Chemical equations determining equilibrium

Analyze We are asked to write the equilibrium-constant expression for a reaction and to determine the value of given the chemical equation and equilibrium constant for the reverse reaction. 

We recall that all sodium salts are soluble and that all soluble ionic salts are completely dissociated in H2O. We recognize that both NaCHsCOO and NaCN are salts of strong bases (which provide the cation) and weak acids (which provide the anion). The anions in such salts hydrolyze to give basic solutions. In the preceding text we determined that for CH3COO = 5.6 X 10" , and in Example 18-19 we determined that K, for CN" = 2.5 X 10 . As we have done before, we first write the appropriate chemical equation and equilibrium constant expression. Then we complete the reaction siunmary, substitute the algebraic representations of equilibriiun concentrations into the equilibrium constant expression, and solve for the desired concentration(s). 

STRATEGY First, we write the chemical equation for the equilibrium and the expression for the solubility product. To evaluate Ksp, we need to know the molarity of each type of ion formed by the salt. We determine the molarities from the molar solubility, the chemical equation for the equilibrium, and the stoichiometric relations between the species. We assume complete dissociation. 

To determine the equilibrium concentrations of all the reactants and products, we must deduce the changes that have occurred. We can assume by the wording of the problem that no C or D was added by the chemist, that some A and B have been used up, and that some D has also been produced. It is perhaps easiest to tabulate the various concentrations. We will use the chemical equation as our table headings, and enter the values that we know now ... 

The first step in the analysis is to determine if the chemical equations A to C are independent by applying the test described above. When one does this one finds that only two of the reactions are independent. We will choose the first two for use in subsequent calculations. Let the variables a and B represent the equilibrium degrees of advancement of reactions A and B, respectively. A mole table indicating the mole numbers of the various species present at equilibrium may be prepared using the following form of equation 1.1.6. 

Conveniently, perhaps even miraculously, the equations developed in Chapter 5 to accomplish basis swaps can be used to balance chemical reactions automatically. Once the equations have been coded into a computer program, there is no need to balance reactions, compute equilibrium constants, or even determine equilibrium equations by hand. Instead, these procedures can be performed quickly and reliably on a small computer. 

We know the initial concentration of NH3 in the buffer solution and can use the pH to find the equilibrium [OH ]. The rest of the solution is organized around the balanced chemical equation. Our first goal is to determine the initial concentration of NH/. 

Because the reaction involves a colour change, you can determine the concentration of Fe(SCN) (aq) by measuring the intensity of the colour. You will find out how to do this in Investigation 7-A. For now, assume that it can be done. From the measurements of colour intensity, you can calculate the equilibrium concentration of Fe(SCN) (aq). Then, knowing the initial concentration of each solution, you can calculate the equilibrium concentration of each ion using the chemical equation. 

Both ways of writing a metabolic reaction have value in biochemistry. Chemical equations are needed when we want to account for all atoms and charges in a reaction, as when we are considering the mechanism of a chemical reaction. Biochemical equations are used to determine in which direction a reaction will proceed spontaneously, given a specified pH and [Mg24], or to calculate the equilibrium constant of such a reaction. 

The integration of Equation (11.22) to determine the equilibrium constant as a function of the temperature or to determine its value at one temperature with the knowledge of its value at another temperature is very similar to the integration of the Clausius-Clapeyron equation as discussed in Section 10.2. The quantity AHB must be known as a function of the temperature. This in turn may be determined from the change in the heat capacity for the change of state represented by the balanced chemical equation with the condition that all substances involved are in their standard states. 

Sanderson and Chien (18) solve Equations (7), (8), and (13) to determine compositions of vapor and liquid phases in chemical and phase equilibrium given temperature and pressure. A set of independent chemical reactions is selected with guesses for extent of reaction. Solution of Equation (13) leads to compositions in phase equilibrium, but applies only for a vapor and liquid in equilibrium. Residuals of Equations (7) and (8) are computed and extents of reaction, g, and moles of species j, n, are adjusted using Marquardt s method (15). 

