Problem solving equilibrium problems

Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system s composition at equilibrium. When we need a more exact quantitative description of the equilibrium condition, a ladder diagram may not be sufficient. In this case we can find an algebraic solution. Perhaps you recall solving equilibrium problems in your earlier coursework in chemistry. In this section we will learn how to set up and solve equilibrium problems. We will start with a simple problem and work toward more complex ones. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

The solubility of a precipitate can be improved by adding a ligand capable of forming a soluble complex with one of the precipitate s ions. For example, the solubility of Agl increases in the presence of NH3 due to the formation of the soluble Ag(NH3)2°" complex. As a final illustration of the systematic approach to solving equilibrium problems, let us find the solubility of Agl in 0.10 M NH3. 

Example 12.4 illustrates a principle that you will find very useful in solving equilibrium problems throughout this (and later) chapters. As a system approaches equilibrium, changes in partial pressures of reactants and products—like changes in molar amounts—are related to one another through the coefficients of the balanced equation. 

Example 7.17 illustrates the utility of the reaction coordinate method for solving equilibrium problems. There are no more equations than there are independent chemical reactions. However, in practical problems such as atmospheric chemistry and combustion, the number of reactions is very large. A relatively complete description of high-temperature equilibria between oxygen and... 

The quantitative treatment of a reaction equilibrium usually involves one of two things. Either the equilibrium constant must be computed from a knowledge of concentrations, or equilibrium concentrations must be determined from a knowledge of initial conditions and Kgq. In this section, we describe the basic reasoning and techniques needed to solve equilibrium problems. Stoichiometry plays a major role in equilibrium calculations, so you may want to review the techniques described in Chapter 4, particularly Section 4- on limiting reactants. 

We consider each of these in more detail in subsequent chapters, but being able to identify types of equilibria helps greatly in solving equilibrium problems. The equilibrium constants for many of these characteristic types of equilibria have been measured and tabulated. Representative Za, K, and Kgp values appear in Appendix E, and tables that are more extensive can be found in the CRC Handbook of Chemistry and Physics. Example provides practice in identifying equilibria. 

C16-0040. Write a paragraph that describes the logic, process, and justification for using approximations in solving equilibrium problems. 

Those equilibrium processes that can be resolved explicitly are straightforwardly modelled in Excel. While it is possible to solve equilibrium problems of essentially any complexity in Excel, it is virtually impossible to develop a reasonable spreadsheet for the modelling of a complex titration. Iterative methods are generally difficult to implement in Excel. 

Solving Equilibrium Problems That Involve Acids and Bases... 

Ilk 6-8 Solving Equilibrium Problems with a Concentration Table and a Spreadsheet... 

We have already considered most of the strategies needed to solve equilibrium problems. The typical procedure for analyzing a chemical equilibrium problem can be summarized as shown below. 

We have seen that fairly complicated calculations are often necessary to solve equilibrium problems. However, under certain conditions, we can make simplifications that greatly reduce the mathematical difficulties. For example, consider gaseous NOCl, which decomposes to form the gases NO and Cl2. At 35°C the equilibrium constant is 1.6 X 10 5 mol/L. In an experiment in which 1.0 mole of NOCl is placed in a 2.0-liter flask, what are the equilibrium concentrations ... 

In the chapters so far we have considered the phase rule somewhat intuitively for example, in solving equilibrium problems we used the obvious principle that an equilibrium problem can be solved if for n unknowns (e.g., activities or concentrations of n species) n equations are available. For example, in a closed dissolved carbonate system we need to define the system (H2CO3, HC03 , CO H, OH ) and two concentration conditions (e.g., Ct and pH, or [Aik] and H2CO ]), in addition to temperature and pressure, because the five species are interconnected by three mass laws (two acid-base equilibria and the ion product of H2O). In the example given P = 1 (aqueous solution), C = 3 le.g., HCO, H", H20(l)], andF = 4 (pressure, temperature, and two concentration conditions). 

So far, we have learned that if we know the chemical equilibria involved in a system, we can write a corresponding system of equations that allows us to solve for the concentrations of all species in the system. Although the systematic method gives us the means to solve equilibrium problems of great complexity, it is sometimes tedious and time consuming, particularly when a system must be solved for various sets of experimental conditions. For example, if we wish to find the solubility of silver chloride as a function of the concentration of added chloride, the system of five equations and five unknowns must be solved repetitively for each different concentration of chloride (see Example 11-9). 

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