Reversible reactions equilibrium constants

It is a relatively straightforward matter to show that the same curves may be applied to the case of a reversible reaction (equilibrium constant K ) provided the dimensionless variables are redefined as follows ... 

This result may be expressed in words when equilibrium is reached in a reversible reaction, at constant temperature, the product of the concentrations of the resultants (the substances on the right-hand side of the equation) divided by the product of the concentrations of the reactants (the substances on the left-hand side of the equation), each concentration being raised to a power equal to the stoichiometric coefficient of the substance concerned in the equation for the reaction, is constant. 

However, considering practical limitations, that is, the availability of optically pure enantiomers, E values are more commonly determined on racemates by evaluating the enantiomeric excess values as a function of the extent of conversion in batch reactions. For irreversible reactions, the E value can be calculated from Equation 1 (when the enantiomeric excess ofthe product is known) or from Equation 2 (when the enantiomeric excess ofthe substrate is knovm) [la]. For reversible reactions, which may be the case in enzymatic resolution carried out in organic solvents (especially at extents of conversion higher than 40%), Equations 3 or 4, in which the reaction equilibrium constant has been introduced, should be used [lb]. 

Equilibrium constant expressions are always written with the concentrations of products in the numerator and the concentrations of reactants in the denominator, and when a reaction is reversed, its equilibrium constant expression is inverted. 

The reader should refer to the original tables for the reference material on which the thermochemical data are based. The reference state used in Chapter 1 was chosen as 298 K consequently, the thermochemical values at this temperature are identified from this listing. The logarithm of the equilibrium constant is to the base 10. The unit notation (J/K/mol) is equivalent to (JK mol ). Supplemental thermochemical data for species included in the reaction listing of Appendix C, and not given in Table A2, are listed in Table A3. These data, in combination with those of Table A2, may be used to calculate heats of reaction and reverse reaction rate constants as described in Chapter 2. References for the thermochemical data cited in Table A3 may be found in the respective references for the chemical mechanisms of Appendix C. 

SURFTHERM Coltrin, M. E. and Moffat, H. K. Sandia National Laboratories. SURFTHERM is a Fortran program (surftherm.f) that is used in combination with CHEMKIN (and SURFACE CHEMKIN) to aid in the development and analysis of chemical mechanisms by presenting in tabular form detailed information about the temperature and pressure dependence of chemical reaction rate constants and their reverse rate constants, reaction equilibrium constants, reaction thermochemistry, chemical species thermochemistry, and transport properties. 

In general, the reactions in the addition phase of both the base- and acid-catalyzed mechanisms are reversible. The equilibrium constant for addition is usually unfavorable for acyclic ketones. The equilibrium constant for the dehydration phase is usually favorable, because of the conjugated a,/ -unsaturated carbonyl system that is formed. When the reaction conditions are sufficiently vigorous to cause dehydration, the overall reaction will go to completion, even if the equilibrium constant for the addition step is unfavorable. Entry 3 in Scheme 2.1 illustrates a clever way of overcoming the unfavorable equilibrium of the addition step. The basic catalyst is contained in a separate compartment of a Soxhlet extractor. Acetone is repeatedly passed over the basic catalyst by distillation and then returns to the reaction flask. The concentration of the addition product builds up in the reaction flask as the more volatile acetone distills preferentially. Because there is no catalyst in the reaction flask, the adduct remains stable. 

As an interesting fact, we can learn from Eq. 12-21 that the time to steady-state (or time to equilibrium) depends on the sum of the forward and reverse reaction rate constants. Thus, even if one rate constant is very small, time to equilibrium can be small, provided that the other rate constant is large. By using Eq. 4 in Box 12.1 (95% of equilibrium reached) we obtain ... 

For each reaction in a surface chemistry mechanism, one must provide a temperature dependent reaction probability or a rate constant for the reaction in both the forward and reverse directions. (The user may specify that a reaction is irreversible or has no temperature dependence, which are special cases of the general statement above.) To simulate the heat consumption or release at a surface due to heterogeneous reactions, the (temperature-dependent) endothermicity or exothermicity of each reaction must also be provided. In developing a surface reaction mechanism, one may choose to specify independently the forward and reverse rate constants for each reaction. An alternative would be to specify the change in free energy (as a function of temperature) for each reaction, and compute the reverse rate constant via the reaction equilibrium constant. 

