As a chemist for an agricultural products company, you have just developed a new

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 9.10 times 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 times 10-3 M ? The pka of acetic acid is 4.76.

Explanation / Answer

CH3COOH   ======>H+ + CH3COO-

Ka of acetic acid is 10-4.76 = 1.74*10-5

If you reverse the acid dissociation of acetic acid, you obtain the equation we want:

H+ + CH3COO- =====>CH3COOH

XCH3COO====>CH3COO- + X+

Sum these two equations, and cancel out acetate ion

XCH3COO + H+ ======> CH3COOH + X+

The K of this new equation is the product of the Ksp and the Ka-1 since we have reversed the acid dissociation equation to create this equation.

Ksp = [X+][CH3COO-] = 8.2*10-6

Ka-1 = 1 / 1.74*10-5 = 57142

Ksp * Ka = K of the new equation = 0.4686 = [x+][CH3COOH]/[H+]

IT is given that the concentration of [CH3COOH] is 1M for technical reasons:

0.4686 = [X+]/[H+]

[X+] is desired to be 2.5*10-3 = 0.0025

[H+] = 0.0025/0.4686 = 0.005335 mol/L

pH = -log[H+] = 2.27

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