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# equation

equation (e-kwa´zhun)

A statement expressing the equality of two things, usually with the use of mathematical or chemical symbols. [L. aequare, to make equal]
alveolar gas e. the e. defining the steady state relation of the alveolar oxygen pressure to the barometric pressure, inspired gas composition, alveolar carbon dioxide pressure, and respiratory exchange ratio; the e. is used in various forms depending upon which simplifying assumptions are acceptable for different applications.
Arrhenius e. an e. relating chemical reaction rate (k) to the absolute temperature (T) by the e.: d(ln k)/dT) = DELTAEa/RT2 where Ea is the activation energy and R is the universal gas constant.
Bohr's e. an e. to calculate the respiratory dead space from the fact that gas expired from the lungs is a mixture of gas from the dead space and gas from the alveoli, i.e., the dead space volume divided by the tidal volume equals the difference between alveolar and mixed expired gas composition, divided by the difference between alveolar and inspired gas composition; gas composition can be expressed in any consistent units of concentration or partial pressure of oxygen or carbon dioxide.
chemical e. an e. on one side of which are the reactants and on the other side the products of a chemical reaction; the two halves may be separated by an equal sign or by arrows.
constant field e. Goldman e
Einthoven's e. Einthoven's law
Gay-Lussac's e. the overall chemical e. for alcoholic fermentation; C6H12O6 = 2CO2 + 2CH3CH2OH.
Gibbs-Helmholtz e. an e. expressing the relationship in a galvanic cell between the chemical energy transformed and the maximal electromotive force obtainable.
Goldman e. an e. derived to predict membrane potentials in terms of the membrane's permeability to ions and their concentrations on either side.constant field e., Goldman-Hodgkin-Katz e., GHK e;
Goldman-Hodgkin-Katz e. , GHK e. Goldman e
Henderson-Hasselbalch e. a formula relating the pH value of a solution to the pKa value of the acid in the solution and the ratio of the acid and the conjugate base concentrations: pH = pKa + log ([A-]/[HA]) where [A-] is the concentration of the conjugate base and [HA] is the concentration of the protonated acid. For the bicarbonate buffer system in blood, pH = pK´ + log ([HCO3-]/[CO2]. The value of pK´ for blood plasma is 6.10 and includes the first dissociation constant of H2CO3, the relation between [H2CO3] and [CO2] and other corrections. The partial pressure of CO2 multiplied by its solubility in plasma at 38°C (0.0301 mm/mm Hg) is commonly substituted for [CO2]; e.g., when the plasma bicarbonate concentration is 24 mEq/liter and the PCO2 is 40 mm Hg, the pH value is 6.10 + log (24/0.0301 x 40) = 7.40.
Hill's e. the e.,y(1-y) = [S]n/Kd, where y is the fractional degree of saturation, [S] is the binding ligand concentration, n is the Hill coefficient, and Kd is the dissociation constant for the ligand. The Hill coefficient is a measure of the cooperativity of the protein; the larger the value, the higher the cooperativity. This coefficient cannot be higher than the number of binding sites. For the oxygen binding curve of hemoglobin, an association constant, Ka, is used and the e. becomes y/(1-y) = Ka[S]n. For human blood, n equals 2.5. Cf. Hill plot.
Hüfner's e. an e. expressing the relationship between myoglobin dissociation and oxygen partial pressure: ([MBO2]/[Mb]) = (K x pO2).
Lineweaver-Burk e. a rearrangement of the Michaelis-Menten e., 1/v = 1/Vmax + (Km/Vmax)(1/[S]). Cf. double-reciprocal plot.
Michaelis-Menten e. an initial-rate e. for a single-substrate non-cooperative enzyme-catalyzed reaction relating the intial velocity to the initial substrate concentration; v = Vmax [S]/(Km + [S]), where v is the initial velocity of the reaction, Vmax is the maximum velocity, [S] is the initial substrate concentration, and Km is the Michaelis constant. Similar equations can be derived for conditions in which the product is present and for multisubstrate enzymes.Victor-Michaelis-Menten e;
Nernst's e. the e. relating the equilibrium potential of electrodes to ion concentrations; the e. relating the electrical potential and concentration gradient of an ion across a permeable membrane at equilibrium: E = [RT / nF] [ln (C1/C 2)], where E = potential, R = absolute gas constant, T = absolute temperature, n = valence, F = the Faraday, ln = the natural logarithm, and C1 and C2 are the ion concentrations on the two sides; in nonideal solutions, concentration should be replaced by activity. See also Nernst's theory, activity (2) .
personal e. a slight error in judgment, perceptual response, or action peculiar to the individual and so constant that it is usually possible to allow for it in accepting the person's statements or conclusions, thus arriving at approximate exactness; observed in persons whose work involves readings of events in time, such as navigators and air traffic controllers.
rate e. a mathematical expression for a chemical, radiochemical, or enzyme-catalyzed reaction.
Rayleigh e. a ratio of red to green required by each observer to match spectral yellow.Rayleigh test;
Svedberg e. See sedimentation constant.
van't Hoff's e. 1. e. for osmotic pressure of dilute solutions. See van't Hoff's law. 2. for any reaction, d(ln Keq/d(1/T) equals -DELTAH/R where Keq is the equilibrium constant, T the absolute temperature, R is the universal gas constant, and DELTAH is the change in enthalpy; thus, plotting ln Keq vs. 1/T allows the determination of DELTAH.
Victor-Michaelis-Menten e. Michaelis-Menten e

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