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Chapter 13 | Fundamental Equilibrium Concepts
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Setting up and solving the quadratic equation gives
Using the positive (physical) root, the equilibrium concentrations are
A less obvious way to solve the problem would be to assume all the HA ionizes first, then the system comes to equilibrium. This could be called the “all product” starting point. Assuming all of the HA ionizes gives
Using these as initial concentrations and “y” to represent the concentration of HA at equilibrium, this is the ICE table for this starting point.
Setting up and solving the quadratic equation gives
Retain a few extra significant figures to minimize rounding problems.
Rounding each solution to three significant figures gives
Using the physically significant root (0.140 M) gives the equilibrium concentrations as
Thus, the two approaches give the same results (to three decimal places), and show that both starting points lead to the same equilibrium conditions. The “all reactant” starting point resulted in a relatively small change (x) because the system was close to equilibrium, while the “all product” starting point had a relatively large change (y) that was nearly the size of the initial concentrations. It can be said that a system that starts “close” to equilibrium will require
