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The reaction of Al upon hydrochloric acid solution (1.5-4N) was investigated based upon the reaction velocity theory. The result is as follows:1. Al reacts on and dissolves in hydrochloric acid solution according to the following chemical equation:Al+3HCl=AlCl3+3/2H22. The dissolving reaction of Al in hydrochloric acid solution consists of the stages of primary and secondary dissolution. The former can be shortened or eliminated by a suitable pretreatment, and the latter becomes the main-part of the reaction.3. In 1.5-4N hydrochloric acid solution the first order reaction of Al will take place, under which the following reaction velocity equation will hold:d(Al)/dt∞dV/dt=3.11×102[HCl]⋅S⋅e-8200/1.986T(V∞-V)(see equation 5, page 357).From this equation, we can determine the life of Al in hydrochloric acid.4. The activation energy is 8200cal/mol; from this figure the reaction is regarded as a diffusion reaction.

Summary A procedure for the selection of an independent sub‐set of chemical equations from a larger set is described and exemplified. The procedure is of a more operational nature than previously employed methods and has been incorporated in a digital computer program.

In a previous paper the atomic weights of several light elements were calculated from nuclear reaction energies using the known values of the atomic weights of He 4 and H 1 . In the present paper it is shown that the atomic weights can be obtained from the reaction energies without making any use of atomic weights determined by other methods. Any atom may be supposed formed by the combination of neutrons and hydrogen atoms according to the reaction equation z 1 H 1 + ( w - z ) 0 n 1 = z A w + z E w , where z E w denotes the energy of formation of the atom z A w . If we consider N different elements including 1 H 1 and 0 n 1 then we have N — 2 energies of formation. If the energies of formation are known then the energy of any nuclear reaction may be calculated.

In the study of problems in chemical kinetics in ordinary solution, reactions which may be represented by chemical equations of the form 3 A + B = C + D (1) are represented kinetically by the differential equations d ( C )/ dt = d ( D / dt = - d ( A )/ dt = - d ( B )/ dt = k ( A )( B ) (2) where ( A ), ( B ), ( C ), ··· , are the concentrations of A , B , C , ··· , and k is the kinetic constant for the reaction (assuming it to be occurring in ordinary solution).

The reactions at 1400.C between rare eatths(III)vanadium(III)mixed oxides;RVO3(Rrare arth elements) and graphite were studied, The products were examined by X-ray diffraction nd weight gain due to oxidation.when the mixed oxides except EuVO3 and graphite were mixed and heated at 1400C for n hour in vacuo, vanadium(III)ions were reduced by graphite quan, titatively to vanadium etal. The reaction equation was as follows when equimolar of graphite to RVOs was added;Rvo3+c-1/3 RvO3+1/3 R208+2/3 v+co (1)On the other hand, if EuVO3 and graphite were reacted, graphite acted as the reductant of europium(III)ions. In this case, Eu2VO4 arid EusViO7, in which Eu(n)ions were contained, were formediBoth, Eu2VOs and Eu3V207 were in the tetragonal systems, and they were decomposedto form EuVO3 at high temperatures as follows:2Eu2VOs.EugV207+EuO t(2)EusV207 .2EuVO, +EuO t (3)

Summary The Ramanspectrum of transformer oils has been investigated both before and after oxidation of the oils. A change in the intensity of the C-H oscillation lines could be shown. The photochemical chlorination of chloroform was followed completely by means of the Ramaneffect, the intensity of the CCI, lines providing an accurate method of estimating the amount of CCI, present. The calibration curve required for this purpose, which gave the relation between the amount of CCI, present in a mixture of CCI, and CHCI 3 and the corresponding intensities of the CCI,, Raman-lines, proved to be a straight line. From this fact the incoherence of the Raman-radiation was inferred. A new way of illuminating a photochemical system has been worked out. Experimental measurements and mathematical calculations concerning the light absorption in such a system are in perfect agreement with one another. The advantages of this “source of light” are summarized. Very simple, but accurate experiments with a selenium photocell confirmed the results obtained with the Ramaneffect. A theoretical interpretation of the empirical reaction equation is given,while the work of S c h u m a c h e r and W o I f f allowed an interesting comparison to be made between the reaction in the liquid- and the gaseous phase. It is maintained that highly unstable chain products can be detected by means of the Ramaneffect.

