Solving Equilibrium Problems

The capacity to solve problems by analogy In the final questiomiaire, the students showed themselves able to apply their understanding of chemical equilibrium to a novel context. 

With multiple rate controlling steps, a steady state is postulated, that is, all rates are equated to the overall rate. Equations for the individual steps are formulated in terms of variables such as interfacial concentrations and various coverages of the catalyst surface. Any such variables that are not measurable are eliminated in terms of measurable partial pressures and the rate, as well as various constants to be evaluated from the data. The solved problems deal with several cases for instance, P6.03.04 has two participants not in adsorptive equilibrium and P6.06.17 treats a process with five steps. 

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. 

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. 

If you already use a spreadsheet, you can skip this section. The computer spreadsheet is an essential tool for manipulating quantitative information. In analytical chemistry, spreadsheets can help us with calibration curves, statistical analysis, titration curves, and equilibrium problems. Spreadsheets allow us to conduct what if experiments such as investigating the effect of a stronger acid or a different ionic strength on a titration curve. We use Microsoft Excel in this book as a tool for solving problems in analytical chemistry. Although you can skip over spreadsheets with no loss of continuity, spreadsheets will enrich your understanding of chemistry and provide a valuable tool for use outside this course. 

Below are given some simple examples to illustrate the use of the above concepts in solving equilibrium speciation problems. To keep things relatively simple no... 

In the case of polyprotic acids, K is often so much greater than K2 that only the equilibrium need be considered to calculate [H+] in a solution of the acid. Examples where this assumption may and may not be made will be given in specific Solved Problems with the reasoning included. 

Boston, J. F. Fournier, R. L., "A Quasi-Newton Algorithm for Solving Multiphase Equilibrium Flash Problems", Paper presented at Miami AIChE Meeting, November 1978. 

Solving problems when not all equilibrium concentrations are known... 

SOLVING PROBLEMS WHEN NOT ALL EQUILIBRIUM CONCENTRATIONS ARE KNOWN... 

The correct answer is (C). When solving problems that require the equilibrium constant, you need to use the Nernst equation ... 

We place 10.0 grams of SbCl5 in a 5.00-liter container at 448°C and allow the reaction to attain equilibrium. How many grams of SbCl5 are present at equilibrium Solve this problem (a) using and molar concentrations and (b) using Kp and partial pressures. 

The Reaction Quotient Solving Problems When Not All Equilibrium Concentrations Are Known... 

We have only discussed two of the sixteen fields given in the figure, the prediction of the direction in which a reaction can proceed spontaneously by means of the chemical potential and the temperature and pressure dependence of p and its application. A next step would be to go over to mass action, i.e., the concentration dependence of p. This leads directly to the deduction of the mass action law, calculation of equilibrium constants, solubilities, and many other data. An expansion of the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc., is easily possible. Furthermore, the same tools allow solving problems even at the atomic and molecular level that are usually treated by quantum statistical methods. 

Solved Problem 12.3 What effect would a decrease in volume have on the following system at equilibrium at 500 °C ... 

Solved Problem 13.1 Write an equilibrium equation for the reaction of NHg and H2O. Indicate the conjugate acids and bases. 

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... 

An alternative to representing liquid-liquid equilibrium data on triangular diagrams is to use rectilinear coordinates. This method is particularly convenient for applying analytical methods for solving problems and considering options in liquid-liquid extraction applications. 

Solve Problem 11.6 graphically, based on the given equilibrium data. 

Several programs have been written specifically for a very restricted class of equilibrium only problems. The Pit Method of Sillen and Warnquist has been widely used to solve for equilibrium constants in inorganic systems that have one or more simultaneous reversible reactions. DeLand uses goal-seeking routines to facilitate the matching of data, but free energy data for all reactants is required. Bos and Meershoek 24) have written a PL/1 program which uses the Newton-Raphson iteration to compute equilibrium constants in complex systems. 

In this form, the Kremser equation is useful for solving problems where N is fixed and an exit composition needs to be calculated. When equilibrium is closely approached (yi yD Equation (3.49) becomes... 

Niaz, M. Response to contradiction Conflict resolution strategies used by students in solving problems of chemical equilibrium. Journal of Science Education and Technology 10(2001), 205... 

The importance of adsorption equilibrium cannot be overstated, since it is often the constraint that has the greatest impact on adsorption applications. In fact, to address most adsorption applications (whether to design a process, to debottleneck an existing process, or even to solve problems in which adsorption is peripherally related), it is necessary to obtain equilibrium data, as described in Section 14.3.2, and then put it into a useful form—usually as a correlation, as described in Sections 14.3.3 and 14.3.4. This section first clarifies what is meant by equilibrium data and heats of adsorption. 

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. 

S. Brewer, Solving Problems in Analytical Chemistry. New York Wiley, 1980. Describes iterative approach for solving equilibrium calculations. 

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. ... 

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