- equation
- A statement expressing the equality of two things, usually with the use of mathematical or
*chemical*symbols. [L. aequare, to make equal]-the e. defining the steady*alveolar*gas e.*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.-an e. relating*Arrhenius*e.*chemical**reaction**rate*(*k*) to the*absolute**temperature*(*T*) by the e.: d(ln k)/dT) = ΔE_{a}/RT^{2}where*E*is the_{a}*activation**energy*and*R*is the universal gas*constant*.-an e. to calculate the*Bohr*e.*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*.-an e. on one*chemical*e.*side*of which are the reactants and on the other*side*of which are the products of a*chemical**reaction*; the two halves may be separated by an equals*sign*or by arrows.-**Gay-Lussac e.**the overall*chemical*e. for*alcoholic**fermentation*; C_{6}H_{12}O_{6}= 2CO_{2}+ 2CH_{3}CH_{2}OH.-**Gibbs-***Helmholtz*e.**1.**an e. expressing the*relationship*in a*galvanic**cell*between the*chemical**energy*transformed and the maximal electromotive*force*obtainable.**2.**ΔG = ΔH = T[∂ΔG/∂T]_{ P}, where ΔG is the*change*in*Gibbs*free*energy*, ΔH is the*change*in*enthalpy*,*T*is the*absolute**temperature*, and*P*is the*pressure*.-an e. derived to predict*Goldman*e.*membrane*potentials in terms of the membrane's*permeability*to ions and their concentrations on either*side*. SYN:*constant**field*e., Goldman-Hodgkin-*Katz*e., GHK e..-**Henderson-**a*Hasselbalch*e.*formula*relating the pH*value*of a*solution*to the pK_{a}*value*of the*acid*in the*solution*and the*ratio*of the*acid*and the*conjugate**base*concentrations: pH = pK_{a}+ 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([HCO_{3}^{−}]/[CO_{2}]. The*value*of pK′ for*blood**plasma*is 6.10 and includes the first*dissociation**constant*of H_{2}CO_{3}, the*relation*between [H_{2}CO_{3}] and [CO_{2}] and other corrections. The partial*pressure*of CO_{2}multiplied by its*solubility*in*plasma*at 38°C (0.0301 mM/mm Hg) is commonly substituted for [CO_{2}]; e.g., when the*plasma**bicarbonate**concentration*is 24 mEq/L and the P_{CO2}is 40 mm Hg, the pH*value*is 6.10 + log(24/0.0301 × 40) = 7.40.-the e. y(1 − y) = [S]*Hill*e.^{n}/K_{d}, where y is the fractional*degree*of*saturation*, [S] is the binding*ligand**concentration*,*n*is the*Hill**coefficient*, and*K*is the_{d}*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*,*K*, is used and the e. becomes y/(1 − y) = K_{a}_{a}[S]^{n}. For human*hemoglobin*,*n*= 2.5. Cf.:Hill plot.-an e. expressing the*Hüfner*e.*relationship*between*myoglobin**dissociation*and*oxygen*partial*pressure*: ([MBO_{2}]/[Mb]) = (*K*× pO_{2}).-**Lineweaver-**a*Burk*e.*rearrangement*of the Michaelis-Menten e., 1/v = 1/V_{max}+ (K_{m}/V_{max})(1/[S]), where v is the*velocity*of the*reaction*,*V*is the_{max}*maximum**velocity*,*K*is the_{m}*Michaelis**constant*; and [S] is the*substrate**concentration*. Cf.:double-reciprocal plot.-**Michaelis-**an initial-rate e. for a single-substrate non-cooperative enzyme-catalyzed*Menten*e.*reaction*relating the initial*velocity*to the initial*substrate**concentration*; v =*V*[S]/(K_{max}_{m}+ [S]), where v is the initial*velocity*of the*reaction*,*V*is the_{max}*maximum**velocity*, [S] is the initial*substrate**concentration*, and*K*is the_{m}*Michaelis**constant*. Similar equations can be derived for conditions in which the*product*is*present*and for*multisubstrate*enzymes. SYN: Henri-Michaelis-*Menten*e..-the e. relating the*Nernst*e.*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 (C_{1}/C_{2})], where*E*=*potential*,*R*=*absolute*gas*constant*,*T*=*absolute**temperature*,*n*=*valence*,*F*= the*Faraday*, ln = the natural*logarithm*, and C_{1}and C_{2}are the ion concentrations on the two sides; in nonideal solutions,*concentration*should be replaced by*activity*. SEE ALSO:*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.-a*Rayleigh*e.*ratio*of red to*green*required by each*observer*to match*spectral**yellow*. SYN:*Rayleigh*test.-See*Svedberg*e.*sedimentation*constant.-*van't Hoff*e.**1.**e. for*osmotic**pressure*of*dilute*solutions. See*van't Hoff*law.**2.**for any*reaction*, d(ln K_{eq}/d(1/T) equals −ΔH/R where*K*is the_{eq}*equilibrium**constant*,*T*the*absolute**temperature*,*R*the universal gas*constant*, and ΔH the*change*in*enthalpy*;*thus*, plotting ln*K*vs. 1/T allows the_{eq}*determination*of ΔH.* * *

**equa·tion i-'kwā-zhənalso -shən***n*an expression representing a chemical reaction quantitatively by means of chemical symbols* * *

equa·tion (e-kwaґzhən) [L.*aequatio,*from*aequare*to make equal] an expression made up of two members connected by the sign of equality, =.

*Medical dictionary.
2011.*