Equilibrium problem-solving strategies

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 ... 

Thoroughly examine the Sample Exercises and the problem-solving strategies. The strategies summarize the approach taken in the text the Sample Exercises follow the strategies step-by-step. Schematics in Chapter 15 also illustrate the logical pathways to solving aqueous equilibrium problems. 

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. 

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). 

In addition to its generality, the form (7.1.48) is important because it leads to a computational strategy for analyzing phase-equilibrium situations. In that strategy, a phase-equilibrium problem is treated as a multivariable optimization in which the Ihs of (7.1.48) is the quantity to be minimized. An alternative strategy, in which the computational problem is to solve a set of coupled nonlinear algebraic equations, arises from the constraints on open-system processes developed in 7.2. 

As mentioned above, in solving equilibrium problems, both concentrations and activity coefficients of the substances participating in the equilibrium must be evaluated. Implicit in Equation 3-3 is the basis for a very important approach to the incorporation of activity coefficients in all equilibrium calculations. As will be discussed below, it will be possible to arrive at a sufficiently good value of the activity coefficient quotient, Q. in terms of a single experimental parameter, the ionic strength. Hence, a useful strategy for taking activities into account in equilibrium calculations consists of ... 

In a similar way, phase equilibrium problems can be solved with the Gibbs energy minimization technique. Some computational strategies are presented in [71-... 

PROBLEM STRATEGY This problem is the reverse of the preceding ones instead of finding K p from the solubility, here you calculate solubility from the K p. You follow the three steps for equilibrium problems, but since the molar solubility is not hnmediately known, you assign it the value x. For Step 1, you obtain the concentration of each ion by multiplying x by the coefficient of the ion in the chemical equation. In Step 2, you obtain AT as a cubic in x. In Step 3, you solve the equilibrium-constant equation... 

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. 

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... 

Strategy According to Equation (18.14) of the text, the equilibrium constant for the reaction is related to the standard free energy change that is, AG° = -RT nK. Since we are given the equilibrium constant in the problem, we can solve for AG°. What temperature unit should be used ... 

The analysis of the remainder of the problem follows predictable lines and the second-best action strategy, which now represents an equilibrium profile, can be obtained using dynamic programming as before. If we let denote the optimal objective value for the optimization problem (4.27)-(4.30), then the second-best equilibrium action strategy can now be obtained by solving the following dynamic programming recursion ... 

The reliability of the phase equilibrium methods proposed must be estimated. According to the nature of the problem we were trying to solve, the Kohonen neural network was employed among several different neural networks as one with the most appropriate architecture and learning strategy. 

If co-crystals are to solve solubility problems one must assess their true or thermodynamic solubility so that development strategies are guided by the fundamental properties of co-crystals. Measuring the solubility of co-crystals that generate supersaturation of the parent drug is often experimentally impossible due to conversion. Eutectic points, described in Section 11.4, provide a measure of co-crystal solubility under thermodynamic equilibrium conditions. The solution at the eutectic point is saturated with co-crystal and solution concentrations represent experimentally accessible thermodynamic solubility values. Once co-crystal solubility is determined at the eutectic, the solubility under different solution conditions (pH, co-former, micelle concentration) can be obtained from solubility models that consider the appropriate solution phase equilibrium expressions. 

PROBLEM STRATEGY Substitute the standard emf into the equation relating this quantity to the thermodynamic equilibrium constant, K. Solve for K. Note that K = K. ... 

Strategy Using the procedure described in Sample Problem 16.12, we construct an equilibrium table and for each concentration of acetic acid, we solve for the equilibrium concentration of H. ... 

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