Chemical changes in which molecules of complex structure take part have recently assumed a particular importance in the theory of the mechanism of reaction velocity. Decompositions of organic compounds in the gaseous state provide excellent examples of such reactions. It is often necessary, in these, to suppose the intermediate formation of unstable radicles which undergo rapid subsequent transformations; and whenever each stage of a reaction is not expressed by conventional chemical equations, involving known substances only, there may always remain a slight doubt whether the course of the reaction has been truly represented. Although this does not prevent the drawing of perfectly valid conclusions about the kinetics of a given reaction, nevertheless an example in which every stage can be represented by a simple chemical equation has undoubted advantages. The decomposition of dimethyl ether, with which this paper deals, provides such an example. CH 3 .O.CH 3 → [CH 4 + HCHO] → CH 4 + H 2 + CO. The complexity of the dimethyl ether molecule is only moderate, and in the light of the discussion in the papers referred to above it is interesting to note that the reaction is an almost perfect example of the transition from the unimolecular to the bimolecular type.

ALL THE methods for the determination of silica in sea water are based on the reaction of orthosilicic acid with molylxlate forming 1 : 12 silicomolybdic acid. The absorbance of this intensely yellow coloured compound or its blue reduction product is measured at selected wave lengths. Though some of the photometric determinations of silica concerned arestandard methods the data on the condition of formation found out empirically are inhomogeneous. The reaction which leads to the formation of silicomolybdic acid is not known in detail. In numerous papers already published the chemical reaction is only suggested (BRLLIEWITZ, 1933; SWANK and MELLON, 1934; ROaINSON and SpooR, 1936;-ARl~STRONG, 1951 ; MULLIN and RILEY, 1955; BI~, 1958; a summary of methods and papers on the matter is given by JEAN, 1955). STRICKLAND (1952) proved the existence of two different modifications of the silicomolybdic acid which are called the ~and E-species. According to-SrO/RLAC (1956) the two modifications only differ in the water of constitution. Below a pH value of 2.5 the predominating species in the formation is the /3-silicornolybdic acid. It has a somewhat different absorption spectrum and a higher molar extinction. As already mentioned by STRICKLAND, the E-acid is unstable and changes irreversibly into the =-form. The velocity of the change depends on the conditions in the solution. According to GRASSHOrF and HAHN (1959) the formation of the heteropoly acid proceeds reversibly. The formal reaction equation is

The present investigation is part of a program aimed at examining the mathematical basis of reaction rate theory (Bartholomay,Bull. Math. Biophys. 20, 1958) from the point of view of individual molecular events. Certain inconsistencies resulting from the classical procedure of using stoichiometric “chemical equations” to represent the kinds of mechanisms involved are pointed out and remedies are suggested by the introduction of set-theoretic notation within the framework of a so-calledMolecular Set Theory. It is concluded that whereas ordinary algebra is a suitable basis for stoichiometry, in discussing mechanisms of chemical reactions,molecular set theory is more appropriate. This is a theory of material transformations which is patterned afterabstract set theory: the individual molecules of a chemical species and chemical transformations from one species to another correspond to the abstract concepts of elements or points of a set and their mappings into other sets respectively. The new notions ofexact molecular sequences andequivalence classes of molecules arising from this study of chemical reactions may be of purely mathematical interest when referred back to the context of abstract set theory.

Many multicomponent solids can be represented by a continuum model. On this basis a thermodynamic theory of multicomponent stressed solids has been constructed. After linearisation, the necessary equations for equilibrium can be separated into purely elastic and purely chemical equations. In particular, the usual Hooke's law coefficients are replaced by new open system coefficients. All the parameters of these equations can be computed from standard measurements. Examples showing the use of these formulae are presented.

1. In a previous report, one of the authors* estimated the necessary activation energy E of the baking reation of resin finishing as approximately 16_??_18kcal/mol, based on data derived from commercial products. The activation energy E and frequency factor A of the reaction presented in this report are calculated by using our experimental measurements. For this purpose, we have made two series of experiments: a) baking of resin on clean glass plates, and b) baking of resin on cotton fabrics.2. Our experimental results fully agreed with the following equation of unimolecular reaction: where a: Unreacted part of resin i.e. in 70°C water soluble part at z=0 by Kyeldhal method. a-x: do. at z=z (min.) k: Reaction velocity constant at temp. T°K z: Baking time (min.) z0: Waiting time (min.)3. In all the experiments, the reaction velocity constant k fully agreed with the Ahrrenius equation: ln k=A+(-E/RT) where R: gas constant.4. From the said results, the activation energy E and frequency factor A are culculated as follows: for series a) E 8.82kcal/mol, A 2, 178 10-1 min. for series b) E 18.85kcal/mol, A 1, 012 10-1 min.5. We have further made cumulative baking at various temperatures and have found that experimental results agreed with the cumulative reaction equation:6. We conclude from the great difference of the activation energy E in the above two series, that in series a) only reaction between resin components occurs, whereas in series b) reaction between resin components and cellulose predominates.

