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In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {\displaystyle \rho (\mathbf {r} )} can be written in terms of a sum of products of basis functions, φ:
Since metals can display multiple oxidation numbers, the exact definition of how many "valence electrons" an element should have in elemental form is somewhat arbitrary, but the following table lists the free electron densities given in Ashcroft and Mermin, which were calculated using the formula above based on reasonable assumptions about ...
In chemistry, a phosphate is an anion, salt, functional group or ester derived from a phosphoric acid. It most commonly means orthophosphate, a derivative of orthophosphoric acid, a.k.a. phosphoric acid H 3 PO 4. The phosphate or orthophosphate ion [PO 4] 3− is derived from phosphoric acid by the removal of three protons H +.
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: = = Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K ...
The general formula of a phosphoric acid is H n+2−2x P n O 3n+1−x, where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure, between 0 and n + 2 / 2 . Pyrophosphate anion. Trimethyl orthophosphate.
The quantum concentration n Q is the particle concentration (i.e. the number of particles per unit volume) of a system where the interparticle distance is equal to the thermal de Broglie wavelength. Quantum effects become appreciable when the particle concentration is greater than or equal to the quantum concentration, which is defined as: [ 1 ]
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant. The law is named after Amedeo Avogadro who, in 1812, [ 2 ] [ 3 ] hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same ...
For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, 35 Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. [7] The difference of the actual isotopic mass minus the mass number of an atom is known as the mass excess, [8] which for 35 Cl is –0.03115.