Occasionally, not all equilibrium concentrations are known. When this occurs you must use equilibrium concepts and stoichiometry concepts to determine K. What you are trying to do in these problems is determine the amounts of materials at equilibrium. In Chapter 12, you learned that the balanced chemical equation shows you the relative amounts of reactants and products during the chemical reaction. For a reaction at equilibrium, the logic is the same. The mole ratios still apply. There is one major difference, however, between the stoichiometry... 

Duhem s theorem states that, for any closed system formed initially given masses of particular chemical species, the equilibrium state is compl determined (extensive as well as intensive properties) by specification of any independent variables. This theorem was developed in Sec. 12.2 for nonrea systems. It was shown there that the difference between the number of indepet] variables that completely determine the state of the system and the number independent equations that can be written connecting these variables is... 

A thermodynamic quantity of considerable importance in many combustion problems is the adiabatic flame temperature. If a given combustible mixture (a closed system) at a specified initial T and p is allowed to approach chemical equilibrium by means of an isobaric, adiabatic process, then the final temperature attained by the system is the adiabatic flame temperature T. Clearly depends on the pressure, the initial temperature and the initial composition of the system. The equations governing the process are p = constant (isobaric), H = constant (adiabatic, isobaric) and the atom-conservation equations combining these with the chemical-equilibrium equations (at p, T ) determines all final conditions (and therefore, in particular, Tj). Detailed procedures for solving the governing equations to obtain Tj> are described in [17], [19], [27], and [30], for example. Essentially, a value of Tf is assumed, the atom-conservation equations and equilibrium equations are solved as indicated at the end of Section A.3, the final enthalpy is computed and compared with the initial enthalpy, and the entire process is repeated for other values of until the initial and final enthalpies agree. 

Comments. At equilibrium no changes in properties occur with time either in the system or in its surroundings. However, under steady state conditions inputs and outputs of the system remain in balance so that the properties of the system are not altered, but changes do occur in the surroundings as a result of such processes. A more scientific characterization is provided in Chapter 6. Number of Independent Components. The least number of chemically distinct species whose mole numbers must be specified to prepare a particular phase. Comments. Due account must be taken of any prevailing chemical equilibria since in such cases the concentrations of the various participating species cannot all be independently altered. The number of independent components may then be determined from the number of distinct chemical compounds present in the system minus the number of chemical equations that specify their interactions. This matter is taken up in Section 2.1. 

Note that even though K is a constant in Eqs. (3.18) and (3.19), the individual activities of D, E, B, and C can vary. The major advantage of these equations is that the K for any balanced chemical reaction can he directly calculated from AG , which in turn can be determined by plugging AG values from thermodynamic tables into Eq. (3.14). In a chemical system at equilibrium the individual activities of reactants and products are closely constrained hy this equation. 

In Examples 18-8 and 18-9 the value of an equilibrium concentration was used to determine the change in concentration. You should become proficient at using a variety of data to determine values that are related via a chemical equation. Let s review what we did in Example 18-9. Only the equilibrium expression, initial concentrations, and the equilibrium concentration of H3O+ were known when we started the reaction summary. The following steps show how we filled in the remaining values in the order indicated by the numbered red arrows. 

In a chemical processing plant, the acetone concentration in a water-acetone solution stream must be lowered. Acetone extraction using vinyl trichloride (VTC) as the solvent is considered, and the required number of equilibrium stages in a countercurrent liquid-liquid extraction system must be determined. Equilibrium relations were developed based on available data at the expected operating conditions. The extract and raffinate phase and tie-line equations are expressed in terms of the extract component (acetone) and raffinate component (water) weight fractions in each phase. 

Further we looked at galvanic cells where it was possible to extract electrical energy from chemical reactions. We looked into cell potentials and standard reduction potentials which are both central and necessary for the electrochemical calculations. We also looked at concentration dependence of cell potentials and introduced the Nemst-equation stating the combination of the reaction fraction and cell potentials. The use of the Nemst equation was presented through examples where er also saw how the equation may be used to determine equilibrium constants. 

As noted earlier, the exponents n, n, and n" are experimentally determined. However, for elementary, single-step reactions, the exponents in the rate expression are numerically equal to the coefficients in the balanced chemical equation. Consequently, for this situation, and all other equilibrium situations that we shall encounter in this book, we shall assume that the exponents in the rate expressions are equal to the coefficients in the balanced chemical equation. Hence,... 

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