A hygiene-challenged ground sloth who likes to hang out with a mammoth and a saber-toothed tiger eats a pound of lemons. This results in a total citrate concentration of 0.0062 M in his stomach. His stomach also contains HCl (0.10 M) and butyric acid (also known as butanoic C4H8O2 acid for all you IUPACers) at a concentration of 0.94 mM. Butyric acid is a monoprotic acid with a pKa of 4.818, while citric acid (C6H8O7) is a triprotic acid with pKa values of 3.128, 4.761, and 6.396. The sloth also ate some dirt with the lemons, which resulted in a magnesium chloride concentration in his stomach of 7.6 x 10-4 M.
A) Write a charge balance equation for everything in the sloth’s stomach.
B) Write a mass balance equation for the butyric acid in the sloth’s stomach.
C) Write a mass balance equation for the citric acid in the sloth’s stomach.
D) What is the concentration of singly deprotonated citric acid in the sloth’s stomach?
Given:
Total citrate concentration in the stomach = 0.0062 M
Citric acid (C6H8O7) pKa = 3.128, 4.761 and 6.396
The charge balance equation for everything in the sloth’s stomach are as follows:
Citric acid is a triprotic acid
C6H8O7 + H2O -----> C6H7O7- + H3O+ pKa = 3.128
C6H7O7- + H2O -----> C6H6O72- + H3O+ pKa = 4.761
C6H6O72- + H2O -----> C6H6O73- + H3O+ pKa = 4.761
Butyric acid is a monoprotic acid
C4H8O2 + H2O -----> C4H7O7- + H3O+ pKa = 4.818
pH= pKa + log (A-/HA)
The concentration of singly deprotonated citric acid is calculated as follows
C6H8O7 -----à C6H7O7- + H+ pKa = 3.128
Original 0.0062 0 0
Change -x +x +x
Equilibrium 0.0062-x x x
pKa = -log Ka
3.128 = -log Ka
Antilog 3.128 = - Ka
Ka = -1342.764 = 1.34 x 10-3
Ka = [C6H7O7-] [H+]/ [C6H8O7]
1.34 x 10-3 = x2/ 0.0062
Therefore x = 3.33 x 10-3 M
The concentration of singly depronated citric acid is 3.33 x 10-3 M
A hygiene-challenged ground sloth who likes to hang out with a mammoth and a saber-toothed tiger...