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 9.30×106.

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 1.50×103M ? The pKa of acetic acid is 4.76.

Explanation / Answer

The required concentration of  X+(aq) is

[X+(aq)] = 1.50x10-3 M

The dissociation reaction of XCH3COO(s) is

XCH3COO(s) + H2O ------- > X+(aq) + CH3COO-(aq) ; Ksp = 9.30x10-6   

Ksp = 9.30x10-6 = [X+(aq)]x[CH3COO-(aq)]

=>  9.30x10-6 = 1.50x10-3 Mx[CH3COO-(aq)]

=> [CH3COO-(aq)] = 9.30x10-6 / 1.50x10-3  = 6.20x10-3 M

The chemical equation for the dissociation of CH3COOH is

CH3COOH ------> CH3COO-(aq) + H+(aq) ; Ka = 10-4.76 = 1.74x10-5  

Ka = 1.74x10-5 = [CH3COO-(aq)]x [H+(aq)] / [CH3COOH]

Given [CH3COOH] = 1 M

[CH3COO-(aq)] = 6.20x10-3 M

Putting the concentration values

Ka = 1.74x10-5 = 6.20x10-3 M x [H+(aq)] / 1 M

=> [H+(aq)] = 1.74x10-5 / 6.20x10-3 = 2.81 x 10-3 M

Hence required pH = - log[H+(aq)] = - log(2.81 x 10-3 M) = 2.55 (answer)

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