Concentration calculating with equilibrium constants

Before doing calculations with equilibrium constants, it is valuable to understand what the magnitude of an equilibrium constant can tell us about the relative concentrations of reactants and products in an equilibrium mixture. It is also useful to consider how the magnitude of any equilibrium constant depends on how the chemical equation is expressed. 

A prime requirement for all our calculations must be stressed at the start Solutions must be at equilibrium in order for calculations with equilibrium constants to be valid. This is obvious, but can cause great difficulty because chemical knowledge must be brought into play to decide whether a chemically stable solution is present. For example, how does one treat the acidity of a mixture which is made so that it will be 0.1 M in hydrochloric acid and 0.2 M in sodium hydroxide No such solution exists. One must know that these are strong electrolytes and that such high concentrations of H and OH react to form water. Thus, the mixture given turns into 0.1 M Na, Cl and 0.1 M Na, OH", that is, half the base is neutralized by the acid present. The approximate pH is 13. We do not follow the procedure of one canny student who replied that the pH of the 0.1 M acid is 1.0 and that of the 0.2 M base is 13.3, and thus the average is 7.15. 

Write an equationforthe reaction of chloroacetic acid (Ka = 1.5 X 103) with trimethylamine (Kj, = 5.9 X 10 5). Calculate die equilibrium constant for die reaction. If 0.10 M solutions of these two species are mixed, what will be their concentrations at equilibrium ... 

If the equilibrium constant is calculated with activity constants derived from Raoul s law instead of concentrations, then K is virtually independent of the water concentration.30 The reported values of AHa for hydrolytic polyamidation are in the order of 25-29 kJ mol-1.29 This means that on decreasing the temperature at a constant water concentration, the equilibrium molecular weight shifts to a higher value. 

In principle, the calculation of concentrations of species of a complexation equilibrium is no different from any other calculation involving equilibrium constant expressions. In practice, we have to consider multiple equilibria whenever a complex is present. This is because each ligand associates with the complex in a separate process with its own equilibrium expression. For instance, the silver-ammonia equilibrium is composed of two steps ... 

The equilibrium constant and dissociation rate constant were determined simultaneously by non-linear least-squares fitting, unless the absorption signal was too low157 or no dependence of relaxation frequency on concentration was observed.159,161,162 The association rate constant was then calculated from the definition of the equilibrium constant. The equilibrium constants determined from the dynamics in this manner agree fairly well with equilibrium constants determined independently. 

Experiments involving the Nernst equation are primarily concerned with concentrations. One or more of the concentrations in the Q portion of the Nernst equation are calculated by measuring the nonstandard cell potential and comparing this to the standard cell potential. Remember, you calculate the concentration from a measured voltage. Once the concentration is determined, it may be combined with other concentrations and used to calculate an equilibrium constant. 

The asymptote with the slope of -3 at high pA (i.e., low [A ]), fits Eq. (4.58), when Pm dominates the denominator (i.e., the aqueous phase), while the asymptote with slope of +1 fits the same equation when the aqueous phase is dominated by PmA). Between these two limiting slopes, the other three PmAg complexes are formed in varying concentrations. A detailed analysis of the curves yielded all equilibrium constants A), and K c (see section 4.14.3), which are plotted in Fig. 4.15. The curves in Fig. 4.14 have been calculated with these constants. K is defined by... 

The binding kinetics were characterized in terms of the apparent time constant (K pp = kf C + k ) where C = analyte concentration kf = association rate constant and k = dissociation rate constant. In closed loop experiments, a plateau value for K pp of 0.0024/s was reached at a linear flow rate of 2.67 mL/min. K ppWas foxmd to decrease with decreasing antigen concentration (C), with equilibrium achieved only at the highest level (1 pg/mL). The association rate constant Kf was calculated at 3.6 x 10 M/s for IgG binding. 

