Equilibrium solving problems involving

In this section, you compared strong and weak acids and bases using your understanding of chemical equilibrium, and you solved problems involving their concentrations and pH. Then you considered the effect on pH of buffer solutions solutions that contain a mixture of acid ions and base ions. In the next section, you will compare pH changes that occur when solutions of acids and bases with different strengths react together. 

To solve equations of state, you must solve algebraic equations as described in this chapter. Later chapters cover other topics governed by algebraic equations, such as phase equilibrium, chemical reaction equilibrium, and processes with recycle streams. This chapter introduces the ideal gas equation of state, then describes how computer programs such as Excel , MATLAB , and Aspen Plus use modified equations of state to easily and accurately solve problems involving gaseous mixtures. 

This chapter shows how to solve problems involving chemical reaction equihbrium. The chemical reaction equilibrium gives the upper limit for the conversion, so knowing the equilibrium conversion is the first step in analyzing a process. The second question, what the rate of reaction is, can then be answered to decide the volume of the reactor. This second question, using kinetics, is treated in Chapter 8. Chemical reaction equilibrium leads to one or more nonlinear algebraic equations which must be solved simultaneously, and such problems are described in this chapter. 

Skill 9.2 Solving problems involving equilibrium constants and reaction quotients... 

The calculation procedures [the 0 method, Kb method, and constant composition method] developed in Chap. 2 for conventional distillation columns are applied to complex distillation columns in Sec. 3-1. For solving problems involving systems of columns interconnected by recycle streams, a variation of the theta method, called the capital 0 method of convergence is presented in Secs. 3-2 and 3-3. For the case where the terminal flow rates are specified, the capital 0 method is used to pick a set of corrected component-flow rates which satisfy the component-material balances enclosing each column and the specified values of the terminal rates simultaneously. For the case where other specifications are made in lieu of the terminal rates, sets of corrected terminal rates which satisfy the material and energy balances enclosing each column as well as the equilibrium relationships of the terminal streams are found by use of the capital 0 method of convergence as described in Chap. 7. 

Equations 10.1-7 and 10.1-8, together with the equilibrium relations, can be used to solve problems involving partial vaporization and condensation processes at constant temperature. For partial vaporization and condensation processes that occur adiabatically, the final temperature of the vapor-liquid mixture is also unknown and must be found as part of the solution. This is done by including the energy balance among the equations to be solved. Since the isothermal partial vaporization or isothermal flash calculation is already tedious (see Illustration 10.1-4), the.adiabatic partial vaporization (or adiabatic flash) problem will not be considered here. ... 

Any of the five diagrams in Fig. 3,10 (or others) can be used for solving problems involving material balances subject to equilibrium constraints, as is demonstrated in the next three examples. 

Plan We will use essentially the same procedure here as used in solving problems involving the ionization of weak acids, that is, write the chemical equation and tabulate initial and equilibrium concentrations. 

Always understand the chemical equilibrium of a reaction before attempting to solve problems involving reaction kinetics. 

This is a quantitative calculation, so it is appropriate to use the seven-step problem-solving strategy. We are asked to determine an equilibrium constant from standard reduction potentials. Visualizing the problem involves breaking the redox reaction into its two half-reactions ... 

The Sample Problems that follow all involve homogeneous equilibrium systems. Each problem illustrates a particular type of system and includes brief tips. Each problem also includes a table like the one on page 339 to organize the data. Because this table is used to record the initial, change, and equilibrium values of the reacting species, it is often called an ICE table. In Chapters 8 and 9, you will use ICE tables again to help you solve problems that involve heterogeneous equilibrium systems. 

The specific enthalpies in the above equation can be determined as described earlier, provided the temperatures of the product streams are known. Evaporative cooling crystallizers (described more completely in Section V) operate at reduced pressure and may be considered adiabatic. In such circumstances, Eq. (9) is modified by setting Q = 0. As with many problems involving equilibrium relationships and mass and energy balances, trial-and-error computations are often involved in solving Eqs. (7) through (9). 