THE PURPOSE of this article is to determine if aids for solving problems, involving chemical equations, for students in high school chemistry are of value. It has long been known that high school text-books on chemistry have a gap between the formula equation, which is the next step after the giv en word equation, and the solving of a weight-weight, weight-vo 1 urn e, or volume-volume problem from a statement. This parallels a gap in the older algebra texts which carries the student from solving written equations of the first or second order to that of deriving equations from statements. The stated problems in algebra most likely to be re mem bered are the "rate up-stream vs. the rate down-stream" type. The pertinent problem in this paper is to devise a step between the two enti ties of solving problems from given equations, and, solving problems but deriving the problem and equation from a statement. Students in high school, generally, find formula writing and the cal culation of molecular weight not too difficult. From this point the student is introduced to equation writing from the word equation, an example of which is

Summary In this paper a stochastic model is set up for a certain type of reversible chemical reaction and a solution given for the equilibrium distribution; this solution is then extended to deal with any system of chemical reactions. Three different types of reaction are considered: (1) Several substances Ai react together and give a set of substances Bj. The reaction is reversible, with the substances Ai appearing only on one side of the reaction equation and the substances Bj only on the other. (2) Several different reactions involving the substances Ai and Bj take place simultaneously, but in each reaction equation the substances Ai can appear only on one side and the Bj only on the other. (3) The restriction of the sets Ai and Bj to different sides of the reaction equations is removed: any reaction involving any of the substances Ai and Bj on either side of the equation is permissible. The paper concludes with some applications of the results to problems of molecular adsorption.

CHEMCSMP is a convenient problem-oriented language based on CSMP/360 and is designed specifically to solve problems in kinetic chemical equations. Users' statements, which resemble conventional chemical nota tion, describe slow and fast reactions in multicompartment systems and flows between compartments. CSMP statements may be inter mixed with chemical equations to provide for a variety of computations and convenient output. CHEMCSMP is implemented via a pre compiler which translates the user's pro gram into pure CSMP. The paper describes the use and implementation of CHEMCSMP and provides an illustrative example.

In the study of problems in chemical kinetics in ordinary solution, reactions which may be represented by chemical equations of the form3 A + B = C + D (1) are represented kinetically by the differ...

This paper demonstrates the combinatorial relationships among the sets of chemical components, reactions, mechanisms catalyzations, etc. in a chemical system by solving a problem of the following nature: 28 chemical equations are given; one of them describes the overall chemical reaction of a particular chemical system, and the other 27 describe elementary reactions which possibly participate in the system; the problem is to determine mathematically every possible mechanism for the system. The formalization presented here does not depend on the particular chemical system used as an illustration, but is applicable to chemical systems with an arbitrarily large and intricate network structure.

The preparation of stable, crystalline compounds of the type (Ph 3 M) 4 M′ is described. They are obtainable according to the following reaction equation: The compounds with M′ = Pb are obtained as follows: Lead compounds are prepared most easily; (PhsGe) 4 M′ could not be obtained.

The authors have studied the reaction in the systemKOH-CaO-Silica gel-H2Oat 20±1°C and the solid phase formed by the reaction.The mixture of CaO and SiO2 gel of the mol ratio CaO/SiO2=2.5 was added to KOH solution whose concentration was changed up to 50g/l. After keeping 95 days with occasional agitation the reaction products were subjected to chemical and X-ray analyses and to the observation under electron microscope.The results obtained are summarized as follows:(1) The solid reaction product came into sight was identified as tobermorite phase which appeared under electron microscope as films or crumpled foils. In general, the individual crystals were smaller than 5μ, which grow comparatively well in the direction of thickness with increasing concentration of K2O, although this effect was not so pronounced as that of Na2O, which had been reported elsewhere.(2) With increasing concentration of K2O the concentration of CaO found in the liquid phase decreased, whereas that of SiO2 increased. The change of CaO was by far larger especially up to about K2O≤5.86g/l. From this point the decrease became slow and the concentration dropped below 0.1gCaO/l. The amount of CaO entered into the reaction to form solid phase was therefore, increased with increasing K2O concentration up to about the same limit.(3) A part of Ca2+ in tobermorite is very likely to be replaced by K+ whose amount seems to be governed by the concentration of K2O in the liquid phase.In the case of 13.78gK2O/l or more in the final concentration the mol ratio K2O/SiO2 of the solid reaction product came up to 0.22. It was also found that there exist a relation(CaO/SiO2 mol. ratio)+(K2O/SiO2 mol. ratio)=1.2-1.3in the solid reaction product.(4) Like NaOH the KOH-solution acts as an accelerator in the formation of tobemorite phase from Ca(OH)2 and silica gel.In the first place there would be the combination of KOH with silica gel to form K2O-SiO2-nH2O, which then acts upon Ca(OH)2 to precipitate tobermorite phase liberating K2O passing again into the liquid phase, so that the reactions are repeating round on the same way. In the mean time the replacement of Ca2+ and K+ would take place.The chemical equation may be written as follows;Si(OH)4+2KOH=K2O⋅SiO2+3H2O SiO2+2KOH=K2O⋅SiO2+H2O}…(1)K2O⋅SiO2+xCa(OH)2+mH2O=zK2O⋅xCaO⋅SiO2⋅yH2O/solid reaction product (tobermorite)+2(1-z)KOH+(x+z+m-y-1)H2O…(2)where, z was estimated to≤0.22 in the present experiment.

