1.
Thermodynamics
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Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. The behavior of these quantities is governed by the four laws of thermodynamics, the laws of thermodynamics are explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a variety of topics in science and engineering, especially physical chemistry, chemical engineering. The initial application of thermodynamics to mechanical heat engines was extended early on to the study of chemical compounds, Chemical thermodynamics studies the nature of the role of entropy in the process of chemical reactions and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged in the following decades, statistical thermodynamics, or statistical mechanics, concerned itself with statistical predictions of the collective motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a mathematical approach to the field in his axiomatic formulation of thermodynamics. A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis, the first law specifies that energy can be exchanged between physical systems as heat and work. In thermodynamics, interactions between large ensembles of objects are studied and categorized, central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes. With these tools, thermodynamics can be used to describe how systems respond to changes in their environment and this can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium, non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field. Guericke was driven to make a vacuum in order to disprove Aristotles long-held supposition that nature abhors a vacuum. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guerickes designs and, in 1656, in coordination with English scientist Robert Hooke, using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyles Law was formulated, which states that pressure, later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and he did not, however, follow through with his design. Nevertheless, in 1697, based on Papins designs, engineer Thomas Savery built the first engine, although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time. Black and Watt performed experiments together, but it was Watt who conceived the idea of the condenser which resulted in a large increase in steam engine efficiency. Drawing on all the work led Sadi Carnot, the father of thermodynamics, to publish Reflections on the Motive Power of Fire
2.
Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
3.
Ideal gas
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An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly elastic collision. The ideal gas concept is useful because it obeys the ideal gas law, an equation of state. One mole of a gas has a volume of 22.710947 litres at STP as defined by IUPAC since 1982. At normal conditions such as temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, the ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants, at high pressures, the volume of a real gas is often considerably greater than that of an ideal gas. At low temperatures, the pressure of a gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, the model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state, the deviation from the ideal gas behaviour can be described by a dimensionless quantity, the compressibility factor, Z. The ideal gas model has been explored in both the Newtonian dynamics and in quantum mechanics, the ideal gas model has also been used to model the behavior of electrons in a metal, and it is one of the most important models in statistical mechanics. There are three classes of ideal gas, the classical or Maxwell–Boltzmann ideal gas, the ideal quantum Bose gas, composed of bosons. The classical ideal gas can be separated into two types, The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas, the behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The ideal gas law is an extension of experimentally discovered gas laws, real fluids at low density and high temperature approximate the behavior of a classical ideal gas. This deviation is expressed as a compressibility factor, the classical thermodynamic properties of an ideal gas can be described by two equations of state. Multiplying the equations representing the three laws, V ∗ V ∗ V = k b a Gives, V ∗ V ∗ V =, under ideal conditions, V = R, that is, P V = n R T. The other equation of state of an ideal gas must express Joules law, in order to switch from macroscopic quantities to microscopic ones, we use n R = N k B where N is the number of gas particles kB is the Boltzmann constant. The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution, the assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas
4.
Volume (thermodynamics)
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In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, a property, is the systems volume per unit of mass. Volume is a function of state and is interdependent with other properties such as pressure and temperature. For example, volume is related to the pressure and temperature of a gas by the ideal gas law. The physical volume of a system may or may not coincide with a control volume used to analyze the system, the volume of a thermodynamic system typically refers to the volume of the working fluid, such as, for example, the fluid within a piston. Changes to this volume may be made through an application of work, an isochoric process however operates at a constant-volume, thus no work can be produced. Many other thermodynamic processes will result in a change in volume, a polytropic process, in particular, causes changes to the system so that the quantity p V n is constant. Note that for specific polytropic indexes a polytropic process will be equivalent to a constant-property process, for instance, for very large values of n approaching infinity, the process becomes constant-volume. Gases are compressible, thus their volumes may be subject to change during thermodynamic processes, liquids, however, are nearly incompressible, thus their volumes can be often taken as constant. In general, compressibility is defined as the volume change of a fluid or solid as a response to a pressure. Similarly, thermal expansion is the tendency of matter to change in volume in response to a change in temperature, many thermodynamic cycles are made up of varying processes, some which maintain a constant volume and some which do not. A vapor-compression refrigeration cycle, for example, follows a sequence where the refrigerant fluid transitions between the liquid and vapor states of matter, typical units for volume are m 3, l, and f t 3. Mechanical work performed on a working fluid causes a change in the constraints of the system, in other words, for work to occur. Hence volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved, volume is one of a pair of conjugate variables, the other being pressure. As with all pairs, the product is a form of energy. The product p V is the energy lost to a due to mechanical work. This product is one term which makes up enthalpy H, H = U + p V, the second law of thermodynamics describes constraints on the amount of useful work which can be extracted from a thermodynamic system. Similarly, the value of heat capacity to use in a given process depends on whether the process produces a change in volume
5.
