Question

As a chemist for an agricultural products company, you have just developed a new herbicide,"Herbigon," that you think has the potential to kill weeds effectively. A sparingly soluble salt, Herbigon is dissolved in 1 M acetic acid for technical reasons having to do with its production. You have determined that the solubility product Ksp of Herbigon is 8.30×10⁻⁶.

Although the formula of this new chemical is a trade secret, it can be revealed that the formula for Herbigon is X-acetate (XCH3COO, where "X" represents the top-secret cation of the salt). It is this cation that kills weeds. Since it is critical to have Herbigon dissolved (it won't kill weeds as a suspension), you are working on adjusting the pH so Herbigon will be soluble at the concentration needed to kill weeds. What pH must the solution have to yield a solution in which the concentration of X+ is 4.50×10⁻³M ? The pKa of acetic acid is 4.76.

Express your answer numerically.

Answer 1

first consider XCH3COO

XCH3COO ---> X+ + CH3COO-

solubility product is given by

Ksp = [X+] [CH3COO-]

given

[X+] = 4.5 x 10-3

and

Ksp = 8.3 x 10-6

so

8.3 x 10-6 = 4.5 x 10-3 x [CH3COO-

[CH3COO-] = 1.844 x 10-3

now

CH3COO- and CH3COOH form a buffer solution

and for buffers

according to hasselbach hendersen equation

pH = pKa + log [ conjugate base / acid ]

so

pH = pKa + log [CH3COO- / CH3COOH]

given

pKa = 4.76

[CH3COOH] = 1

ao

pH = 4.76 + log [ 1.844 x 10-3 / 1]

pH = 2.026

so

pH of the solution should be 2.026