Systematic treatment of equilibrium

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 

The coefficient of each term in the charge balance equals the magnitude of the charge on each ion. 

The mass balance is a statement of the conservation of matter. It really refers to conservation of atoms, not to mass. 

The systematic procedure is to write as many independent algebraic equations as there are unknowns (species) in the problem. The equations are generated by writing all the chemical equilibrium conditions plus two more the balances of charge and of mass. There is only one charge balance in a given system, but there could be several mass balances. 

The charge balance is an algebraic statement of electroneutrality The sum of the positive charges in solution equals the sum of the negative charges in solution. 

Now that we have learned about the charge and mass balances, we are ready for the systematic treatment of equilibrium. The general prescription follows these steps  

Step 2. Write the charge balance equation. There is only one. 

Step 3. Write mass balance equations. There may be more than one. 

Step 4. Write the equilibrium constant for each chemical reaction. This step is the only one in which activity coefficients enter. 

Step 5. Count equations and unknowns. At this point, you should have as many equations as unknowns (chemical concentrations). If not, you must either find more equilibria or fix some concentrations at known values. 

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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... 

If Reaction 12-12 takes place, then the solubility of CaF2 is greater than that predicted by the solubility product because F produced in Reaction 12-11 is consumed in Reaction 12-12. According to Le Chatelier s principle, Reaction 12-11 will be driven to the right. The systematic treatment of equilibrium allows us to find the net effect of three reactions. 

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