Question

The normal \(\mathrm{pH}\) range for blood plasma is 7.35-7.45. Under these conditions, would you expect the carboxyl group of lactic acid ( \(\mathrm{p} K_{\mathrm{a}} 3.08\) ) to exist primarily as a carboxyl group or as a carboxylic anion? Explain.

Short answer

Under the normal pH range for blood plasma, the carboxylic acid group of lactic acid exists primarily as a carboxylate anion.

Step-by-step solution

Determine the given pH and pKa values

We are given the following information: - The normal pH range for blood plasma is 7.35 - 7.45. - pKa of the carboxyl group of lactic acid is 3.08.

Compare pH and pKa values

In this step, we compare the pH of the blood plasma with the pKa value of the carboxyl group of lactic acid: - The pH values of the blood plasma are higher than the pKa value (7.35 - 7.45 > 3.08). This information alone indicates that the carboxylic acid group will be mostly in the form of a carboxylate anion, as the pH of the environment is higher than the pH where the acid would be half-dissociated (equal amount of protonated and deprotonated species).

Use the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH, pKa, and the ratio of the concentrations of the deprotonated species (A-) to the protonated species (HA): pH = pKa + log10([A-] / [HA]) Here, we want to find the ratio of carboxylic anion ([A-]) to the carboxyl group ([HA]). We can rearrange the equation to solve for this ratio: [A-] / [HA] = 10^(pH - pKa)

Calculate the ratio of carboxylic anion to carboxyl group

Now, we will calculate the ratio of carboxylic anion to carboxyl group at both ends of the pH range for blood plasma (7.35 and 7.45): a. At pH 7.35: [A-] / [HA] = 10^(7.35 - 3.08) = 10^4.27 ≈ 18550 b. At pH 7.45: [A-] / [HA] = 10^(7.45 - 3.08) = 10^4.37 ≈ 23442

Conclusion

The ratio of carboxylic anion to carboxyl group is higher than 1 in both cases (18550 and 23442), which indicates that under the normal pH range for blood plasma (7.35 - 7.45), the carboxyl group of lactic acid will exist primarily as a carboxylic anion.