Phosphorus-31 NMR has been used to measure internal equilibrium constants within enzyme-substrate (ES) complexes.663 685 687 By having both substrate and product concentrations high enough to saturate the enzyme, all of the enzyme exists as ES and enzyme-product (EP) complexes in equilibrium with each other. For a phosphotransferase at least one substrate and one product contain phosphorus. Although the NMR resonances are broadened by binding to the large, slowly tumbling protein, their areas can be measured satisfactorily and can be used to calculate an equilibrium constant such as that for Eq. 12-32 ... 

Haber started one experiment with a mixture consisting of 0.500 molT-1 N2 and 0.800 mol-L 1 H2 and allowed it to reach equilibrium with the product, ammonia. At equilibrium at a certain temperature, the concentration of NH3 was 0.150 mol-L-1. Calculate the equilibrium constant Kc, for the reaction at that temperature. 

A 0.100M KI solution (0.100M I-) actually dissolves 12.5 g iodine per liter, most of which is converted to I. (a) Assuming that the concentration of I2 in all saturated solutions is the same, calculate the equilibrium constant for the above reaction with 1 molar solutions as standard states, (b) What is the effect of adding water to a saturated solution of I2 in the KI solution ... 

Within the range of the study, the ratio of impregnation R varies linearly with the concentration of aTA in the ethanolic solution It is then possible to calculate the equilibrium constant K defined by K = R/C. 

Using Eqs. (4), (5), and (6) and the results of runs 4 to 6, calculate the equilibrium concentrations of Ij, I3, and in each of the aqueous solutions. In each case use the appropriate value of k as read from the smooth curve of k versus (l2)cci,- Calculate the equilibrium constant for each run. If any variation of /q. with concentration is found, do... 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

When more than one conjugate add-base pair is in equilibrium with water, the exact mathematical relations for calculation of [H" "] become complex, especially if a single equation is to represent all possible initial conditions. The derivation of such equations can clarify the nature of approximations made in practical applications. In many cases, however, simplification may be achieved at the outset by using approximate calculations to estimate the concentrations of the major species concerned and then testing the validity of the approximations. If the concentration levels or equilibrium constants for a system are so unusual that the simple equations are not valid, exact equations can be used. " ... 

The results calculated are in reasonable agreement with the seawater speciation data from Turner et al. (1981) quoted in Table 6.5 and with the qualitative features of the Garrels and Thompson model. Of course, the selection of different suites of stability constants leads to somewhat different speciation pictures. For example, the calculations made by Garrels and Thompson, Dickson et al., and in Tableau 6.6 are based on the assumption that chloride complexes with the major cations are unimportant. This assumption may be wrong and ion pairs with CP may represent nonnegligible fractions of the major cation concentration. Then, of course, a different speciation picture would result however, the extension of these results to trace metals (see the column for seawater in Table 6.5) would require a reinterpretation of the original experimental coordination data with equilibrium constants with the CP ion pairing model. 

Strictly speaking, the letters in brackets represent activities, but we will usually follow the practice of substituting molar concentrations for activities in most calculations. Thus, if some participating species A is a solute, [A] is the concentration of A in moles per liter. If A is a gas, [A] in Equation 18-12 is replaced by p, the partial pressure of A in atmospheres. If A is a pure liquid, a pure solid, or the solvent, its activity is unity, and no term for A is included in the equation. The rationale for these assumptions is the same as that de.scribed in Section 9B-2, which deals with equilibrium-constant expressions. 

We have used the subscript eq to emphasize that the concentrations in the equilibrium constant expression are those at equilibrium. For the remainder of this text, we shall omit these subscripts, remembering that calculations with K,. values always involve equilibrium values of concentrations. 

Rather than attempting to allow for the concentration dependence of activity coefficients of ions M" " " and when we calculate an equilibrium constant K, we can vary and [X ] with constant activity coefficients... 

The equilibrium constants Kf are not measurable and we must resort to statistical thermodynamics to estimate these values theoretically. The partition function (Q) is a quantity with no simple physical significance but it may be substituted for concentrations in the calculation of equilibrium constants (Eqns. 4 and 5) [5], (It is assumed that there is no isotopic substitution in B.) Partition functions may be expressed as the product of contributions to the total energy from translational, rotational and vibrational motion (Eqn. 6). 

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