Equilibrium systematic treatment

The systematic treatment of equilibrium is a way to deal with all types of chemical equilibria, regardless of their complexity. After setting up general equations, we often introduce specific conditions or judicious approximations that allow simplification. Even simplified calculations are usually very tedious, so we make liberal use of spreadsheets for numerical... 

Now that we have considered the charge and mass balances, we are ready for the systematic treatment of equilibrium.10 Here is the general prescription ... 

The systematic treatment of equilibrium is best understood by studying some examples. 

Clearly, there is something wrong with our calculation. In particular, we have not considered the contribution of OH from the ionization of water. In pure water, [OH" ] = 1.0 X 10-7 M, which is greater than the amount of KOH added to the solution. To handle this problem, we resort to the systematic treatment of equilibrium. 

The problem is to find the pH of a solution of the weak acid HA, given the formal concentration of HA and the value of Ka.4 Let s call the formal concentration F and use the systematic treatment of equilibrium ... 

Strong acids or bases. For practical concentrations (a 10 6 M), pH or pOH can be found by inspection. When the concentration is near 10 7 M, we use the systematic treatment of equilibrium to calculate pH. At still lower concentrations, the pH is 7.00, set by autoprotolysis of the solvent. 

Systematic treatment of equilibrium. The acidity of Al3+ is determined by the following reactions. Write the equations needed to find the pH of A1(C104)3 at a formal concentration F. 

To treat this case, we resort to the systematic treatment of equilibrium. The procedure is applied to leucine, whose intermediate form (HL) has no net charge. However, the results apply to the intermediate form of any diprotic acid, regardless of its charge. 

This optional chapter provides tools to compute the concentrations of species in systems with many simultaneous equilibria.3 The most important tool is the systematic treatment of equilibrium from Chapter 8. The other tool is a spreadsheet for numerical solution of the equilibrium equations. We will also see how to incorporate activity coefficients into equilibrium calculations. Later chapters in this book do not depend on this chapter. 

SH Considering just acid-base chemistry, not ion pairing and not activity coefficients, use the systematic treatment of equilibrium to find the pH and concentrations of species in 1.00 L of solution containing 0.100 mol ethylenediamine and 0.035 mol HBr. Compare the pH with that found by the methods of Chapter 11. 

HH A solution containing 0.008 695 m KH2P04 and 0.030 43 m Na2HP04 is a primary standard buffer with a stated pH of 7.413 at 25°C. Calculate the pH of this solution by using the systematic treatment of equilibrium with activity coefficients from... 

Two chapters on activity coefficients and the systematic treatment of equilibrium from the sixth edition were condensed into Chapter 8. A new, advanced treatment of equilibrium appears in Chapter 13. This chapter, which requires spreadsheets, is going to be skipped in introductory courses but should be of value for advanced undergraduate or graduate work. New topics in the rest of this book include the acidity of metal ions in Chapter 6, a revised discussion of ion sizes and an example of experimental design in Chapter 8. pH of zero charge for colloids... 

The quantitative evaluation of the systematic relations that determine equilibrium concentrations (or activities) of a solution constitutes a purely mathematical problem, which is amenable to exact and systematic treatment. 

It would be of the greatest interest in the dynamics of organic synthesis if the very incomplete material in this field could be augmented by a rather more systematic treatment of several cis-trans-isomerisms and by equilibrium and velocity measurements. 

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