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 9.10×10⁻⁶.

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 5.50×10⁻³M ? The pKa of acetic acid is 4.76.

Answer 1

The dissociation of given acid

XCH3COO = X+ + CH3COO-

Solubility product constant of the reaction

Ksp = [X+][CH3COO-] = 9.1*10^-6

The given concentration of cation [X+] = 5.50*10^-3 M

9.1*10^-6 = (5.50*10^-3) [CH3COO-]

[CH3COO-] = 0.00165454 M

Acid dissociation constant
pKa = -logKa
4.76 = -logKa
Ka = 1.738*10^-5

The reaction with ICE TABLE

HC2H3O2 = H+ + C2H3O2-

I 1 0.001654

C - x +x +x

E (1-x) x (0.001654+x)

Equilibrium constant expression of the reaction

Ka = [H+][C2H3O2-]/[HC2H3O2]
Ka = (x)(0.001654+x)/(1-x)

x << 1

1.738*10^-5 = (x)(0.001654)

x = 0.01051 = [H+]

pH = -log[H+]
pH = -log(0.01051)
pH = 1.98