Question

Cocaine, C17H23O4N, is a weak base with Kb=4.0x10^-9. It can be made into a salt called cocaine hydrochloride, C17H23O4NHCl, that is soluble in water (forming ions C17H23O4NH+ and Cl-. What is the pH of a 0.20 M solution of C17H23O4NHCl?

Answer 1

C₁₇H₂₃O₄N is CONVOLVAMINE, not cocaine. Cocaine is C₁₇H₂₁O₄N. C₁₇H₂₃O₄NHCl is CONVOLVAMINE HYDROCHLORIDE. C₁₇H₂₁O₄NHCl is cocaine hydrochloride.

Given, 0.20M C₁₇H₂₃O₄NHCl
the weak base molecule dissociates into..
C₁₇H₂₃O₄NHCl + H₂O <--------> C₁₇H₂₃O₄NH⁺ + Cl^-
I:           0.20         -                        0                0
C:           -x                                    +x              +x
E:       0.20-x                                  x                x

Now, Kb = [C₁₇H₂₃O₄NH⁺][Cl^-] / C₁₇H₂₃O₄NHCl

      4.0x10^-9 = x² / 0.20-x

      x^{2 =} 4.0x10^-9 * (0.20-x)

     x^{2 =} (8.0x10^-10) -(4.0x10^-9 x)

    x² - (8.0x10^-10) + (4.0x10^-9 x) = 0

solve for x, using quadratic equation, x = (2.83 x 10^-5) M

Now, pOH = - log [OH^-]

       pOH = -log (2.83 x 10^-5)

       pOH = - (-4.55)

      pOH = 4.55

As we know, pH + pOH = 14

                   pH = 14 - pOH

                   pH = 14 - 4.55

                   pH = 9.45