Stoichiometry substitution equilibria

Interactions between tertiary aliphatic amines or N,N-dialkylanilines and substituted phenols are generally reported as models of O—H- N hydrogen bonds affording molecular complexes (equilibrium 4). A number of complexes between primary, secondary and tertiary aliphatic amines and dihydroxy benzenes (or dihydroxynaphthalenes) were isolated55 to investigate the stoichiometry of these complexes. The phenol/amine ratios observed included values of 1 1, 2 1, 3 1 and 3 2. 

For 1 1 stoichiometry as expressed in Eq. (1), the functional dependence of a reagent [A] (which is measured by CE, e.g., from the peak heights or areas) can be derived by substituting the relations between the initial and the equilibrium concentrations in Eq. (2) according to... 

Clearly, if the concentrations or pressures of all the components of a reaction are known, then the value of K can be found by simple substitution. Observing individual concentrations or partial pressures directly may be not always be practical, however. If one of the components is colored, the extent to which it absorbs light of an appropriate wavelength may serve as an index of its concentration. Pressure measurements are ordinarily able to measure only the total pressure of a gaseous mixture, so if two or more gaseous products are present in the equilibrium mixture, the partial pressure of one may need to be inferred from that of the other, taking into account the stoichiometry of the reaction. 

We are given the initial Pqo and Piota, at equilibrium. To find A"p, we must find the equilibrium pressures of CO2 and CO, which requires solving a stoichiometry problem, and then substitute them into the expression for <2p. 

Arts. Pure solids do not appear in the equilibrium constant expression. Therefore, = [NH3IHCI]. The stoichiometry of the reaction requires that, whatever the final concentrations of the equilibrium components, they must be equal to each other. We will let each concentration equal x, substitute that unknown into the equilibrium constant expression, and solve for the unknown ... 

The stoichiometry of the equilibrium dictates that 2x mol/L of F are produced for each X mol/L of Cap2 that dissolve. We now use the expression for K p and substitute the equilibrium concentrations to solve for the value of x ... 

The stoichiometry of the equilibrium constant expression for water indicates that the theoretical concentrations of hydrogen and hydroxide ions in pure water must be equal. If x = [H ] = [OH ], then substituting into the K expression gives... 

In most cases, we do not know the change that must occur for the system to reach equilibrium, so the change in the concentration of HjO"" is written as x and the reaction stoichiometry is used to write the corresponding changes in the other species. When the values at equilibrium (the last row of the table) are substituted into the expression for the acidity constant, we obtain an equation for x in terms of K. This equation can be solved for x. In general, solution of the equation for x results in several mathematically possible values of x. We select the chemically acceptable solution by considering the signs of the predicted concentrations they must be positive. 

If a binary compound MX exhibits negative deviations from the stoichiometric composition, the predominant defects may be either X vacancies, M interstitials, or M substitutionals. Comparison of Eqs. (31), (39), and (45) shows that for each defect, the equilibrium pressure is equal to a constant times some function of d. However, in each case the function of S is different. Therefore, the nature of the defect responsible for the negative deviation from stoichiometry may be deduced by comparing experimental data of pressure (or activity) as a function of 3 with each of Eqs. (31), (39) and (45) at large deviations from stoichiometry. This may be done by calculating the equilibrium constant for each experimental point assuming each type of defect. The equilibrium constant should not vary with composition (or ) for the correct defect. 

Compounds exhibiting large positive deviations from stoichiometry may be treated in the same manner. In this case, the possible defects are M vacancies, X interstitials, and X substitutionals. Here again, a different functional relationship between activity and 5 is obtained for each type of defect as can be seen from Eqs. (33), (36), and (42). An example of the use of these equations to deduce the nature of the defects is given for the intermetallic compound AuZn. From Zn activity measurements as a function of composition, equilibrium constants were calculated for each point defect. AuZn has the CsCl-type structure where a = 6 and s = 1. The results are shown in Table 3. It can be seen that d change with composition... 

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