Question

The pKa of the side chain of glutamatic acid (an amino acid) is 4.1. glutamic acid ⇌ glutamate + H+ The pH in the lumen (inside) of the vacuole (a subcellular organelle typical of plant cells, which we will talk about later in the course) in cells of ripe lemon fruits is ~2.5. What is the concentration ratio of the deprotonated form (glutamate) of the side chain Glu vs the protonated form (glutamic acid) in the vacuolar lumen of lemon fruit cells? Group of answer choices

Answer 1

Explanation:

According to the Henderson Hasselbach equation,

           pH = $pK_{a} + log [\frac{\text{conjugate base}}{acid}]$

             pH = $pK_{a} + log [\frac{glutamate}{\text{glutamic acid}}]$

The given data is as follows.

         pH = 2.5

   $pK_{a}$ of side chain of glutamic acid = 4.1

Now, rearranging the equation as follows.

      $log [\frac{glutamate}{\text{glutamic acid}}]$ = $pH - pK_{a}$

         $log [\frac{glutamate}{\text{glutamic acid}}]$ = 2.5 - 4.1

                                      = -1.6

      $[\frac{glutamate}{\text{glutamic acid}}]$ = Antilog (-1.6)

                                   = 0.0251

or,                               = $2.5 \times 10^{-2}$

Thus, we can conclude that the concentration ratio of the deprotonated form (glutamate) of the side chain Glu vs the protonated form (glutamic acid) in the vacuolar lumen of lemon fruit cells is $2.5 \times 10^{-2}$.