Partial molar volume
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Essentially it is the partial derivative of the extensive property with respect to the amount of the component of interest. Every extensive property of a mixture has a partial molar property. The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the volume of the solution. However, there is more to it than this, When one mole of water is added to a volume of water at 25 °C. The molar volume of water would thus be reported as 18 cm3 mol−1. However, addition of one mole of water to a volume of pure ethanol results in an increase in volume of only 14 cm3. The reason that the increase is different is that the occupied by a given number of water molecules depends upon the identity of the surrounding molecules. The value 14 cm3 is said to be the partial molar volume of water in ethanol, in general, the partial molar volume of a substance X in a mixture is the change in volume per mole of X added to the mixture. The partial molar volumes of the components of a mixture vary with the composition of the mixture, for a mixture with m components, this is expressed as Z = Z. Now if temperature T and pressure P are held constant, Z = Z is a function of degree 1. More generally, for any λ, Z = λ Z, by Eulers second theorem for homogeneous functions, Z i ¯ is a homogeneous function of degree 0 which means that for any λ, Z i ¯ = Z i ¯. The partial molar property is thus an intensive property - it does not depend on the size of the system and they are especially useful when considering specific properties of pure substances and properties of mixing. By definition, properties of mixing are related to those of the substances by. Here ∗ denotes a substance, M the mixing property. From the definition of partial molar properties, z = ∑ i x i Z i ¯, substitution yields, so from knowledge of the partial molar properties, deviation of properties of mixing from single components can be calculated. Partial molar properties satisfy relations analogous to those of the extensive properties and this last partial derivative is the same as G i ¯, the partial molar Gibbs free energy. This means that the partial molar Gibbs free energy and the potential, one of the most important properties in thermodynamics. Under isobaric and isothermal conditions, knowledge of the potentials, μ i
6.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
7.
Mole (unit)
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The mole is the unit of measurement in the International System of Units for amount of substance. This number is expressed by the Avogadro constant, which has a value of 6. 022140857×1023 mol−1, the mole is one of the base units of the SI, and has the unit symbol mol. The mole is used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2 H2 + O2 →2 H2O implies that 2 moles of dihydrogen and 1 mole of dioxygen react to form 2 moles of water. The mole may also be used to express the number of atoms, ions, the concentration of a solution is commonly expressed by its molarity, defined as the number of moles of the dissolved substance per litre of solution. For example, the relative molecular mass of natural water is about 18.015, therefore. The term gram-molecule was formerly used for essentially the same concept, the term gram-atom has been used for a related but distinct concept, namely a quantity of a substance that contains Avogadros number of atoms, whether isolated or combined in molecules. Thus, for example,1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2, in honor of the unit, some chemists celebrate October 23, which is a reference to the 1023 scale of the Avogadro constant, as Mole Day. Some also do the same for February 6 and June 2, thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the number of molecules as X moles of any other substance. The mass per mole of a substance is called its molar mass, the number of elementary entities in a sample of a substance is technically called its amount. Therefore, the mole is a convenient unit for that physical quantity, one can determine the chemical amount of a known substance, in moles, by dividing the samples mass by the substances molar mass. Other methods include the use of the volume or the measurement of electric charge. The mass of one mole of a substance depends not only on its molecular formula, since the definition of the gram is not mathematically tied to that of the atomic mass unit, the number NA of molecules in a mole must be determined experimentally. The value adopted by CODATA in 2010 is NA =6. 02214129×1023 ±0. 00000027×1023, in 2011 the measurement was refined to 6. 02214078×1023 ±0. 00000018×1023. The number of moles of a sample is the sample mass divided by the mass of the material. The history of the mole is intertwined with that of mass, atomic mass unit, Avogadros number. The first table of atomic mass was published by John Dalton in 1805
8.
