function or Gibbs Energy

For a "bulk" (unstructured) system they are the last remaining extensive variables. For an unstructured, homogeneous "bulk" system, there are still various extensive compositional variables { N_i } that G depends on, which specify the composition, the amounts of each chemical substance, expressed as the numbers of molecules present or (dividing by Avogadro's number = 6.023 × 10²³), the numbers of moles

${\displaystyle G=G(T,P,\{N_{i}\})\,.}$

For the case where only PV work is possible

${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}$

in which μ_i is the chemical potential for the i-th component in the system

${\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}$

The expression for dG is especially useful at constant T and P, conditions which are easy to achieve experimentally and which approximates the condition in living creatures

${\displaystyle (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}$

Chemical affinity

While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a process involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components ( N_i ) can be changed independently. All real processes obey conservation of mass, and in addition, conservation of the numbers of atoms of each kind. Whatever molecules are transferred to or from should be considered part of the "system".

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress variable ξ for the extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to the use of the partial derivative ∂G/∂ξ (in place of the widely used "ΔG", since the quantity at issue is not a finite change). The result is an understandable expression for the dependence of dG on chemical reactions (or other processes). If there is just one reaction

${\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}$

If we introduce the stoichiometric coefficient for the i-th component in the reaction

${\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}$

which tells how many molecules of i are produced or consumed, we obtain an algebraic expression for the partial derivative

${\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}$

where, (De Donder; Progoine & Defay, p. 69; Guggenheim, pp. 37,240), we introduce a concise and historical name for this quantity, the "affinity", symbolized by A, as introduced by Théophile de Donder in 1923. The minus sign comes from the fact the affinity was defined to represent the rule that spontaneous changes will ensue only when the change in the Gibbs free energy of the process is negative, meaning that the chemical species have a positive affinity for each other. The differential for G takes on a simple form which displays its dependence on compositional change

${\displaystyle (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}$

If there are a number of chemical reactions going on simultaneously, as is usually the case

${\displaystyle (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}$

a set of reaction coordinates { ξ_j }, avoiding the notion that the amounts of the components ( N_i ) can be changed independently. The expressions above are equal to zero at thermodynamic equilibrium, while in the general case for real systems, they are negative because all chemical reactions proceeding at a finite rate produce entropy. This can be made even more explicit by introducing the reaction rates dξ_j/dt. For each and every physically independent process (Prigogine & Defay, p. 38; Prigogine, p. 24)

${\displaystyle \mathbb {A} \ {\dot {\xi }}\leq 0\,.}$

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether the temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (−T times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See Constraints below.)

We now relax the requirement of a homogeneous “bulk” system by letting the chemical potentials and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the entropy production due to irreversible processes, the inequality for dG is now replaced by an equality

${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+W'\,}$

or

${\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+W'.\,}$

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that the extent of reaction for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such a way that one can advance only if the other one also does. The coupling may occasionally be rigid, but it is often flexible and variable.

Solutions

In solution chemistry and biochemistry, the Gibbs free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔG) is commonly used as a surrogate for (−T times) the entropy produced by spontaneous chemical reactions in situations where there is no work being done; or at least no "useful" work; i.e., other than perhaps some ± P dV. The assertion that all spontaneous reactions have a negative ΔG is merely a restatement of the fundamental thermodynamic relation, giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When there is no useful work being done, it would be less misleading to use the Legendre transforms of the entropy appropriate for constant T, or for constant T and P, the Massieu functions −F/T and −G/T respectively.

Non equilibrium

Generally the systems treated with the conventional chemical thermodynamics are either at equilibrium or near equilibrium. Ilya Prigogine developed the thermodynamic treatment of open systems that are far from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has found surprising applications in a wide variety of fields.

The non equilibrium thermodynamics has been applied for explaining how ordered structures e.g. the biological systems, can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain the occurrence of ordered structures.

Prigogine called these systems dissipative systems, because they are formed and maintained by the dissipative processes which take place because of the exchange of energy between the system and its environment and because they disappear if that exchange ceases. They may be said to live in symbiosis with their environment.

The method which Prigogine used to study the stability of the dissipative structures to perturbations is of very great general interest. It makes it possible to study the most varied problems, such as city traffic problems, the stability of insect communities, the development of ordered biological structures and the growth of cancer cells to mention but a few examples.

System constraints

In this regard, it is crucial to understand the role of walls and other constraints, and the distinction between independent processes and coupling. Contrary to the clear implications of many reference sources, the previous analysis is not restricted to homogeneous, isotropic bulk systems which can deliver only PdV work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of the same, overall process. An independent process is one that could proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a “thought experiment” in chemical kinetics, but actual examples exist.

A gas reaction which results in an increase in the number of molecules will lead to an increase in volume at constant external pressure. If it occurs inside a cylinder closed with a piston, the equilibrated reaction can proceed only by doing work against an external force on the piston. The extent variable for the reaction can increase only if the piston moves, and conversely, if the piston is pushed inward, the reaction is driven backwards.

Similarly, a redox reaction might occur in an electrochemical cell with the passage of current in wires connecting the electrodes. The half-cell reactions at the electrodes are constrained if no current is allowed to flow. The current might be dissipated as joule heating, or it might in turn run an electrical device like a motor doing mechanical work. An automobile lead-acid battery can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work.

The hydrolysis of ATP to ADP and phosphate can drive the force times distance work delivered by living muscles, and synthesis of ATP is in turn driven by a redox chain in mitochondria and chloroplasts, which involves the transport of ions across the membranes of these cellular organelles. The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of a rubber balloon. Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling coefficient, which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work"; a misnomer for the free energy of another chemical process.