Rate constants kY (M 1 s 1) and ksoiv (s 1) for the reversible addition of methanethiol to 48 and the overall reaction equilibrium constant (Scheme 51) have been reported.83 It was shown that the transition state for addition of RSH... 

The numerical case studied is derived from a flowsheet given in Stanford Research Institute Report 91, Isomerization of Paraffins for Gasoline. Since no kinetic information is given in this report, only reactor inlet and exit conditions, we will assume two different types of kinetics. In Case 1 we consider that the reaction is irreversible. An activation energy of 30,000 Btudb mol is used, and the preexponential factor is adjusted to give the same conversion reported in the SRI report. In Case 2 we assume that the reaction is reversible. The equilibrium constant decreases with increasing temperature because the reaction is exothermic. We also increase the size of the reactor so that the effluent leaves essentially at chemical equilibrium. 

In the absence of added nucleophiles, nitrosation occurs virtually irreversibly by an acid-catalysed pathway, presumably by attack by HjNO or NO". The third order rate constant from the rate equation equivalent to (46) has a value of 840 dm moF s- at 31°C (c/. 456 and 6960 dm mol- s for cysteine and thiourea respectively at 25°C) which suggests that for this neutral substrate the reaction rate is somewhat less than that expected for an encounter-controlled process. There is a major difference between the nitrosation of alcohols and that of thiols in that, whilst the former reactions are reversible (with equilibrium constants around 1), the reactions of thiols are virtually irreversible. It is possible to effect denitrosation of thionitrites but only at high acidity and in the presence of a nitrous acid trap to ensure reversibility (Al-Kaabi et al., 1982). Direct comparisons are not possible, but it is likely that nitrosation at sulphur is much more favoured than reaction at oxygen (by comparison of the reactions of N-acetylpenicillamine and t-butyl alcohol). This is in line with the greater nucleophilicity expected of the sulphur atom in the thiol. For the reverse reaction of denitrosation [(52) and (53)], the acid catalysis observed suggests the intermediacy of the protonated forms... 

Carnot s equations, 146-147 Carnot s theorem, 142-143 Chemical potential, 298, 302, 303 as equilibrium criterion, 298-299, 503 for ideal gas, 302 for ideal solution, 303 Chemical reaction equilibrium constant for, 504-516 equilibrium conversion of, 518-528, 533-542 heat effects of, 116-133 reaction coordinate for, 497-501 reversible, 41-42, 505-507 standard property changes for, 125, 505 stoichiometry, 497-501... 

The equilibrium constants fCj, K2, and K3 for the elementary reactions are equal to the ratio of the forward and reverse reaction rate constants ... 

Whereas radioactive decay is never a reversible reaction, many first-order chemical reactions are reversible. In this case the characteristic life time is determined by the sum of the forward and reverse reaction rate constants (Table 9.5). The reason for this maybe understood by a simple thought experiment. Consider two reactions that have the same rate constant driving them to the right, but one is irreversible and one is reversible (e.g. k in first-order equation (a) of Table 9.5 and ki in first-order reversible equation (b) of the same table). The characteristic time to steady state tvill be shorter for the reversible reaction because the difference between the initial and final concentrations of the reactant has to be less if the reaction goes both ways. In the irreversible case all reactant will be consumed in the irreversible case the system tvill come to an equilibrium in which the reactant will be of some greater value. The difference in the characteristic life time between the two examples is determined by the magnitude of the reverse reaction rate constant, k. If k were zero the characteristic life times for the reversible and irreversible reactions would be the same. If k = k+ then the characteristic time for the reversible reaction is half that of the irreversible rate. 

Or using just the reactants, the Afgq = lOlP abH P aHAl- The derivation of this quick method is straightforward. Any proton transfer reaction can be considered to be the sum of two Afa equilibria, one written in the forward direction and the second written in the reverse. The equilibrium constant for the reverse reaction is the reciprocal of K. ... 