Molar concentration
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A commonly used unit for molar concentration in chemistry is the molar, which is defined as the number of moles per litre. A solution with a concentration of 1 mol/L is equivalent to 1 molar, Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. Or more simply,1 molar =1 M =1 mole/litre, in thermodynamics the use of molar concentration is often not convenient, because the volume of most solutions slightly depends on temperature due to thermal expansion. This problem is resolved by introducing temperature correction factors, or by using a temperature-independent measure of concentration such as molality. The reciprocal quantity represents the dilution which can appear in Ostwalds law of dilution, in the International System of Units the base unit for molar concentration is mol/m3. However, this is impractical for most laboratory purposes and most chemical literature traditionally uses mol/dm3, or mol dm−3, the words millimolar and micromolar refer to mM and μM, respectively. The conversion to number concentration C i is given by, C i = c i ⋅ N A where N A is the Avogadro constant, approximately 6. 022×1023 mol−1. The conversion to mass concentration ρ i is given by, ρ i = c i ⋅ M i where M i is the mass of constituent i. A simpler relation can be obtained by considering the total molar concentration namely the sum of molar concentrations of all the components of the mixture, in an ionic solution, ionic strength is proportional to the sum of molar concentration of salts. The sum of products between these quantities equals one, ∑ i c i ⋅ V i ¯ =1 Molar concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature the dependence is, c i = c i, T0 where c i, T0 is the concentration at a reference temperature. Molar and mass concentration have different values in space where diffusion happens, example 1, Consider 11.6 g of NaCl dissolved in 100 g of water. Example 2, Another typical task in chemistry is the preparation of 100 mL of a 2 mol/L solution of NaCl in water, example 3, The density of water is approximately 1000 g/L and its molar mass is 18.02 g/mol. Example 4, A typical protein in bacteria, such as E. coli, may have about 60 copies, and the volume of a bacterium is about 10 −15 L. For example, if a sodium carbonate solution has a concentration of c =1 mol/L. Molar Solution Concentration Calculator Experiment to determine the concentration of vinegar by titration
9.
Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
10.
Amount of substance
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Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount, the International System of Units defines the amount of substance to be proportional to the number of elementary entities present. The SI unit for amount of substance is the mole and it has the unit symbol mol. The proportionality constant is the inverse of the Avogadro constant, the mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 12g of the isotope carbon-12. This number is called Avogadros number and has the value 6. 022140857×1023 and it is the numerical value of the Avogadro constant which has the unit 1/mol, and relates the molar mass of an amount of substance to its mass. Therefore, the amount of substance of a sample is calculated as the sample mass divided by the mass of the substance. Amount of substance appears in thermodynamic relations such as the gas law. Another unit of amount of substance in use in engineering in the United States is the pound-mole. When quoting an amount of substance, it is necessary to specify the entity involved, unless there is no risk of ambiguity. One mole of chlorine could refer either to chlorine atoms, as in 58.44 g of sodium chloride, or to chlorine molecules, the simplest way to avoid ambiguity is to replace the term substance by the name of the entity or to quote the empirical formula. The main derived quantity in which amount of substance enters into the numerator is amount of substance concentration and this name is often abbreviated to amount concentration, except in clinical chemistry where substance concentration is the preferred term to avoid ambiguity with mass concentration. The term molar concentration is incorrect, but commonly used, the alchemists, and especially the early metallurgists, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758, Mikhail Lomonosov questioned the idea that mass was the measure of the quantity of matter. The development of the concept of amount of substance was coincidental with, and vital to,1777, Wenzel publishes Lessons on Affinity, in which he demonstrates that the proportions of the base component and the acid component remain the same during reactions between two neutral salts. 1789, Lavoisier publishes Treatise of Elementary Chemistry, introducing the concept of a chemical element,1792, Richter publishes the first volume of Stoichiometry or the Art of Measuring the Chemical Elements. The term stoichiometry is used for the first time, the first tables of equivalent weights are published for acid–base reactions. Richter also notes that, for an acid, the equivalent mass of the acid is proportional to the mass of oxygen in the base. 1794, Prousts Law of definite proportions generalizes the concept of equivalent weights to all types of chemical reaction,1805, Dalton publishes his first paper on modern atomic theory, including a Table of the relative weights of the ultimate particles of gaseous and other bodies
11.
