Guldberg

J. Guldberg, ed., Neutron-Transmutation-Doped Silicon, Proceedings of the Third International Conference on Transmutation Doping of Silicon, Copenhagen, Denmark, Plenum Press, Inc., New York, 1981. 

Guldberg and Waage (1867) clearly stated the Law of Mass Action (sometimes termed the Law of Chemical Equilibrium) in the form The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances . Active mass was interpreted as concentration and expressed in moles per litre. By applying the law to homogeneous systems, that is to systems in which all the reactants are present in one phase, for example in solution, we can arrive at a mathematical expression for the condition of equilibrium in a reversible reaction. 

Guldberg HC, Marsden CA (1975) Catechol-O-methyl transferase Pharmacological aspects and physiological role. Pharmacol Rev 27 135-206... 

Lemma.—The boiling-points under atmospheric pressure are approximately reduced temperatures ( = f) for all substances (Guldberg, 1890). 

The vapour pressure of the solution at the freezing-point is equal to that of pure ice at the same temperature (Guldberg, 1870). For if we take the system ice, solution, vapour, at the freezing-point, and suppose that p p" are the vapour pressures of solution and ice, , v" the specific volumes of the vapour under these pressures, and V, V" the specific volumes of solution and ice, we may execute the following isothermal cycle ... 

Equation (5), in a slightly more general form, was deduced by Guldberg (1870). The latter allowed for the change of f with temperature, which has been neglected above on account of its very small magnitude. 

We see that in determining the equilibrium the concentrations of the solids do not appear at all. This important result was first stated by Guldberg and Waage in 1867 in the form that the active mass of a solid is constant. It is true only when the solids are of unvarying composition. 

Graphical representation, 423 Gravity, 21, 201 Griineisen s relation, 486 Guldberg s rule, 234... 

In 1864, before Haber began his work, the Norwegians Cato Guldberg (a mathematician) and Peter Waage (a chemist) had discovered the mathematical relation that summarizes the composition of a reaction mixture at equilibrium. As an example of their approach, look at the data in Table 9.1 for the reaction between SOz and 02 ... 

In the experiments reported in Table 9.1, five mixtures with different initial compositions of the three gases were prepared and allowed to reach equilibrium at 1000. I<. The compositions of the equilibrium mixtures and the total pressure P were then determined. At first, there seemed to be no pattern in the data. However, Guldberg and Waage noticed an extraordinary relation the value of the quantity... 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

It was shown by Guldberg and Waage that when solids are present in a system, their active masses may be taken as constant and included in the equilibrium constant, K. For example, in the reaction ... 

For reversible reactions one normally assumes that the observed rate can be expressed as a difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction. Thermodynamics does not require that the rate expression be restricted to two terms or that one associate individual terms with intrinsic rates for forward and reverse reactions. This section is devoted to a discussion of the limitations that thermodynamics places on reaction rate expressions. The analysis is based on the idea that at equilibrium the net rate of reaction becomes zero, a concept that dates back to the historic studies of Guldberg and Waage (2) on the law of mass action. We will consider only cases where the net rate expression consists of two terms, one for the forward direction and one for the reverse direction. Cases where the net rate expression consists of a summation of several terms are usually viewed as corresponding to reactions with two or more parallel paths linking reactants and products. One may associate a pair of terms with each parallel path and use the technique outlined below to determine the thermodynamic restrictions on the form of the concentration dependence within each pair. This type of analysis is based on the principle of detailed balancing discussed in Section 4.1.5.4. 

Guldberg, C. M., and Waage, P., Etudes sur les ajfinites chimiques, Br0gger and Christie, Christiania, Oslo, 1867. 

Dove SG, Hoegh-Guldberg O, Ranganathan S (2001) Major colour patterns of reef-building corals are due to a family of GFP-like proteins. Coral Reefs 19 197-204... 

Salih A, Larkum A, Cox G, Kuhl M, Hoegh-Guldberg O (2000) Fluorescent pigments in corals are photoprotective. Nature 408 850-853... 

Gasser, R, Nansen, P. and Guldberg, P. (1996a) Fingerprinting sequence variation in ribosomal DNA of parasites by DGGE. Molecular and Cellular Probes 10, 99-105. 

Gasser, R.B., Zhu, X.Q., Chilton, N.B., Newton, L.A., Nedergaard, T. and Guldberg, P. (1998e) Analysis of sequence homogenisation in rDNA arrays of Haemonchus contortusby DGGE. Electrophoresis 19, 2391—2395. 

Guldberg, P., Levy, H. L., Hanley, W. B. et al. Phenylalanine hydroxylase gene mutations in the United States report from the Maternal PKU Collaborative Study. Am. J. Hum. Genet. 59 84-94,1996. 

Jones, RJ. and O. Hoegh-Guldberg. 1999. Effects of cyanide on coral photosynthesis implications for identifying the cause of coral bleaching and for assessing the environmental effects of cyanide fishing. Mar. Ecol. Prog. Ser. 177 83-91. 

The fundamental law of chemical equilibrium is the law of mass action, formulated in 1864 by Cato Maximilian Guldberg and Peter Waage. It has since been redefined several times. Consider the equilibrium between the four chemical species A, B, C and D ... 

In this connection, Servos mentions, among others, Robert Bunsen at Heidelberg, who invented the carbon-zinc battery and the spectroscope H. H. Landolt at Bonn, later Berlin, who studied the refractive power of the molecule in relation to the refractivities of its atoms Heinrich Rose at Berlin, who followed up on Berthollet s theory of mass action and Cato Guldberg and Peter Waage in Norway, who did so more thoroughly. See John W. Servos, Physical Chemistry from Ostwald to Pauling, 1115. 

Quantitative measurements of simple and enzyme-catalyzed reaction rates were under way by the 1850s. In that year Wilhelmy derived first order equations for acid-catalyzed hydrolysis of sucrose which he could follow by the inversion of rotation of plane polarized light. Berthellot (1862) derived second-order equations for the rates of ester formation and, shortly after, Harcourt observed that rates of reaction doubled for each 10 °C rise in temperature. Guldberg and Waage (1864-67) demonstrated that the equilibrium of the reaction was affected by the concentration ) of the reacting substance(s). By 1877 Arrhenius had derived the definition of the equilbrium constant for a reaction from the rate constants of the forward and backward reactions. Ostwald in 1884 showed that sucrose and ester hydrolyses were affected by H+ concentration (pH). 

In 1864, two Norwegian chemists, Cato Guldberg and Peter Waage, summarized their experiments on chemical equilibrium in the law of chemical equilibrium At equilibrium, there is a constant ratio between the concentrations of the products and reactants in any change. 

Hansen HCB, Guldberg S, Erbs M, Koch CB (2001) Appl Clay Sci 18 81... 

Guldberg and Waage law See mass action law. gult berk and vag-3, 16 ) gum accroldes See acaroid resin. gam a kroi dez)... 

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