Sorbic acid, HC6H702 (pKa=4.77), is widely used in the food industry as a preservative. For example, its potassium salt (potassium sorbate) is added to cheese to inhibit the formation of mold. What is the pH of 0.37M KC6H702(aq)?
Let's call sorbic acid HSorb.
HSorb ==> H^+ _ Sorb^-
Ka = (H^+)(Sorb^-)/(HSorb) = Ka.
So (H^+) = x
(Sorb^-) = x
(HSorb) = 0.37 - x
Substitute into the Ka expression and solve for x.
Note: It would be a good idea to convert pKa to Ka first.
To find the pH of a solution of potassium sorbate (KC6H702), we need to consider the dissociation of the compound in water. KC6H702 will dissociate into K+ ions and C6H702- ions. The C6H702- ions will then react with water to form sorbic acid (HC6H702) and hydroxide ions (OH-).
The key information we need is the pKa value of sorbic acid, which is given as 4.77. The pKa is a measure of the acidity of an acid and represents the negative logarithm of the acid dissociation constant (Ka).
To calculate the pH of the solution, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa and the concentration of the acid and its conjugate base:
pH = pKa + log([conjugate base]/[acid])
In this case, the conjugate base is C6H702- and the acid is HC6H702. The concentration of C6H702- can be determined using the concentration of KC6H702 (given as 0.37M) and the dissociation of KC6H702:
C6H702- = [KC6H702]
The concentration of HC6H702 is unknown, but we can assume it is small compared to the concentration of KC6H702, as KC6H702 is a salt of sorbic acid. Therefore, we can neglect it in the denominator of the Henderson-Hasselbalch equation.
Now, let's plug in the information we have into the equation:
pH = 4.77 + log([KC6H702]/[HC6H702])
Since we can disregard the concentration of HC6H702, the equation simplifies to:
pH = 4.77 + log([KC6H702])
Substituting the concentration of KC6H702 (0.37M) into the equation, we get:
pH = 4.77 + log(0.37)
Calculating this using a calculator, we find:
pH ≈ 4.77 + (-0.431) ≈ 4.34
Therefore, the pH of the 0.37M KC6H702 solution is approximately 4.34.