Here k and k-i are the forward and reverse reaction rate constants for substrate binding, while the process of conversion of the enzyme-substrate complex ES is assumed to be irreversible, thus having only one reaction rate constant, 2, for the forward reaction. The MM kinetic equation is derived assuming, among other things, that the reaction is operating away from the thermodynamic equilibrium and that the concentration of the ES complex is constant. Skipping the derivation, the final MM equation can be written in the familiar form... 

In general, the reactions in the addition phase of both the base- and acid-catalyzed mechanisms are reversible. The equilibrium constant for addition is usually unfavorable for ketones. The equilibrium constant for the dehydration phase is usually favorable because of the conjugated a,6-unsaturated carbonyl system that is formed. When the reaction conditions are sufficiently vigorous to cause dehydration, the overall reaction can go to completion, even if the equilibrium constant for the addition step is unfavorable. 

In equation (11), is the reverse reaction rate constant, and it is independent of n. The concentration of vacant states in the semiconductor and the concentration of filled states in the metal has been incorporated into the value of This rate is called the reverse rate, because it represents the formation of the species on the left-hand side of the reaction represented in equation (9). At equilibrium (when s = so), these rates must be equal to each other (fc = n so)-... 

Michaelis constant of product in reversible enzyme reactions equilibrium constant at constant pressure... 

When striving for high reactor conversions, it may be necessary to consider the reverse reaction even when the reaction is considered to be irreversible. This is the case for the hydrodealkylation of toluene. A rate equation for the reverse reaction can be derived from the rate equation for the forward reaction, given by Eq. (8.2), by assuming that the two rate equations are consistent with the chemical-reaction equilibrium constant. Assume that the gas reacting mixture is ideal at the high temperature of the reaction. Then, the chemical equilibrium constant can be expressed in terms of concentrations and equated to the ratio of the rate constants by ... 

The Equilibrium (Mass Action) Expression Gas Phase Equilibria Kp vs. Kp Homogeneous and Heterogeneous Equilibria Numerical Importance of the Equilibrium Expression Mathematical Manipulation of Equilibrium Constants Reversing the Chemical Equation Adjusting the Stoichiometry of the Chemical Reaction Equilibrium Constants for a Series of Reactions Units and the Equilibrium Constant... 

The first reaction is catalysed by orotate phosphoribosyltransferase (orotidine 5 -phosphate pyrophosphate phosphoribosyltransferase, EC 2.4.2.10) which is readily reversible. The equilibrium constant for the forward reaction [109] is about 0.1. The reaction is specific for orotate (the enzyme usually does not accept uracil) and some synthetic analogues of orotic acid (Chapter 6). Orotate phosphoribosyltransferase activity was found in many animal tissues [110] and there are several phosphoribosyl-transferases of broad specifity which are distinct from the enzyme involved in the orotate pathway [111-113]. 

According to Equation 10.9, the A//° and AS of the reaction can be obtained from the slope and the intercept by plotting In(K q) against l/T, respectively. Such plots are called van t Hoff plots. Figure 10.7a and b show the van t Hoff plots of an endothermic and an exothermic reaction, respectively. Since the reaction enthalpy of endothermic reactions is a positive value, the slope of the van t Hoff plot is negative in the case of an exothermic reaction, the slope is positive. Notably, van t Hoff plots are different from Arrhenius plots although they all represent the relationships between temperature and constants associated with stoichiometric reactions. The difference, however, lies in that the Arrhenius plots concern the reaction rate constants in elementary reactions, whereas the van t Hoff plots concern equilibrium constants, which comprise forward and reverse reaction rate constants. 

Since the overall reaction equilibrium constant K is also equal to the quotient of the velocity constants for the forward and reverse reactions K = kj/kr), both reactions are accelerated by the same factor. This does not, however, suggest that all the reactions in a multiple reaction system are accelerated to the same extent quite the reverse, the merit of a successful catalyst is to accelerate only the desirable reaction(s). 

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