Discussion: The propensity of a compound to donate a proton is measured as its acid ionization constant, or K_a.  These K_a values cover a wide range of 10¹⁰ for the strongest acids such as sulfuric acid to 10^-50 for the weakest acids such as methane.  A more convenient scale of acidity is pK_a which is the negative logarithm of the K_a (pK_a = -log K_a).  Thus a K_a of 10¹⁰ becomes a pK_a of -10, and a K_a of 10^-50 becomes a pK_a of 50.  More generally, more negative pK_a values correspond to stronger acids and more positive pK_a values correspond to weaker acids.  The exact pK_a of an acid is a function of molecular structure (i.e., functional groups) and must be determined experimentally.  We know that similar functional groups react in similar ways, so we can estimate pK_a values by comparing the structure and functional groups of an unknown with the structure and functional groups of acids whose pK_a values are known.
 

Example 1: By comparison with the compounds in Table 2.1 (page 43) of the  Brown text (or Table 3.1, page 105 of Brown and Foote 2nd edition), estimate the pK_a of protons in red the following compounds.

a. CH₃CH₂CH₂CO₂H (butyric acid)   b. CH₃OH₂⁺ (an oxonium ion).
 

Solution 1:

a. Butyric acid is similar in structure to CH₃CO₂H (acetic acid), in that both are carboxylic acids.  The pK_a of acetic acid is 4.78.  Therefore we can estimate the pK_a of butyric acid to be approximately 4 - 5.

b. The closest structural match for the oxonium ion in the pK_a table is the hydronium ion (H₃O⁺), pKa -1.74.  Thus we can estimate the pK_a of CH₃OH₂⁺ to be approximately -2.
 

The pK_a table is also useful to estimate the position of a proton transfer equilibrium.  Such reactions are common in many aspects of chemistry and biology.  Any equilibrium favors the thermodynamically most stable side.  In the case of a proton transfer reaction, the equilibrium favors the side with the weakest acid and weakest base.  Because a stronger conjugate acid yields a weaker conjugate base, base strength can be determined from the pK_a table.
 

Example 2: Determine the position of the equilibrium shown below.

Solution 2: This is a proton transfer equilibrium, so the position can be determined using pK_a values.  The acids (proton donors) in this equilibrium are H₂CO₃ (carbonic acid, pK_a 6.36) and NH₄⁺ (ammonium ion, pK_a 9.24).  The ammonium ion has the higher pK_a than carbonic acid, and is therefore a weaker acid than carbonic acid.  To analyze relative basicity, we need to recall that lower pK_a corresponds to a stronger acid, and deprotonation of this stronger acid will give a weaker conjugate base.  The bases (proton acceptors) in this equilibrium are NH₃ (ammonia; conjugate acid NH₄⁺, pK_a 9.24) and HCO₃^- (bicarbonate ion; conjugate acid H₂CO₃, pK_a 6.36).  Because H₂CO₃ is a stronger acid than NH4+, we can deduce that HCO₃^- is a weaker base than NH₃.

Analysis of the relative acid and base strengths suggests that this equilibrium lies to the right.
 

Exercises:

Estimate the pK_a of the circled hydrogens.

d. Determine the most acidic hydrogen in the compound shown below.

Determine the position of each of the following equilibria.

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