Atomic mass
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The atomic mass is the mass of an atom. Its unit is the atomic mass units where 1 unified atomic mass unit is defined as 1⁄12 of the mass of a single carbon-12 atom. For atoms, the protons and neutrons of the account for almost all of the mass. When divided by unified atomic mass units or daltons to form a pure numeric ratio, thus, the atomic mass of a carbon-12 atom is 12 u or 12 daltons, but the relative isotopic mass of a carbon-12 atom is simply 12. By contrast, atomic mass figures refer to an individual species, as atoms of the same species are identical. Atomic mass figures are commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the ranking of isotopes for each element. It is usually about the value as the atomic mass of the most abundant isotope. The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to binding energy mass loss. Relative isotopic mass is similar to mass and has exactly the same numerical value as atomic mass. The only difference in case, is that relative isotopic mass is a pure number with no units. This loss of results from the use of a scaling ratio with respect to a carbon-12 standard. The relative isotopic mass, then, is the mass of an isotope, when this value is scaled by the mass of carbon-12. Equivalently, the isotopic mass of an isotope or nuclide is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom. For example, the isotopic mass of a carbon-12 atom is exactly 12. For comparison, the mass of a carbon-12 atom is exactly 12 daltons or 12 unified atomic mass units. Alternately, the mass of a carbon-12 atom may be expressed in any other mass units, for example. As in the case of mass, no nuclides other than carbon-12 have exactly whole-number values of relative isotopic mass
12.
Avogadro constant
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In chemistry and physics, the Avogadro constant is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole. Thus, it is the proportionality factor that relates the mass of a compound to the mass of a sample. Avogadros constant, often designated with the symbol NA or L, has the value 7023602214085700000♠6. 022140857×1023 mol−1 in the International System of Units and this number is also known as Loschmidt constant in German literature. The constant was later redefined as the number of atoms in 12 grams of the isotope carbon-12, for instance, to a first approximation,1 gram of hydrogen element, having the atomic number 1, has 7023602200000000000♠6. 022×1023 hydrogen atoms. Similarly,12 grams of 12C, with the mass number 12, has the number of carbon atoms. Avogadros number is a quantity, and has the same numerical value of the Avogadro constant given in base units. In contrast, the Avogadro constant has the dimension of reciprocal amount of substance, the Avogadro constant can also be expressed as 0.602214. ML mol−1 Å−3, which can be used to convert from volume per molecule in cubic ångströms to molar volume in millilitres per mole, revisions in the base set of SI units necessitated redefinitions of the concepts of chemical quantity. Avogadros number, and its definition, was deprecated in favor of the Avogadro constant, the French physicist Jean Perrin in 1909 proposed naming the constant in honor of Avogadro. Perrin won the 1926 Nobel Prize in Physics, largely for his work in determining the Avogadro constant by several different methods, accurate determinations of Avogadros number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron in 1910, the electric charge per mole of electrons is a constant called the Faraday constant and had been known since 1834 when Michael Faraday published his works on electrolysis. By dividing the charge on a mole of electrons by the charge on a single electron the value of Avogadros number is obtained, since 1910, newer calculations have more accurately determined the values for the Faraday constant and the elementary charge. Perrin originally proposed the name Avogadros number to refer to the number of molecules in one gram-molecule of oxygen, with this recognition, the Avogadro constant was no longer a pure number, but had a unit of measurement, the reciprocal mole. While it is rare to use units of amount of other than the mole, the Avogadro constant can also be expressed in units such as the pound mole. NA = 7026273159734000000♠2. 73159734×1026 −1 = 7025170724843400000♠1. 707248434×1025 −1 Avogadros constant is a factor between macroscopic and microscopic observations of nature. As such, it provides the relationship between other physical constants and properties. The Avogadro constant also enters into the definition of the atomic mass unit. The earliest accurate method to measure the value of the Avogadro constant was based on coulometry
13.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
14.
