Caprytic acid, also called octanoic acid, is an 8-carbon fatty acid that is used as a sanitizer on dairy equipment that comes in contact with milk.The acid has a molar mass of 144.21 g/mol. An aqueous solution of the sanitizer containing 12.25 g/L has a pH of 2.98. What is the acid-dissociation constant, Ka, for caprytic acid?

Question

Caprytic acid, also called octanoic acid, is an 8-carbon fatty acid that is used as a sanitizer on dairy equipment that comes in contact with milk.The acid has a molar mass of 144.21 g/mol. An aqueous solution of the sanitizer containing 12.25 g/L has a pH of 2.98. What is the acid-dissociation constant, Ka, for caprytic acid?

Answer 1

R HCA + H2O = CA- + H3O+

I 12.25/144.21 0 0
C. -x. +x +x
E. 0.0849-x x. x
Ka= x^2/ 0.0849-x
x= 10^-pH= 10^-2.98
Ka= 1.3 x 10^-5

Answer 2

To find the acid-dissociation constant (Ka) for caprytic acid, we need to use the given information about the molar mass, concentration, and pH of the aqueous solution.

First, let's find the concentration of the caprytic acid in moles per liter (mol/L) using the molar mass:

Concentration (C) = mass / molar mass

C = 12.25 g/L / 144.21 g/mol

C ≈ 0.0849 mol/L

Next, we need to determine the concentration of the dissociated form of the acid. Since caprytic acid is a monoprotic acid, it dissociates to form one hydrogen ion (H+) and one caprytate ion (C8H15O2-). The concentration of H+ can be determined from the pH of the solution:

[H+] = 10^(-pH)

[H+] = 10^(-2.98)

[H+] ≈ 1.07 x 10^(-3) mol/L

Now, we can set up the equation for the dissociation of caprytic acid:

C8H16O2 ⇌ H+ + C8H15O2-

The initial concentration of caprytic acid (C) is approximately 0.0849 mol/L. The change in concentration of caprytic acid and the concentration of H+ and C8H15O2- at equilibrium are not known.

We can assume that the change in concentration of caprytic acid is small compared to the initial concentration, so we can assume that (C - x) ≈ C, where x is the change in concentration.

Using the equation for the acid-dissociation constant (Ka) where Ka = [H+][C8H15O2-] / [C8H16O2], we can substitute the values we have:

Ka = (1.07 x 10^(-3))(1.07 x 10^(-3)) / (0.0849 - x)

Since x is assumed to be small, we can neglect it in comparison to the initial concentration:

Ka = (1.07 x 10^(-3))(1.07 x 10^(-3)) / 0.0849

Ka ≈ 1.15 x 10^(-5) mol/L

Therefore, the acid-dissociation constant (Ka) for caprylic acid is approximately 1.15 x 10^(-5) mol/L.