Concentration calculating equilibrium constant from

Calculate equilibrium constants from concentration data. 

Calculating equilibrium constants from pressures or concentrations... 

So far, we have calculated equilibrium constants from values of the equilibrium concentrations of all the reactants and products. In most cases, however, we need only know the initial concentrations of the reactant(s) and the equilibrium concentration of any one reactant or product. We can deduce the other equilibrium concentrations from the stoichiometry of the reaction. For example, consider the simple reaction ... 

CALCULATING EQUILIBRIUM CONSTANTS FROM GIBBS ENERGY TABLES AND THEN USING EQUILIBRIUM CONSTANTS TO CALCULATE EQUILIBRIUM CONCENTRATIONS... 

That the photoreactive species is the carbonium ion and not the corresponding alcohol is clearly indicated by the relative concentrations of the two species present. The calculated equilibrium constant for 5% aqueous sulfuric acid implies an alcohol content of 2 7 x 10 %, much too low to account for any detectable photoreaction from this covalent species. In addition, when the tropylium salt is irradiated in the absence of acid, neither 3 nor 4 is detected as a product, but rather ditropyl (5) and its photoisomer (6) are observed. 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

From changes in free energy in standard reference conditions it is possible to calculate equilibrium constants for reactions involving several reactants and products. Consider, for example, the chemical reaction aA + bB = cC + dD at equilibrium in solution. For this reaction we can define a stoichiometric equilibrium constant in terms of the concentrations of the reactants and products as... 

The concentration of M = I(T3 molar. Suppose we want to reduce the concentration of M to 10 5. When we calculate the equilibrium constant from the first example and then calculate the required concentration ofLatM= 1(T5 molar we find the following rule of thumb if an excess ofL is needed, keep [L] the same and lower fM] only ... 

According to C Hj yield and concentrations of the four components, the equilibrium constant of the reaction in Scheme 2.6 was determined as 4 X 10 . The value calculated from the potential difference was 4.4 X 10. Consequently, there is a coincidence between the calculated equilibrium constant based on the electrode potentials and the equilibrium constant determined from the liquid-phase experiment. 

One of the most useful applications of standard potentials is the calculation of equilibrium constants from electrochemical data. The techniques we are going to develop here can be applied to reactions that involve a difference in concentration, the neutralization of an acid by a base, a precipitation, or any chemical reaction, including redox reactions. It may seem puzzling at first that electrochemical data can be used to calculate the equilibrium constants for reactions that are not redox reactions, but we shall see that this is the case. 

In some cases, the reaction rates are very fast and a pseudoequilibrium approach is used to model the system (4.30). This approach consists of assuming that the concentration of species is always close to the equilibrium conditions and hence, they can be calculated using equilibrium constants from the values of other species present in the reaction system. This approach is especially important for the modeling processes in which the reaction rates are fast and when the kinetic rates are ill-defined (because of a large number of species or a lack of experimental data that makes difficult the kinetic analysis)... 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

In this experiment you will use wide-range acid-base indicator paper, acid-base indicator solutions, and a pH meter to measure the pH of solutions of electrolytes, and you will interpret such pH data in terms of the molar concentrations of H and OH present. From these concentrations you will calculate equilibrium constants for some of the equilibria. 

Calculate an equilibrium constant from concentration measurements (Section 15.5). 

D24.3 The Eyring equation (eqn 24.53) results from activated complex theory, which is an attempt to account for the rate constants of bimolecular reactions of the form A + B iC -vPin terms of the formation of an activated complex. In the formulation of the theory, it is assumed that the activated complex and the reactants are in equilibrium, and the concentration of activated complex is calculated in terms of an equilibrium constant, which in turn is calculated from the partition functions of the reactants and a postulated form of the activated complex. It is further supposed that one normal mode of the activated complex, the one corresponding to displaconent along the reaction coordinate, has a very low force constant and displacement along this normal mode leads to products provided that the complex enters a certain configuration of its atoms, which is known as the transition stale. The derivation of the equilibrium constant from the partition functions leads to eqn 24.51 and in turn to eqn 24.53, the Eyring equation. See Section 24.4 for a more complete discussion of a complicated subject. 

A different approach to a systematic study of the effects of experimental errors has also appeared. A computer program was developed which enabled ready calculation of the equilibrium constant from input experimental data. Beginning with synthetic data (no errors) small errors were deliberately introduced into the input data—for example, amounting to a weighing error of 0.3 mg in 20-500 mg, or an instrumental error of +0.003 absorbance units. Recalculation of the constant revealed that for certain concentration situations the determined equilibrium constant could be extremely sensitive to small experimental errors. The same conclusion was reached when K was determined by a graphical method with the same data. This again emphasizes the need for careful planning of experimental conditions. 

To calculate the equilibrium constants from the equilibrium concentration, it is necessary to know which equilibria are being considered. In addition, it must be established whether concentration and activity are identical. Three simple cases can be distinguished ... 

If Eq. (9) is to be useful in the calculation of kinetic isotope effects, values for Ki and X2 must be known. Because they are not conventional equilibrium constants, and because concentrations of transition states are too small ever to be measured, the usual means of arriving at equilibrium constants from equilibrium concentrations are useless. We know from thermodynamics, however, that equilibrium constants can be calculated not only from concentrations but also from relative free energies of reactants and products. The following is in no sense a derivation, but an attempt to sketch the main features of a somewhat indirect way of doing this. This approach, and many of its consequences, were developed by Bigeleisen. 

Let s also look at the units of equilibrium constants. For reasons beyond the scope of this course, a rigorous treatment of equilibrium constant calculations results in an equilibrium constant with no units. In practice, determining the value of the equilibrium constant from solution concentrations in moles per liter or from gas partial pressures simplifies the calculations and generally results in an insignificant error for most situations. Therefore, we omit units on K values. 

The results obtained from Lineweaver-Burk plots, are used for calculation of kinetic constants. The secondary plots of the slopes and intersects vs. activator concentrations are not linear (data not shown), but the reciprocal of the change in slope and intercept (Aslope and Ainiercept) that are determined by subtracting the values in the paesence of activator from that in its absence, are hnear. The intercepts of a plot 1/Aslope and 1/Airtercept 1/ [Al ] on 1/A axis, and intercepts of both plots on l/[ Al ] axis are used for calculating equilibrium constants Kms and Kma for dissociation of formed binary enzyme-activator (Al ) and ternary enzyme activator- substrate complexes (Figure 4). The calculated values for constants are (0.904 + 0.083) mM and (8.56 + 0.51) mM, respiectively. 

Calculating the Equilibrium Constant from Measured Equilibrium Concentrations 662... 

We can calculate the equilibrium constant from equilibrium concentrations or partial pressures by substituting measured values into the expression for the equilibrium constant (as obtained from the law of mass action). 

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