Kelvin temperature
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Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is defined by the law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the constituents of matter have minimal motion. In the quantum-mechanical description, matter at absolute zero is in its ground state, the International System of Units specifies a particular scale for thermodynamic temperature. It uses the Kelvin scale for measurement and selects the point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically, the Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a means of estimating the thermodynamic temperature to a very high degree of accuracy. Internal energy is called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a degree of freedom. At equilibrium, each degree of freedom will have on average the energy, k B T /2 where k B is the Boltzmann constant. Temperature is a measure of the random submicroscopic motions and vibrations of the constituents of matter. These motions comprise the internal energy of a substance, more specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the average kinetic energy per classical degree of freedom of its constituent particles. Translational motions are almost always in the classical regime, translational motions are ordinary, whole-body movements in three-dimensional space in which particles move about and exchange energy in collisions. Figure 1 below shows translational motion in gases, Figure 4 below shows translational motion in solids, Zero kinetic energy remains in a substance at absolute zero. Throughout the scientific world where measurements are made in SI units, many engineering fields in the U. S. however, measure thermodynamic temperature using the Rankine scale. By international agreement, the kelvin and its scale are defined by two points, absolute zero, and the triple point of Vienna Standard Mean Ocean Water. Absolute zero, the lowest possible temperature, is defined as being precisely 0 K, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things, It fixes the magnitude of the unit as being precisely 1 part in 273.15 kelvins
15.
Charles's law
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Charless law is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charless law is, When the pressure on a sample of a dry gas is constant, the Kelvin temperature. This directly proportional relationship can be written as, V ∝ T or V T = k and this law describes how a gas expands as the temperature increases, conversely, a decrease in temperature will lead to a decrease in volume. The equation shows that, as temperature increases, the volume of the gas also increases in proportion. The law was named after scientist Jacques Charles, who formulated the law in his unpublished work from the 1780s. The basic principles had already described by Guillaume Amontons and Francis Hauksbee a century earlier. Dalton was the first to demonstrate that the law applied generally to all gases, with measurements only at the two thermometric fixed points of water, Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function. On mathematical grounds alone, Gay-Lussacs paper does not permit the assignment of any law stating the linear relation and this equation does not contain the temperature and so has nothing to do with what became known as Charless Law. Gay-Lussacs value for k, was identical to Daltons earlier value for vapours, Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787. In the absence of a record, the gas law relating volume to temperature cannot be named after Charles. Daltons measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the points of water. His conclusion for vapours is a statement of what become known wrongly as Charless Law, then even more wrongly as Gay-Lussacs law. His 1st law was that of partial pressures, Charless law appears to imply that the volume of a gas will descend to zero at a certain temperature or −273.15 °C. Gay-Lussac had no experience of air, although he appears to believe that the permanent gases such as air. However, the zero on the Kelvin temperature scale was originally defined in terms of the second law of thermodynamics. Thomson did not assume that this was equal to the point of Charless law. The two can be shown to be equivalent by Ludwig Boltzmanns statistical view of entropy, however, Charles also stated, The volume of a fixed mass of dry gas increases or decreases by 1⁄273 times the volume at 0 °C for every 1 °C rise or fall in temperature. Thus, V T = V0 + × T V T = V0 where VT is the volume of gas at temperature T, under this definition, the demonstration of Charless law is almost trivial
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Boyle's law
