Question

During exercise when the body lacks an adequate supply of oxygen to support energy production, the pyruvate that is produced from the breakdown of glucose is converted into lactate. High lactate levels can lead to acidity in the muscle cells as some of the lactate hydrolyzes to lactic acid. 

The dissociation of lactic acid to lactate is shown in the reaction below. Lactic acid has a pKa of 3.86.

 A solution containing a mixture of lactic acid and lactate was found to have a pH of 3.56. Calculate the ratio of the lactate concentration to the lactic acid concentration in this solution.

 What fraction of the lactic acid/lactate mixture is lactic acid?

Answer 1

\(\mathrm{pH}\) of buffered solution is \(3.56\)

\(\mathrm{pK}_{\mathrm{a}}\) of lactic acid is \(3.86\) According to the Henderson - hasselbach equation is as follows:

\(\mathrm{pH}=\mathrm{pK}_{\mathrm{a}}+\log \frac{[\text { lactate }]}{[\text { lactic acid }]}\)

\(3.56=3.86+\log \frac{[\text { lactate }]}{[\text { lactic acid }]}\)

\(\log \frac{[\text { lactate }]}{\text { [lactic acid }]}=3.56-3.86\)

\(=-0.3\)

\(\frac{[\text { lactate }]}{[\text { lactic acid }]}=10^{-0.3}\)

\(=0.501\)

Hence, the ratio of \(\frac{[\text { lactate }]}{[\text { lactic acid }]}\) is \(0.501\)

Calculate the fraction of lactic acid is as follows:

\(\frac{[\text { lactate }]}{[\text { lactic acid }]}+1=1+0.501\)

\(\frac{[\text { lactate }]+[\text { lactic acid }]}{[\text { lactic acid }]}=1.501\) \(\frac{[\text { lactic acid }]}{[\text { lactate }]+[\text { lactic acid }]}=0.666\)

hence, the fraction of lactic acid is \(0.666\)