Equibbrium constants

The additional number of differential equations and increased complexities of the equilibrium relationships may also be compounded by computational problems caused by widely differing magnitudes in the equibbrium constants for the various components. As discussed in Section 3.3.2, it is shown that this can lead to widely differing values in the equation time constants and hence to stiffness problems for the numerical solution. 

These equations can be used as the first approximation for calculating, for example, the conversion of ethylene and ethylbenzene in a tubular plug flow reactor. The calculations can be based on the preceding kinetic equations using the concentrations of the external reactants B, E, EB, and DEB and equibbrium constants Kpi of the stepwise processes under consideration ... 

Tabular and calculated standard equibbrium constants characterize interrelations between components of individual reactions under standard conditions (at temperature 25 °C and pressure 1 bar). Water is practically incompressible, so the effect of pressure not important. With pressure increase from 100 to 10 kPa (1-1,000 bar) values pFC in water solutions change by about 0.1- 0.2. Temperature has much greater effect. With temperature increase by 100 °C the values of equibbrium constant can change by 1-2, sometimes by 3 orders of magnitude. For this reason under conditions close to surficial, the pressure effect may be disregarded. 

Correlation equibbrium constant vs. temperature is expressed by the Van t Hoff equation for the selected reaction... 

In order to determine the temperature effect on the values of equibbrium constants, equation (1.106) is integrated by the temperature in the interval between 298.15 K to T ... 

The constant C has units of concentration and denotes the concentration at which intramolecular and intermolecular reactions have the same rate. In the 1970s, the term effective molarity (EM) was widely adopted to describe this parameter and characterize the rate enhancements observed for intramolecular reactions. The EM defined by Eq. (1) is a kinetic EM, because it is based on the ratio of two reaction rates, but it is possible to define a thermodynamic EM in the same way, if equibbrium constants are substituted for rate constants (Eq. (2)). In this review, we will use thermodynamic EM to quantify the chelate cooperativity associated with multivalent noncovalent interactions in supramolecular systems. 

In this equation R is the ideal-gas constant, 8.314 J/mol-K T is the absolute temperature and Q is the reaction quotient for the reaction mixture of interest. 000 (Section 15.6) Recall that the reaction quotient Q is calculated hke an equibbrium constant, except that you use the concentrations at emy point of interest in the reaction if Q = JC, then the reaction is at equibbrium. Under standard conditions, the concentrations of all the reactants and products axe equal to 1 M. Thus, under standard conditions Q = 1, In Q = 0, and Equation 19.19 reduces to AG = AG° under standard conditions, as it should. 

Step 3 From the preceding discussion and Table 15.3 we write the equibbrium constant of hydrolysis, or the base ionization constant, as... 

E] enzyme concentration [S] substrate concentration [ES] concentration of the enzyme-substrate complex [P] product concentration ki association equibbrium rate constant k i dissociation equilibrium rate constant (rate constant of the back reaction). 

Kgure 7. Product inhibition by Q in the Rapid Equibbrium Random Bi Bi system with a dead-end EBQ complex. Graphical presentation of Eq. C8.30) with B as a constant and A as a variable substrate. 

Representation of three-component systems as a set of quasi-binary cross-sections is not quite rigorous for the most real ternary mixtures because a ratio of second and third components in equibbrium phases is not usually constant. However, if we intend to study the phase behavior from the point of view of topological schemes, the sequence of binary phase diagrams of quasi-binary sections (including the sections through the ternary nonvariant points) give an exhaustive description of possible phase equilibria and phase transformations in ternary systems. 

If the ejqieritnental conditions are such that we are very far finm the equibbrium (that means, since all the steps other than the rate-determining one are constantly at equilibrium, and the rate-determining step is itself far finm equibbrium and therefore, we can neglect the rate of its reverse reaction), then in equation [7.48] the exponential is negligible as compared to 1 and according to equation [7.42], the rate is reduced to ... 

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