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Boyles law is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases. Mathematically, Boyles law can be stated as P ∝1 V or P V = k where P is the pressure of the gas, V is the volume of the gas, and k is a constant. The equation states that product of pressure and volume is a constant for a mass of confined gas as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be expressed as P1 V1 = P2 V2. The equation shows that, as increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases, the law was named after chemist and physicist Robert Boyle, who published the original law in 1662. This relationship between pressure and volume was first noted by Richard Towneley and Henry Power, Robert Boyle confirmed their discovery through experiments and published the results. According to Robert Gunther and other authorities, it was Boyles assistant, Robert Hooke, Boyles law is based on experiments with air, which he considered to be a fluid of particles at rest in between small invisible springs. At that time, air was still seen as one of the four elements, Boyles interest was probably to understand air as an essential element of life, for example, he published works on the growth of plants without air. Boyle used a closed J-shaped tube and after pouring mercury from one side he forced the air on the side to contract under the pressure of mercury. The French physicist Edme Mariotte discovered the law independent of Boyle in 1679. Thus this law is referred to as Mariottes law or the Boyle–Mariotte law. Instead of a static theory a kinetic theory is needed, which was provided two centuries later by Maxwell and Boltzmann and this law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities. The law itself can be stated as follows, Or Boyles law is a gas law, stating that the pressure and volume of a gas have an inverse relationship, if volume increases, then pressure decreases and vice versa, when temperature is held constant. Therefore, when the volume is halved, the pressure is doubled, and if the volume is doubled, Boyles law states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional. The law can also be stated in a different manner. Most gases behave like ideal gases at moderate pressures and temperatures, the technology of the 17th century could not produce high pressures or low temperatures. Hence, the law was not likely to have deviations at the time of publication, the deviation is expressed as the compressibility factor
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Gay-Lussac's law
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He is most often recognized for the Pressure Law which established that the pressure of an enclosed gas is directly proportional to its temperature and which he was the first to formulate. These laws are known variously as the Pressure Law or Amontonss law. For example, Gay-Lussac found that 2 volumes of hydrogen and 1 volume of oxygen would react to form 2 volumes of gaseous water, based on Gay-Lussacs results, Amedeo Avogadro theorized that, at the same temperature and pressure, equal volumes of gas contain equal numbers of molecules. The law of combining gases was made public by Joseph Louis Gay-Lussac in 1808, Avogadros hypothesis, however, was not initially accepted by chemists until the Italian chemist Stanislao Cannizzaro was able to convince the First International Chemical Congress in 1860. Amontons discovered this while building an air thermometer, the pressure of a gas of fixed mass and fixed volume is directly proportional to the gass absolute temperature. If a gass temperature increases, then so does its pressure if the mass, the law has a particularly simple mathematical form if the temperature is measured on an absolute scale, such as in kelvins. The law can then be expressed mathematically as P ∝ T, or P T = k, where, P is the pressure of the gas, T is the temperature of the gas, k is a constant. For comparing the same substance under two different sets of conditions, the law can be written as, P1 T1 = P2 T2 or P1 T2 = P2 T1. Because Amontons discovered the law beforehand, Gay-Lussacs name is now generally associated within chemistry with the law of combining volumes discussed in the section above, some introductory physics textbooks still define the pressure-temperature relationship as Gay-Lussacs law. Gay-Lussac primarily investigated the relationship between volume and temperature and published it in 1802, but his work did cover some comparison between pressure and temperature, however, in recent years the term has fallen out of favor. Gay-Lussacs law, Charless law, and Boyles law form the gas law. These three gas laws in combination with Avogadros law can be generalized by the gas law. Avogadros law Boyles law Charless law Combined gas law Castka, Joseph F. Metcalfe, H. Clark, Davis, Raymond E. Williams, the Complete Idiots Guide to Chemistry. How to Prepare for the SAT II Chemistry
