Equilibrium expression definition

It should also be noted that when the rate of change in the protein-ligand complex concentration is zero (by definition, when the system is at equilibrium), this equation reduces to the equilibrium expression below, with the binding affinity constant defined as the ratio of the dissociation rate koff to tho association rate kon-... 

By extending the definition of chemical potentials (equation 3.47) to cations In ( )), and converting equation 3.51 from logarithmic to exponential form, the equilibrium expression becomes ... 

The equation describing the equilibrium reaction is called an equilibrium expression, and K q, the equilibrium constant, is a definite numerical value for each equihbrium reaction. The equihbrium constant for a particular reaction is specific for that reaction and changes only with variations in temperature. The presence of a catalyst does not alter K q but does cause the reaction to reach equihbrium more rapidly. 

A condition closely related to detailed balance which also can be used to help understand the second example is that the equilibrium state is independent of the reaction path. This, of course, follows from the definition of thermodynamic equilibrium. A further important consequence of these equilibrium principles is that if the rate law for the reaction in the forward direction is known, the rate law for the reverse reaction can be derived from it and the equilibrium expression for the overall reaction. As an example. 

We use the definition of the equilibrium expression. Write the products in the numerator and the reactants in the denominator. The exponent for each concentration term is given by the corresponding stoichiometric coefficient fi-om the chemical equation. 

Hence, strictly speaking, the equilibrium expressions in Eqs. 5.7 and 5.9 should be expressed in terms of the activities (a) of the entities, not their concentrations as given. Likewise, the definition of pH in Eq. 5.11 should really include the activity of H3O, not its concentration, because activity is what the pH meter really measures. 

To write an equilibrium expression for a chemical reaction, examine the chemical equation and follow the preceding definition. For example, suppose we want to write an equilibrium expression for the reaction ... 

Examine the definition of the equilibrium constant in the Chemical Principles section (page 562). To write the equilibrium expression for a reaction, write the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients. Remember that if the reaction contains reactants or products that are liquids or solids, these are omitted from the equilibrium expression. 

Figurel. Equilibrium potential / pH diagram of the Pb/H20 system at 25 °C, according to Pourbaix [10], but simplified for a = lmol L 1. The pH value is used to express the acidity of the solution. Its definition is pH = -log( H.) pH stands for the negative logarithm of the activity of the H+ ions.

There is thus assumed to be a one-to-one correspondence between the most probable distribution and the thermodynamic state. The equilibrium ensemble corresponding to any given thermodynamic state is then used to compute averages over the ensemble of other (not necessarily thermodynamic) properties of the systems represented in the ensemble. The first step in developing this theory is thus a suitable definition of the probability of a distribution in a collection of systems. In classical statistics we are familiar with the fact that the logarithm of the probability of a distribution w[n is — J(n) w n) In w n, and that the classical expression for entropy in the ensemble is20... 

To express the composition of the vapor in equilibrium with the liquid phase of a binary liquid mixture, we first note that the definition of partial pressure (PA = xAP for component A) and Dalton s law (P = PA + PB) allow us to express the composition of the vapor of a mixture of liquids A and B in terms of the partial pressures of the components ... 

A logarithmic scale is useful not only for expressing hydronium ion concentrations, but also for expressing hydroxide ion concentrations and equilibrium constants. That is, the pH definition can be generalized to other quantities pOH = - log [OH ] p Tg = - log Tg p log... 

Fig. 2 The experimentally determined potential energy V(), expressed as a wavenumber for convenience, as a function of the angle in the hydrogen-bonded complex H20- HF. The definition of

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

In the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). The concentrations of pure solids and pure liquids are omitted from the equilibrium constant expression because their activity is taken to be 1. 

The first term in expression (4.2.38) for T has a simple physical meaning it sums the perturbed leaving rates from each level of the subsystem taking into account the equilibrium probabilities for their occupation. On the other hand, the second term depends on the unperturbed rates for transitions between states of the subsystem and is inversely proportional to them by virtue of the definition of... 

Many definitions are used to express the solubility of gases in liquids, but usually the equilibrium law is defined as ... 

The energy and mass conservation equations used in the determination of the flame temperature are more conveniently written in terms of moles thus, it is best to write the partial pressure in Kp in terms of moles and the total pressure P. This conversion is accomplished through the relationship between partial pressure p and total pressure P, as given by Eq. (1.30). Substituting this expression for p, [Eq. (1.30)] in the definition of the equilibrium constant [Eq. (1.40)], one obtains... 

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