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:Â Â Â Â Â Â Â Â Â Â
0.20Â Â Â Â Â Â Â Â
-Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
0
C:Â Â Â Â Â Â Â Â Â Â
-x                                  Â
+x            Â
+x
E:Â Â Â Â Â Â
0.20-x                                Â
x              Â
x
Now, Kb =
[C17H23O4NH+][Cl-]
/ C17H23O4NHCl
     4.0x10-9 =
x2 / 0.20-x
     x2 =
4.0x10-9 * (0.20-x)
    x2 = (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
                 Â
pH = 14 - pOH
                 Â
pH = 14 - 4.55
                 Â
pH = 9.45