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Combined gas law
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The combined gas law is a gas law that combines Charless law, Boyles law, and Gay-Lussacs law. There is no official founder for this law, it is merely an amalgamation of the three previously discovered laws and these laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charless law states that volume and temperature are directly proportional to other as long as pressure is held constant. Boyles law asserts that pressure and volume are inversely proportional to each other at fixed temperature, finally, Gay-Lussacs law introduces a direct proportionality between temperature and pressure as long as it is at a constant volume. By combining and either of or, we can gain a new equation with P, V and T, if we divide equation by temperature and multiply equation by pressure we will get, P V T = k 1 T P V T = k 2 P. As the left-hand side of both equations is the same, we arrive at k 1 T = k 2 P, substituting in Avogadros Law yields the ideal gas equation. A derivation of the gas law using only elementary algebra can contain surprises. A physical derivation, longer but more reliable, begins by realizing that the constant volume parameter in Gay-Lussacs law will change as the volume changes. At constant volume, V1 the law might appear P = k1T, rather, it should first be determined in what sense these equations are compatible with one another. To gain insight into this, recall that any two variables determine the third, choosing P and V to be independent, we picture the T values forming a surface above the PV-plane. A definite V0 and P0 define a T0, a point on that surface, the ratio of the slopes of these two lines depends only on the value of P0/V0 at that point. Note that the form of did not depend on the particular point chosen. The same formula would have arisen for any combination of P and V values. Therefore, one can write k V k P = P V ∀ P, ∀ V This says that each point on the surface has its own pair of lines through it. Whereas is a relation between specific slopes and variable values, is a relation between slope functions and function variables and it holds true for any point on the surface, i. e. for any and all combinations of P and V values. To solve this equation for the function kV, first separate the variables, V on the left, V k V = P k P Choose any pressure P1. The right side evaluates to some value, call it karb. V k V = k arb This particular equation must now hold true, not just for one value of V, the only definition of kV that guarantees this for all V and arbitrary karb is k V = k arb V which may be verified by substitution in
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Ideal gas law
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The ideal gas law is the equation of state of a hypothetical ideal gas. It is an approximation of the behavior of many gases under many conditions. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyles law, Charless law and it can also be derived microscopically from kinetic theory, as was achieved by August Krönig in 1856 and Rudolf Clausius in 1857. The state of an amount of gas is determined by its pressure, volume, the modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature, in SI units, P is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins. R has the value 8.314 J/ ≈2 cal/, how much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, a form of the ideal gas law may be useful. The chemical amount is equal to the mass of the gas divided by the molar mass. By replacing n with m/M and subsequently introducing density ρ = m/V, we get, defining the specific gas constant Rspecific as the ratio R/M, P = ρ R specific T. This form of the gas law is very useful because it links pressure, density. Alternatively, the law may be written in terms of the specific volume v and it is common, especially in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the gas constant is usually given a different symbol such as R ¯ to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to. KB =R/NA The number density contrasts to the formulation, which uses n, the number of moles and V. This relation implies that R = NAkB, where NA is Avogadros constant, in extreme conditions the principles of statistical mechanics may break down as some of the assumptions relating a real life example to an ideal gas become untrue. In SI units, P is measured in pascals, V in cubic metres, Y is a dimensionless number, KB has the value 1. 38·10−23 J/K in SI units. According to the assumptions of the theory of gases, we assumed that there are no inter molecular attractions between the molecules of an ideal gas its potential energy is zero. Hence, all the energy possessed by the gas is kinetic energy, E =32 R T This is the kinetic energy of one mole of a gas