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?
48. Citric acid, C6H8O7(aq), is used to add a sour taste
to foods and soft drinks. It is prepared in a solution
with a concentration of 0.52 mol/L, and has a pH
of 1.72. Calculate the acid-dissociation constant for
citric acid. What percentage of citric acid molecules
ionizes in the solution?
49. Creatine is a naturally occurring organic acid that
helps supply energy to all cells in the body, with
particular emphasis on muscle cells. It has a molar
mass of 131 g/mol. An aqueous solution containing
2.68 g/L has a pH of 2.23. What percentage of
creatine molecules ionizes in the solution?
50. Uracil is one of the four nucleotide monomers that
make up the nucleic acid RNA. It was originally
isolated in 1900, by the hydrolysis of yeast nuclein
found in bovine thymus and spleen. Uracil has
a molar mass of 112 g/mol. A biologist prepares
a solution of the acid by dissolving 1.24 g of the
compound in 1.0 L of solution. The pH of the
solution is 5.71. Calculate the acid-dissociation
constant, Ka, for uracil.
Practice Problems
512 MHR
Solutions of acetic acid and hydrochloric acid of the same concentration are not equally acidic. Which of the two solutions has a lower pH? Why?
To calculate the acid-dissociation constant (Ka) for each of the given acids, we can use the pH of the solution and the concentration of the acid in solution. The Ka for a weak acid is given by the equation:
Ka = [H+][A-] / [HA]
Let's calculate Ka for each acid step-by-step:
48. Citric acid (C6H8O7):
- Concentration of citric acid = 0.52 mol/L
- pH of the solution = 1.72
To calculate Ka, we first need to determine the concentration of H+ ions in the solution. Since the pH is given, we can use the formula:
pH = -log[H+]
1.72 = -log[H+]
[H+] = 10^(-1.72)
Next, we calculate the concentration of A- ions. Since citric acid has three ionizable hydrogen atoms, the concentration of A- ions will be three times the concentration of H+ ions.
[H+] = 10^(-1.72) mol/L
[A-] = 3[H+] = 3 * 10^(-1.72) mol/L
Finally, we calculate the concentration of the undissociated acid (HA) using the concentration of the acid solution:
[HA] = concentration of acid solution = 0.52 mol/L
Now we can substitute these values into the equation for Ka:
Ka = [H+][A-] / [HA] = (10^(-1.72) mol/L)(3 * 10^(-1.72) mol/L) / (0.52 mol/L)
= 3 * 10^(-1.72 - 1.72) / (0.52)
Calculate this expression to find the value of Ka for citric acid.
49. Creatine:
- Concentration of creatine = 2.68 g/L
- pH of the solution = 2.23
Follow the same steps as before to calculate Ka for creatine.
50. Uracil:
- Concentration of uracil = 1.24 g/L
- pH of the solution = 5.71
Again, follow the same steps to calculate Ka for uracil.
By following these step-by-step calculations, you should be able to determine the acid-dissociation constant (Ka) for each of the given acids.
To solve these problems, we need to use the formula for calculating the acid-dissociation constant, Ka, which is the ratio of the concentration of the dissociated form of the acid (H+) to the concentration of the undissociated form of the acid (HA):
Ka = [H+][A-] / [HA]
To determine the percentage of acid molecules that ionize in the solution, we need to calculate the degree of ionization, which is the ratio of the concentration of the dissociated form of the acid to the initial concentration of the acid:
Degree of ionization = [H+]/[HA] * 100%
Let's solve these problems step by step:
48. To calculate the acid-dissociation constant for citric acid, we need to determine the concentration of H+ ions [H+] and the concentration of citric acid [HA].
Given information:
- Concentration of citric acid solution = 0.52 mol/L
- pH of the solution = 1.72
To find [H+], we need to convert the pH to [H+] using the formula:
[H+] = 10^(-pH)
[H+] = 10^(-1.72) = 0.0196 mol/L
Since citric acid is a triprotic acid (can release three H+ ions), the concentration of citric acid [HA] is the same as the initial concentration of the solution, which is 0.52 mol/L.
Now, we can plug the values into the formula for Ka:
Ka = [H+][A-] / [HA]
Ka = (0.0196 mol/L)(0.0196 mol/L) / 0.52 mol/L
Ka = 0.000384
To calculate the percentage of citric acid molecules that ionize, we can use the formula for the degree of ionization:
Degree of ionization = [H+]/[HA] * 100%
Degree of ionization = (0.0196 mol/L / 0.52 mol/L) * 100%
Degree of ionization = 3.77%
Therefore, the acid-dissociation constant for citric acid is 0.000384, and approximately 3.77% of citric acid molecules ionize in the solution.
Now, you can follow the same steps to solve problems 49 and 50.