Chemical reaction stoichiometric

Stoichiometry is the study of the relative quantities of reactants and products in chemical reactions. Stoichiometric calculations are used for many purposes. One purpose is determining how much of a reactant is needed to carry out a reaction. This kind of knowledge is useful for any chemical reaction, and it can even be a matter of life or death. 

Although two chemical reactions take place here, both of them provide the same information on the proportions among the individual species. This is because Reaction 2.4.1b is the reverse of Reaction 2.4.1a, and its stoichiometric coefficients have the negative values of those of Reaction 2.4.1a. In mathematical terms, we say that the two reactions are linearly dependent. Hence, only one chemical reaction (stoichiometric relation) is needed to determine the species compositions. 

One of the most important areas of chemical arithmetic is based on balanced chemical equations. Chemists call this area of endeavor stoichiometry (stoy-key-om -ah-tree), which concerns the quantitative relationships between the reactants and products in chemical reactions. Stoichiometric calculations can be used to determine the amount of one reactant needed to completely react with another, or to determine the amount of reactant needed to produce a desired amount of product. The key to understanding how this is done is found in the way balanced chemical equations can be interpreted. So that is the place to begin learning the arithmetic of balanced chemical equations. 

Stoichiometry is the quantitative study of products and reactants in chemical reactions. Stoichiometric calculations are best done by expressing both the known and unknown quantities in terms of moles and then converting to other units if necessary. A limiting reagent is the reactant that is present in the smallest stoichiometric amount. It limits the amount of product that can be formed. The amount of product obtained in a reaction (the actual yield) may be less than the maximum possible amount (the theoretical yield). The ratio of the two is expressed as the percent yield. 

Suppose we have a chemical reaction involving n elements E1, E2,...,En, making up m different molecules M ,...Mm where molecule Mj has ay atoms of element E . Suppose seme quantity of feed has Oj moles of Mj, and the product from this quantity of feed has pj moles of Mj. The chemical reaction (stoichiometric) equation fin- this process is ... 

Stoichiometry is the quantitative study of products and reactants in chemical reactions. Stoichiometric calculations are best done by expressing both the known and unknown quantities in terms of moles and then converting to other units if necessary. 

Gases in Chemical Reactions Stoichiometric calculations involving gases are similar to those that do not involve gases in that the coefficients in a balanced chemical equation provide conversion factors among moles of reactants and products in the reaction. For gases, the amoimt of a reactant or product is often specified by the volume of reactant or product at a given temperature and pressiue. The ideal gas law is then used to convert from these quantities to moles of reactant or product. Alternatively at standard temperature and pressure, volume can be converted directly to moles with ffie equality ... 

The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction for one mole of true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. This gives... 

In reaction kinetics it is conventional to define reaction rates in the context of chemical reactions with a well defined stoichiometric equation... 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

In section 11.3 vie showed that the difficult problem of solving the flux relations can be circumvented rather simply when the stoichiometric relations are satisfied by the flux vectors, but the treatment given there was limited to the case of a single Independent chemical reaction, when the stoichiometric relations permit all the flux vectors to be expressed in terms of any one of them. The question then arises whether any comparable simplification is possible v en the reactants participate in more than one independent reaction. 

Normality makes use of the chemical equivalent, which is the amount of one chemical species reacting stoichiometrically with another chemical species. Note that this definition makes an equivalent, and thus normality, a function of the chemical reaction in which the species participates. Although a solution of 1T2S04 has a fixed molarity, its normality depends on how it reacts. 

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of determining the amount of oxalic acid, H2C2O4, in rhubarb. One method for this analysis uses the following reaction in which we oxidize oxalic acid to CO2. 

The balanced chemical reaction provides the stoichiometric relationship between the moles of Fe used and the moles of oxalic acid in the sample being analyzed— specifically, one mole of oxalic acid reacts with two moles of Fe. As shown in Example 2.6, the balanced chemical reaction can be used to determine the amount of oxalic acid in a sample, provided that information about the number of moles of Fe is known. 

Stoichiometric relationships and calculations are important in many quantitative analyses. The stoichiometry between the reactants and products of a chemical reaction is given by the coefficients of a balanced chemical reaction. When it is inconvenient to balance reactions, conservation principles can be used to establish the stoichiometric relationships. 

Rates determined by monitoring different species in a chemical reaction need not have the same value. The rate R in equation A5.2 and the rate R in equation A5.3 will have the same value only if the stoichiometric coefficients of A and C in reaction A5.1 are the same. In general, the relationship between the rates R and R is... 

The stoichiometric numbers provide relations among the changes in mole numbers of chemical species which occur as the result of chemical reaction. Thus, for reactionj ... 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

In the second chemical reaction to be considered, insufficient oxygen is supplied to the fuel for stoichiometric combustion (50%), but steam is also supplied (Fig. 8.5c). Now the chemical reactions involved in the partial combustion are ... 

The chemical reactions that occnr in flames transform an initial reactant mixtnre into final reaction prodncts. In the case of fnel-oxygen combns-tion, the final prodncts are principally water vapor and carbon dioxide, althongh nnmerons other prodncts snch as carbon monoxide may be formed, depending on the reactant composition and other factors. If the ratio of fnel-to-oxygen is stoichiometric, the final reaction prodncts, by definition, contain no excess fnel or oxygen. Theoretically, this means that partial oxidation prodncts snch as CO (itself a fnel) are not formed. In reality, partial oxidation prodncts snch as CO or OH are formed by high tem-peratnre reactions. For example, the molar stoichiometric reaction of methane is written ... 

These equilibria effect a rapid exchange of N atoms between the various species and only a single N nmr signal is seen at the weighted average position of HNO3, [NOa]" " and [N03]. They also account for the high electrical conductivity of the pure (stoichiometric) liquid (Table 11.13), and are an important factor in the chemical reactions of nitric acid and its non-aqueous solutions see below. 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

The two basic principles permit the algebraic manipulation of chemical reactions (represented by their stoichiometric equations and associated enthalpy changes) in order to achieve desired thermochemical results. 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

The equation for a chemical reaction speaks in terms of molecules or of moles. It contains the basis for stoichiometric calculations. However, in the laboratory a chemist measures amounts in such units as grams and milliliters. The first step in any quantitative calculation, then, is to convert the measured amounts to moles. In mole units, the balanced reaction connects quantities of reactants and products. Finally, the result is expressed in the desired units (which may not necessarily be the same as the original units). 

A balanced chemical equation symbolizes both the qualitative and the quantitative changes that take place in a chemical reaction. The stoichiometric coefficients tell us the relative numbers of moles of reactants and products taking part in the reaction. 

A chemical equation expresses a chemical reaction in terms of chemical formulas the stoichiometric coefficients are chosen to show that atoms are neither created nor destroyed in the reaction. 

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