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

The concentration ratio of glutamate to glutamic acid in the acidic lumen of lemon fruit vacuoles favors the protonated form, glutamic acid, due to the pH being lower than the pKa of glutamic acid's side chain.

Step-by-step explanation:

The question deals with the acid-base equilibrium of glutamic acid in the acidic environment of a lemon fruit's vacuole, which has a pH of ~2.5. Since the pKa of the side chain of glutamic acid is 4.1, and the pH in the vacuole is significantly lower than the pKa, the protonated form (glutamic acid) is favored over the deprotonated form (glutamate). To calculate the concentration ratio of glutamate to glutamic acid, we use the Henderson-Hasselbalch equation: pH = pKa + log([glutamate]/[glutamic acid]), which allows us to solve for the ratio [glutamate]/[glutamic acid]. Since the pH is 2.5 and the pKa is 4.1, the equation becomes 2.5 = 4.1 + log([glutamate]/[glutamic acid]). Solving for the ratio gives us a negative value, which means the concentration of glutamic acid is much higher than that of glutamate.

Answer 2

Step-by-step 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 * 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 * 10^(-2)`.