Stoichiometric calculations equilibrium problems

These relationships provide complete stoichiometric information regarding the equilibrium. Just as amounts tables are usetiil in doing stoichiometric calculations, a concentration table that provides initial concentrations, changes in concentrations, and equilibrium concentrations is an excellent way to organize Step 5 of the problem-solving... 

The best approach to this problem involves two distinct steps (1) assume the reaction goes to completion and carry out the stoichiometric calculations -then (2) carry out the equilibrium calculations. 

Do the problem in two parts. First, you assume that the H30 ion from the strong acid and the conjugate base from the buffer react completely. This is a stoichiometric calculation. Actually, the HgO ion and the base from the buffer reach equilibrium just before complete reaction. So you now solve the equilibrium problem using concentrations from the stoichiometric calculation. Because these concentrations are not far from equilibrium, you can use the usual simplifying assumption about x. 

Because acetic acid is a weak add, you can assume as a first approximation that the reaction goes to completion. This part of the problem is simply a stoichiometric calculation. Then you assume that the acetic add ionizes slightly. This part of the problem involves an acid-ionization equilibrium. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

In some problems, concentrations at equilibrium are provided, hi other problems concentrations at equilibrium must be calculated, usually by using amounts tables (see Chapter In this example, we are told that a solution of LiF at chemical equilibrium has [F ]gg =6.16x 10 M. The stoichiometric ratio of LiF is 1 1, so an equal amount of Li dissolves [Li+]gg = 6.16 X 10 M. 

When several reactions occur simultaneously a degree of advancement is associated with each stoichiometric equation. Problem P4.01.26 is a application of this point. Some processes, for instance cracking of petroleum fractions, involve many substances. Then a correct number of independent stoichiometric equations must be formulated before equilibrium can be calculated. Another technique is to apply the principle that equilibrium is at a minimum of Gibbs free energy. This problem, however, is beyond the scope of this book. 

In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log h2o with pATR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant AR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pA,s of protonated alcohols240 (e.g. pAa = -2.05 for CthOHi1") for the required corrections to be made readily. 

Kinetic results which apparently do not fit the above treatment of the primary salt effect do so when the observed rates are correlated with the actual ionic strengths rather than the stoichiometric values. The actual concentrations in the reaction solution are calculated using the known value of the equilibrium constant describing the ion pair. This is discussed in Problem 7.5. 

The second problem with this program has been discussed in Section 7.3 it is the fact that when h2o is a reactant the stoichiometric number matrix v is inconsistent with the conservation matrix A because [h2o] is not included in the expression for the apparent equilibrium constant. A second program equcalcrx was developed (4) to solve these problems. This program takes advantage of the fact that a basis for the conservation matrix can be calculated from the stoichiometric number matrix for the system. 

Note that we solved this problem by first performing a stoichiometric (limiting reactant) calculation and then an equilibrium calculation. A similar strategy works if a strong base such as OH is added instead of a strong acid. The base reacts with formic acid to produce formate ions. Adding 0.10 mol of OH to the HCOOH/HCOO buffer of Example 15.7 increases the pH only to 3.58. In the absence of the buffer system, the same base would raise the pH to 13.00. 

The principle of microscopic reversibility allows one to express the backward rate constant in terms of the forward rate constant divided by Kp, which is the equilibrium constant based on gas-phase partial pressures. Kp has units of pressure to the power 5, where 5 is the sum of the stoichiometric coefficients (i.e., 8 = —2 for this problem). Handbook values for standard-state free energies of formation at 298 K are used to calculate the Gibbs free-energy change for reaction at 298 K (i.e., 29s) thi to calculate a dimensionless... 

A common problem is to calculate the composition of a reacting mixture at equilibrium at a specified temperature. To do this, it is always easier if we start with the stoichiometric table of the reaction. The first step is to express all the concentrations in terms of the extent of reaction, . We then calculate the activity of each species and finally, we equate the product of activities to the equilibrium constant. This produces an equation where the only unknown is Once the extent of reaction is known, all the mole fractions can be computed from the stoichiometric table. If the temperature of the calculation is at 25 C, the equilibrium constant is obtained directly from tabulated values of the standard Gibbs free energy of formation. To calculate the equilibrium constant at another temperature, an additional step is needed to obtain the heat of reaction and the Gibbs energy at the desired temperature. This procedure is demonstrated with examples below. 

To calculate how the pH of a buffer solution changes when small amounts of a strong acid or base are added, we must first use stoichiometric principles to establish how much of one buffer component is consumed and how much of the other component is produced. Then the new concentrations of weak acid (or weak base) and its salt can be used to calculate the pH of the buffer solution. Essentially, this problem is solved in two steps. First, we assume that the neutralization reaction proceeds to completion and determine new stoichiometric concentrations. Then these new stoichiometric concentrations are substituted into the equilibrium constant expression and the expression is solved for [H30 ], which is converted to pH. This method is applied in Example 17-6 and illustrated in Figure 17-6. 

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