The much-abused drug cocaine is an alkaloid. Alkaloids are noted for their bitter taste, an indication their basic properties. Cocaine C17H21O4N, is soluble in water the the extent of 0.17g/100 mL solution, and a saturated solution has a PH = 10.08. What is the value of Kb for cocaine?

C17H21O4N + H2O --> <--- C17H21O4NH+ + OH- Kb = ?

I would appreciate if someone would do this problem without skipping any steps, I need to understand it completely for an exam. With the data 0.17g/100 mL how do I find M (concentration)? Thanks.

5 answers

pH + pOH = 14
pOH = 14-10.08 = 3.92
[OH-]=-log^-1(3.92)=1.2002x10^-4
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Kb = [BH+][OH-] / [B], with B = base
here,
Kb = [C17H21O4NH+][OH-] / [C17H21O4N]
since [C17H21O4NH+]=[OH-]
Kb = [OH-]^2 / {[C17H21O4N]-[OH-]}
Since [OH-] is much smaller than the overall concentration of the base, we can approximate:
Kb = [OH-]^2 / [C17H21O4N]
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Find the molarity of C17H21O4N and substitute it into the formula for Kb along with the value of [OH-].

If the solubility is 0.17 g/100 mL, that is equivalent to 1.7 g/1000 mL. And moles = grams/molar mass will give you the molarity.
Use the equation given.
You know pH, convert that to pOH, then to OH^-.
Kb = (C17H21O4NHH^+)(OH^-)/(C17H21O4N).
You know OH^- now, that is the same as C17H21O4NH^+, and the C17H21O4N is 1.7/molar mass - (OH^-). You may be able to neglect OH^- in the denominator if it is small in comparison to the cocaine molarity. Post your work if you get stuck.

kb=2,6 x 10^-6
is it correct?

Is 3.3*10^-9