Question

Sorbic acid (HC6H7O2) is a weak monoprotic acid with Ka=1.7×10−5. Its salt (potassium sorbate) is added to cheese to inhibit the formation of mold.

What is the pH of a solution containing 11.75 g of potassium sorbate in 1.70 L of solution?

Answer 1

potassium sorbate   weight = 11.75 g

potassium sorbate molecular weight = 150 g / mol

potassium sorbate moles = weight / molecular weight

                                          = 11.75 / 150

                                          = 0.0783

molarity = moles / volume

             = 0.0783 / 1.70

             = 0.046 M

C6H7O2- + H2O --------------------------> HC6H7O2 + OH-

0.046                                                        0                  0 --------------> initial

0.046-x                                                    x                  x----------------> equilibrium

Kb = [HC6H7O2 ][OH-]/[C6H7O2- ]

Kw / Ka = [HC6H7O2 ][OH-]/[C6H7O2- ]

1 x 10^-14 / 1.7 x10^-5 = x^2 / 0.046-x

7.14 x 10^-10 = x^2 / 0.046-x

x^2 + 7.14 x 10^-10 x - 3.28 x10^-11 = 0

x = 5.73 x 10^-6

[OH-] = x = 5.73 x 10^-6 M

pOH = -log [OH-]

pOH = -log(5.73 x 10^-6)

pOH = 5.24

pH + pOH = 14

pH = 8.76