This problem illustrates all the important steps required for solving a typical equilibrium problem involving a weak acid. These steps are summarized below. 

Typical problems you may be asked to solve that involve the use of the equilibrium coefficient K, are ... 

If we wish to calculate the solubility of barium sulfate in a system containing hydronium and acetate ions, we must take into account not only the solubility equilibrium but also the other three equilibria. We find, however, that using four equilibrium-constant expressions to calculate solubility is much more difficult and complex than the simple procedure illustrated in Examples 9-4, 9-5, and 9-6. To solve this type of problem, the systematic approach described in Section llA is helpful. We then use this approach to illustrate the effect of pH and complex fonna-tion on the solubility of typical analytical precipitates. In later chapters, we use this same systematic method for solution of problems involving multiple equilibria of several types. 

The concept of eqnilibrinm constants is extremely important in chemistry. As you will soon see, equilibrinm constants are the key to solving a wide variety of stoichiometry problems involving eqnilibrium systems. For example, an industrial chemist who wants to maximize the yield of sulfuric acid, say, must have a clear understanding of the equilibrium constants for all the steps in the process, starting from the oxidation of sulfur and ending with the formation of the final product. A physician specializing in clinical cases of acid-base imbalance needs to know the equilibrium constants of weak acids and bases. And a knowledge of equilibrium constants of pertinent gas-phase reactions will help an atmospheric chemist better understand the process of ozone destraction in the stratosphere. 

To solve distillation problems involving multicomponent mixtures, vapor-liquid equilibrium data and enthalpy data are needed. The methods used to obtain these data may be classified as follows (1) the use of a single equation of state and (2) the use of multiple equations of state and/or correlations for the prediction of the liquid and vapor parts of the K values and the enthalpies. This classification was suggested by Adler et al.2 in an excellent paper on the industrial uses of equations of state. Although the first approach, the use of a single equation of state, is the more desirable, many industrial problems are encountered in which this approach is too inaccurate and the second approach is used. 

The second type of equilibrium problem involving weak acids gives some concentration data and the value and asks for the equilibrium concentration of some component. Such problems are very similar to those we solved in Chapter 17 in which a substance with a given initial concentration reacted to an unknown extent (see Sample Problems 17.6 to 17.8). 

Simultaneous Reactions, When two isothermal reactions take place simultaneously, the calculation is slightly more involved, but may be solved readily. The solution of this type of problem involves two unknowns. The procedure is to set up the equations involving the equilibrium constant for each reaction and to solve the simultaneous equations graphically. 

A typical equilibrium problem Involves finding the equilibrium concentrations (or pressures) of reactants and products, given the value of the equilibrium constant and the initial concentrations (or pressures). However, since such problems sometimes become complicated mathematically, we will develop useful strategies for solving them by considering cases for which we know one or more of the equilibrium concentrations (or pressures). 

The proton condition is a special type of mass balance equation on protons. It is an essential component of equilibrium problem solving if either or OH are involved in the equilibria. It is used in this section only to solve problems related to solutions made up in the laboratory. In later sections and chapters it is used to solve natural water problems. 

The unique exception to these generalised studies was conducted by BouJaoude (1993) with a sample of USA first year chemistry students. The main focus of his study was on students errors when solving chemical equilibrium problems. However, as the course followed a conventional approach to the teaching of chemical equilibrium, i.e. one in which chemical equilibrium is explained in terms of kinetics, the author had to include a problem involving chemical kinetics in his research instrument. The problem... 

Plan Solving this problem involves the two steps outlined in Figure 17.3. First we do a stoichiometry calculation to determine how the added OH affects the buffer composition. Then we use the resultant buffer composition and either the Henderson- Hasselbalch equation or the equilibrium-constant expression for the buffer to determine the pH. 

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