Acids & Bases Problem Set

Acids & Bases Problem Set

Question 11: pH and buffering capacity of a mixed solution

Tutorial to help answer the question

If equal volumes of 0.05 M NaH₂PO₄ and 0.05 M H₃PO₄ are mixed, which of the following best describes the resulting solution? (pK_a's for phosphoric acid are 2.0, 6.8 and 12.0)

A. pH 2 and poorly buffered.

B. pH 2 and well buffered.

C. pH 6.8 and well buffered.

D. pH 12 and well buffered.

E. pH 6.8 and poorly buffered.

Tutorial

Recognizing the appropriate protonated and deprotonated forms of an acid with multiple ionizations

Phosphoric acid undergoes three ionizations, hence it has three pK_a values (given as 2.0, 6.8 and 12.0 in the question). Phosphoric acid has great biological significance due to its role in DNA/RNA, energy molecules such as ATP, protein phosphorylation, etc; therefore, it is worthwhile to spend a moment examining its ionization reactions.

Imagine the starting form as being completely protonated. Intuitively, complete protonation should occur when the [H⁺] is very high, ie. at a low pH. Thus, at pH 1 or less, phosphoric acid exists as >90% H₃PO₄.

Now imagine adding NaOH to a solution of H₃PO₄ at pH 1. The OH^- ion combines with H⁺ to produce water, raising pH and leaving Na⁺ in solution. As the pH rises towards 2.0, however, what happens to the H₃PO₄? Since 2.0 is the first pK_a , the first proton will begin coming off. This has two consequences, one concerning the chemical form of the H₃PO₄ and the other concerning buffering.

The chemical form of the H₃PO₄

Concerning the chemical form of H₃PO₄ , after the first H⁺ has completely come off (which occurs when the pH has risen above 3 or so), we are left with H₂PO₄ ^-. But since Na⁺ is also left by this reaction (the OH^- and the H⁺ having combined to produce water), we can express the ions in solution as being Na⁺H₂PO₄ ^-, or just NaH₂PO₄ (also called monobasic sodium phosphate).

Thus, the first ionization is written as follows:

NaOH + H₃PO₄ H₂O + NaH₂PO₄ ; pK_a = 2.0

What is the equation for the second ionization?

What is the equation for the third ionization?

Buffering

As for the buffering part, one only needs to realize that, during the transition between pH 1.0 and 3.0, a lot of the H⁺ used to combine with OH^- comes from H₃PO₄. The protons do not come from water, and the relationship [H⁺] x [OH^-] = 10 ^- 14 still holds; therefore, the pH does not change much when NaOH is added during the 1-3 pH transition. This is not the case between, say pH 3.0 and 5.8, when addition of NaOH does not take H⁺ from phosphate, because there is no pK_a value for phosphate dissociation in this range (the second pK_a skips from 2.0 all the way up to 6.8). Thus, any H⁺ must come from water, and the pH changes rapidly in this range.

The concept of buffering can also be shown graphically, as seen below.

At or near their pK_a , both weak acids and weak bases will resist changes in pH, thus acting as buffers. As described above, this is due to their affinity for protons, which are the species that determine pH. Thus, a solution will resist pH change at values near its pK_a (see shaded area in figure above).

In this problem, the phosphoric acid solution will continue to resist pH changes as NaOH is added until nearly all of H₃PO₄ has been converted from to the H₂PO₄^- form. At pH values >> pK_a , the affinity of phosphoric acid for protons is not sufficient to bind H⁺ until the next pK_a is reached, and at pH values << pK_a , nearly all of the phosphoric acid has already bound H⁺ and is thus no longer available to bind additional H⁺. Therefore, phosphoric acid, like any other weak acid or base, is only effective as a buffer at pH values within one pH unit of its pK_a .

The Biology Project
The University of Arizona
January 6, 1999
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