Principle of mass action

The principle of mass action explains the relationship between concentration and complexation. The abundance of ion pairs in aqueous solution is controlled by... 

The kinetic behavior of the reductive dissolution mechanisms given in Figure 2 can be found by applying the Principle of Mass Action to the elementary reaction steps. The rate expression for precursor complex formation via an inner-sphere mechanism is given by ... 

From the chemist s point of view as a user, these simulation techniques require him to provide computer code for the time derivative of each chemical species in the mechanism. According to the principle of mass-action, the derivative of the r-th species concentration in a mechanism of M reactions involving P chemical species is given by... 

The forward rate constants are k/ = 1 and kf2 = 1000, the equilibrium constants are K — 0.01 and K2 =, and the reverse rate constants are krt = kjJK and kn = kfr/Ki- The rate constants and species concentrations used here are taken to be unitless. Based on the principles of mass-action kinetics, the transient behavior of the system can be represented in differential-equation form as... 

Based on the principles of mass-action kinetics the transient behavior of the system can be represented in differential-equation form as... 

This step is catalyzed by a separate enzyme, malate dehydrogenase. It has a very unfavorable AG° of about +7 kcal/ mole. When this reaction is followed by reaction (17), the combined AG9 is about —1.3 kcal/mole, so the equilibrium constant for the overall sequence is favorable. You can view this simply as an illustration of the principle of mass action (17) pulls (18) along by removing one of the products. 

The kinetics of the reductive dissolution mechanisms shown in Fig. 8.1 can be derived using the principle of mass action. The kinetic expression for precursor complex formation by way of an inner-sphere mechanism (Stone, 1986) is... 

Application of the principle of mass action to the reaction scheme... 

From basic principles of mass action, we know the relationship between these rate constants and the association (KA) and dissociation (KD) equilibrium constants ... 

Mechanisms for most chemical processes involve two or more elementary reactions. Our goal is to determine concentrations of reactants, intermediates, and products as a function of time. In order to do this, we must know the rate constants for all pertinent elementary reactions. The principle of mass action is used to write differential equations expressing rates of change for each chemical involved in the process. These differential equations are then integrated with the help of stoichiometric relationships and an appropriate set of boundary conditions (e.g., initial concentrations). For simple cases, analytical solutions are readily obtained. Complex sets of elementary reactions may require numerical solutions. 

From the principle of mass action, rates of the first and second steps are given by... 

I tu li step or molecular event in a reaction mechanism is called an elementary mid ion . Hach elementary reaction listed above is balanced for both mass and tJuirge. The rate at which an elementary reaction takes place is proportional to the concentration of each species participating in the molecular event im r rasing participant concentrations yields a proportional increase in encounter liri iicncy. This observation, called the principle of mass action (Gardiner. 1969) In I he basis for quantitative treatment of reaction kinetics. Reaction 7, which n piesents the overall reaction stoichiometry, is also balanced for mass and... 

Rates of each reaction step can be calculated by use of the principle of mass action and values of pertinent rate constants. The rate of the hydroxide ion addition to the ester is given by... 

Irving Langmuir, the Nobel prize-winning industrial physical chemist who worked at General Electric, built an elegant structure upon this foundation in kinetic theory. He reasoned that not every molecule would adsorb, but only some would do so. Furthermore, one reason for this was that to be adsorbed there should be a site for adsorption to occur. It stands to reason then that on the basis of mass action, the rate of adsorption should be proportional to the concentration of molecules in the gas phase and to the number of sites available on the surface. Additionally, the rate should be related at any time to the number of sites not covered at that time rather than to the total number of sites present per unit area. Conversely, and again by the principle of mass action, the rate of desorption should be proportional to the number of sites currently occupied at that time. Using ka and kd as the proportionality constants (that we will call the rate constant for adsorption and desorption, respectively), we can write the net rate of adsorption for gas phase species i as the difference between the rate of adsorption and the rate of desorption ... 

Once a reaction mechanism consisting of a sequence of individual elementary reactions has been proposed it is possible to develop rate equations, which predict the dependence of the observed reaction rate on concentration. The principle of mass action, which states the rate at which an elementary reaction takes place is proportional to the concentration of each chemical species participating in the molecular event, is used to write differential rate equations for each elementary reaction in the proposed reaction mechanism. The goal is then to obtain explicit functions of time, which are referred to as integrated rate laws, from these differential rate equations. For simple cases, analytical solutions are readily obtained. Complex sets of elementary reactions may require numerical solutions. 

The concentration of hydrogen ions in chemically pure, neutral water is 1 10 g/1, corresponding to the dissociation constant of the water = 10 at 25 °C deducible from the principle of mass action ... 

Elementary Rate Laws and the Principle of Mass Action... 

Hydrolysis is a chemical reaction that follows the principle of mass action. That means that the equilibrium constant depends on the concentration of initial substances and temperature. The aim of every resin formulation is to minimize the... 

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