Exact Treatment of Buffered Solutions

Note that the addition of HC1 only slightly decreases the pH (from 9.05 to 8.73), as we would expect in a buffered solution. 

We can now summarize the most important characteristics of buffered solutions. 

Because buffered solutions can have a pH value of 7, the question naturally arises about the possible importance of water as a contributor to the [H+] under these conditions. To derive a general equation for buffered solutions that includes any possible contribution from water, we will use the approach developed in Section 7.9. 

In an aqueous buffered solution containing the weak acid HA and its salt NaA, the equilibria of interest are 

we can substitute into the Ka expression for HA using the expressions for [A-] and [HA] obtained above  

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Unless conditions require the use of the exact solution, approximate equations are preferable because they are easier to apply and provide greater physical insight. If a calculation (ignoring water autoionization) of the ionization of a weak acid gives a concentration of H30 smaller than 10 M or if a calculation of base ionization gives a concentration of OH smaller than M, then we have to use the more exact treatment. For buffer solutions, a pH near 7 does not necessarily mean that water ionization is important, unless the acid or base concentration becomes very small. 

In Section 8.3, an equation was derived for the exact treatment of HA/NaA-type buffers. What would be the expression for B/BHCl-type buffers stated in terms of Kb, [OH-], [B], and [BH+] Would it be necessary to use this exact expression to solve for the pH of a solution containing 1.0 x 10-4 M HONH2 and 1.0 x 10 5 M HONH3CI Explain. 

A very simple type of a bubble column, which was not mentioned above is a gas-wash bottle. This very small-scale system (VL = 0.2-1.0 L) may be used for basic studies, in which general effects (e. g. influence of pH and/or buffer solutions specific ozone dose) are to be assessed. Its use is not recommended for detailed studies, because the mass-transfer coefficient is often low and its dependency on the gas flow rate is unknown or difficult to measure. Often there is no possibility to insert sensors or establish a reliable measuring system for exact balancing of the ozone consumption. An optimal mode of operation would comprise treatment of the (waste-)water for a certain period of time, preferably without withdrawal of solution during the ozonation. In this way different ozonation conditions can be tested by varying the ozonation time or the ozone gas concentration. A variation of the gas flow rate is not recommended. 

Sections 15.4 and 15.5 outline methods for calculating equilibria involving weak acids, bases, and buffer solutions. There we assume that the amount of hydronium ion (or hydroxide ion) resulting from the ionization of water can be neglected in comparison with that produced by the ionization of dissolved acids or bases. In this section, we replace that approximation by a treatment of acid-base equilibria that is exact, within the limits of the mass-action law. This approach leads to somewhat more complicated equations, but it serves several purposes. It has great practical importance in cases in which the previous approximations no longer hold, such as very weak acids or bases or very dilute solutions. It includes as special cases the various aspects of acid-base equilibrium considered earlier. Finally, it provides a foundation for treating amphoteric equilibrium later in this section. 

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