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Energy dh + qdq = 0 (4) where p, p, h, g, and 6 are the pressure, density, enthalpy, velocity and flow inclination, respectively, s and n are the distances along the streamline and its normal direction, respectively. e = 1 is for axisymmetrical flow and e = 0 is for two-dimensional flow, y is the distance from the axis of symmetry. The thermod3mamic aspect of a nonequilibrium dissociated gas (e.g., N2) is treated below. Consider the dissociation of a unit mass of the mixture, the chemical equation is represented as N2 ^ 27V. Let a be the degree of dissociation, m\ and m? the masses of the reacting N and N2, respectively; then dmi = vida where vx = 1 and v2 = — 1. If the enthalpy of a mixture of perfect gases is chosen as a function of p, S and nn, the second law of thermodynamics may be written as

The objective of this book is to interpret the chemist’s shorthand — chemical symbolism and formulation — and to introduce the subject of stoichiometry. Stoichiometry is the branch of chemical mathematics concerned with the relative amounts of substances that interact. Derived from the Greek stoicheion, meaning element, stoichiometry originally treated only of the different weights of elements that combine to form specific compounds. Modern usage, however, has expanded the generic applicability of the term to any and all aspects of chemical reactivity that can be validly interpreted by a balanced chemical equation. Consequently, stoichiometry encompasses within its purview not only weights but also volumes, gaseous and liquid, and even thermochemical and photochemical quanta of reaction.

Publisher Summary This chapter discusses chemical reactions from the physical point of view with respect to the properties that are common to all reactions, whatever the chemical nature of the reacting substances. Any chemical reaction is accompanied by the absorption or evolution of heat. In the former case, the reaction is said to be endothermic and in the latter case, the reaction is exothermic. It is clear that if a reaction is exothermic, the reverse reaction is endothermic and vice versa. The heat involved in a reaction depends in general on the conditions under which it occurs. Hence, the quantity of heat is distinguished accordingly as the reaction occurs at constant pressure or at constant volume. In practice, however, the difference is usually very slight. The heat of reaction is written in the reaction equation with a positive sign on the side where heat is evolved or with a negative sign where it is absorbed. As a chemical reaction proceeds, the quantities of the original substances decrease and reaction products accumulate. Ultimately, the reaction leads to a state in which the quantities of all the substances no longer vary. This is called a state of chemical equilibrium, a particular case of thermal equilibrium. The chapter explains chemical equilibrium. It also discusses strong and weak electrolytes, activations energy, the molecularity of reactions, and chain reactions.

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THE general scheme of a chemical transformation can be reproduced by the equation: . A, B, C represent chemical elements or groups of elements, which are transferred as whole complexes from one side to the other of the chemical equation (i.e. NH4, SO4, NO2, etc.). We shall call these groups of elements for short the elementids of a chemical equation; the chemical elements are thus the simplest elementids. It is evident that in determining the number of elementids of a chemical equation the minimum rule must be observed—that is, the elements must be brought together into groups, so that the number of these groups (elementids) shall be the smallest possible. The composition of these groups must fulfil one condition: that their number taken as a whole and for each formula individually should be the same on the right and on the left side of the chemical equation. In most cases the problem of determining the elementids is simplified by the fact that the number of elementids is the same as the number of elements.

THE recent report of the Joint Committee of the Chemical, Faraday, and Physical Societies on Symbols for Thermodynamical and Physico-Chemical Quantities may be taken as an occasion for some remarks on the sign and symbol of heat of reaction and allied quantities. As is familiar, the heat of a reaction may be defined as the heat generated or lost by the system, when unit mass of reactants passes into resultants, the unit of mass being the number of grams represented by the sum of the molecular weights multiplied by their respective coefficients on either side of the chemical equation.

An introductory experiment in which students deduce the products by comparing their observations to descriptions of possible substances and write balanced chemical equations to represent the reactions.

The mathematical method of diophantine equations is shown to apply to two problems in chemistry: the balancing of chemical equations, and determining the molecular formula of a compound.

Students titrate phosphoric acid with sodium hydroxide to determine the chemical formula of Na2HPO4.

Availability of a Fortran IV program that uses the matrix method for balancing chemical equations.