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Van Der Waals Radius
The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state.Contents1 Van der Waals volume 2 Methods of determination2.1 Van der Waals equation
Van der Waals equation
of state 2.2 Crystallographic measurements 2.3 Molar refractivity 2.4 Polarizability3 References3.1 Further reading4 External linksVan der Waals volume[edit]This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed
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Angstrom
The ångström (/ˈæŋstrəm, -strʌm/,[1][2]ANG-strəm; ANG-strum Swedish: [²ɔŋstrœm])[1] or angstrom is a unit of length equal to 6990100000000000000♠10−10 m (one ten-billionth of a metre) or 0.1 nanometre. Its symbol is Å, a letter in the Swedish alphabet. The natural sciences and technology often use ångström to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. Atoms of phosphorus, sulfur, and chlorine are about an ångström in covalent radius, while a hydrogen atom is about half an ångström; see atomic radius. Visible light
Visible light
has wavelengths in the range of 4000–7000 Å. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The symbol is always written with a ring diacritic, as the letter in the Swedish alphabet
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Van Der Waals Constants (data Page)
The following table lists the van der Waals constants (from the van der Waals equation) for a number of common gases and volatile liquids.[1] To convert from L 2 b a r / m o l 2 displaystyle L^ 2 bar/mol^ 2 to L 2 k P a / m o l 2 displaystyle L^ 2 kPa/mol^ 2 , multiply by 100.  a (L2bar/mol2) b (L/mol)Acetic acid 17.71 0.1065Acetic anhydride 20.158 0.1263Acetone 16.02 0.1124Acetonitrile 17.81 0.1168Acetylene 4.516 0.0522Ammonia 4.225 0.0371Argon 1.355 0.03201Benzene 18.24 0.1154Bromobenzene 28.94 0.1539Butane 14.66 0.1226Carbon dioxide 3.640 0.04267Carbon disulfide 11.77 0.07685


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Molar Volume
The molar volume, symbol Vm,[1] is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit
SI unit
cubic metres per mole (m3/mol),[1] although it is more practical to use the units cubic decimetres per mole (dm3/mol) for gases and cubic centimetres per mole (cm3/mol) for liquids and solids.Contents1 Calculation 2 Ideal gases 3 Crystalline solids3.1 Molar volume
Molar volume
of silicon4 See also 5 References 6 External linksCalculation[edit]The molar volume of a substance can be found by measuring its molar mass and density then applying the relation V m = M ρ displaystyle V_ rm m = M over rho .If the sample is a mixture containing N components, the molar volume is complex
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Standard Temperature And Pressure
Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards
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Mechanics
Mechanics
Mechanics
(Greek μηχανική) is that area of science which is concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece
Ancient Greece
with the writings of Aristotle
Aristotle
and Archimedes[1][2][3] (see History of classical mechanics
History of classical mechanics
and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton, laid the foundation for what is now known as classical mechanics. It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light
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Critical Point (thermodynamics)
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid-vapor critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone
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Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.[1][2] In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word crystal derives from the Ancient Greek
Ancient Greek
word κρύσταλλος (krustallos), meaning both "ice" and "rock crystal",[3] from κρύος (kruos), "icy cold, frost".[4][5] Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid
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Picometre
The picometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the metric system, equal to 6988100000000000000♠1×10−12 m, or one trillionth (1/7012100000000000000♠1000000000000) of a metre, which is the SI base unit of length. The picometre is one thousandth of a nanometre, one millionth of a micrometre (also known as a micron), and used to be called micromicron, stigma, or bicron.[2] The symbol µµ was once used for it.[3] It is also one hundredth of an angstrom, an internationally recognised (but non-SI) unit of length. Use[edit] The picometre's length is of an order such that its application is almost entirely confined to particle physics, quantum physics, chemistry and acoustics. Atoms are between 62 and 520 pm in diameter, and the typical length of a carbon-carbon single bond is 154 pm
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Weighted Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean
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Ideal Gas Law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations
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Real Gas
Real gases are non-hypothetical gases whose molecules occupy space and have interactions; consequently, they adhere to gas laws. To understand the behaviour of real gases, the following must be taken into account:compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects; issues with molecular dissociation and elementary reactions with variable compositionFor most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. On the other hand, real-gas models have to be used near the condensation point of gases, near critical points, at very high pressures, to explain the Joule–Thomson effect
Joule–Thomson effect
and in other less usual cases
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Van Der Waals Force
In molecular physics, the van der Waals forces, named after Dutch scientist Johannes Diderik van der Waals, are distance-dependent interactions between atoms or molecules. Unlike ionic or covalent bonds, these attractions are not a result of any chemical electronic bond, and they are comparatively weak and more susceptible to being perturbed. Van der Waals forces quickly vanish at longer distances between interacting molecules. Van der Waals forces play a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. Van der Waals forces also define many properties of organic compounds and molecular solids, including their solubility in polar and non-polar media. If no other forces are present, the point at which the force becomes repulsive rather than attractive as two atoms near one another is called the van der Waals contact distance
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Mole (unit)
The mole is the unit of measurement for amount of substance in the International System of Units
International System of Units
(SI). The unit is defined as the amount or sample of a chemical substance that contains as many constitutive particles, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of carbon-12 (12C), the isotope of carbon with standard atomic weight 12 by definition. This number is expressed by the Avogadro constant, which has a value of approximately 7023602214085700000♠6.022140857×1023 mol−1. The mole is an SI base unit, with the unit symbol mol. The mole is widely 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 → 2H2O implies that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O)
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Cubic Functions
In algebra, a cubic function is a function of the form f ( x ) = a x 3 + b x 2 + c x + d displaystyle f(x)=ax^ 3 +bx^ 2 +cx+d in which a is nonzero. Setting f(x) = 0 produces a cubic equation of the form a x 3 + b x 2 + c x + d = 0. displaystyle ax^ 3 +bx^ 2 +cx+d=0., The solutions of this equation are called roots of the polynomial f(x). If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd degree polynomials). All of the roots of the cubic equation can be found algebraically
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