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 9.50×10^−6. Although the formula of this new chemical is a trade secret, it can be revealed that the formula for Herbigon is X-acetate (XCH_3COO, 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 5.00×10^−3 M ? The pKa of acetic acid is 4.76.

Answer 1

PH to maximize the dissociation of acetic acid so as to push back the amount of acetate dissociating from the mystery compound. 

Ksp = [X+][C2H3O2-] = 9.5*10^-6 

Substituting in the desired value for [X+] 

9.5*10^-6 = (5.0*10^-3)x 

x, or acetate concentration, is .0019

Now, we calculate the Ka of acetic acid: 
pKa = -logKa 
4.76 = -logKa 
Ka = 1.738*10^-5 

We want the concentration of acetate to be .0019, so we plug that into our acid dissociation constant expression: 
Ka = [H+][C2H3O2-]/[HC2H3O2] 
1.738*10^-5 = [H+](.0019)/1

[H+] = .00915

pH = -log[H+] 
pH = -log(.00915) 
pH = 2.04