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Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = -1, which is known as Euler's identity.
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates.The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and ...
The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka of the acid, and the concentrations of the species in solution. [2] Simulated titration of an acidified solution of a weak acid ( pKa = 4.7) with alkali. To derive the equation a number of ...
The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the Resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E. Goldman of Columbia University, and the Medicine ...
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The Edwards equation in organic chemistry is a two-parameter equation for correlating nucleophilic reactivity, as defined by relative rate constants, with the basicity of the nucleophile (relative to protons) and its polarizability. This equation was first developed by John O. Edwards in 1954 [1] and later revised based on additional work in 1956.
Antoine equation. The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine [ fr] (1825–1897).
Brus equation. The Brus equation or confinement energy equation can be used to describe the emission energy of quantum dot semiconductor nanocrystals in terms of the band gap energy Egap, Planck's constant h, the radius of the quantum dot r, as well as the effective mass of the excited electron me * and of the excited hole mh *. [1]