Q.2-2-12P - Organic Chemistry (Mcmurry)

Question

Question: The amino acid phenylalanine has pK_a=1.83 , and tryptophan has pK_a=1.83 Which is the stronger acid?

                                  

Step-by-Step Solution

Answer

Answer

A stronger acid has a smaller pK_a  and a weaker acid has a larger pK_a  . Accordingly, phenylalanine (pK_a=1.83 ) is a stronger acid than tryptophan (pK_a=2.83) .

Step 1: Acid and base strength

Acids differ in their ability to donate H⁺. Stronger acids, such as HCl, react almost completely with water, whereas weaker acids, such as acetic acid (CH₃COOH), react only slightly. The exact strength of a given acid, HA in water solution is described using the acidity constant (K_a) for the acid-dissociation equilibrium.

Example:

                                                          $$\begin{gathered} {\text{HA + H}}_{2}O\rightleftarrows A^{-} + H3O \\ {K}_a=\frac{\left[H3O^{+ }\right] \left[A^{-}\right]}{\left[HA\right]} \end{gathered}$$

Acid strengths normally uses pK_a  values rather than K_a  values, where the pK_a  is the negative common logarithm of K_a :

pK_{a =log Ka} 

Step 2: Determine stronger acid between phenylalanine and tryptophan

A stronger acid has a smaller pK_a and a weaker acid has a larger pK_a  . Accordingly, phenylalanine (pK_a =1.83) is a stronger acid than tryptophan (pK_a =2.83). It is because the acid must be stronger in aqueous solution than a hydronium ion, therefore, the stronger acids have a smaller value of pK_a  .

Phenylalanine (pK_a =1.83)        Tryptophan (pK_a =2.83)