Question

Nicotine is responsible for the addictive properties of tobacco. assume kb1 = 1.0×10-6 and kb2 = 1.3×10-11 . determine the ph of a 1.85×10-3 m solution of nicotine.]

Answer 1

If we abbreviate the formula for nicotine as Nic, then the equations for two different equilibria of Nic in water are 
     Nic + H2O ---> NicH+ + OH- 
     NicH+ + H2O ---> NicH2 2+ + OH-  

We can write the Kb1 expression for the first equation as 
     Kb1 = 1.0×10^-6 = [NicH+][OH-] / [Nic] 
     1.0×10^-6 = x^2 / 1.85×10^-3 - x 
Approximating that x is negligible compared to 1.85×10^-3 simplifies the equation to   
     1.0×10^-6 = x^2 / 1.85×10^-3 
     x = 0.0000430 
     x = [OH-] = 4.30×10^-5 M  

From the Kb2 expression 
     Kb2 = 1.3×10-11 = [NicH2 2+][OH-] / [NicH+]  
     1.1×10^-10 = x^2 / 4.30×10^-5 - x 
Approximating that x is negligible compared to 4.30×10^-5 simplifies the equation to 
     1.1×10^-10 = x^2 / 4.30×10^-5 
     x =  [OH-] = 6.88×10^-8  

The concentration [OH-] can be computed as 
     [OH-] = 4.30×10^-5 M + 6.88×10^-8 M = 4.30×10^-5 M  
This shows that the second equilibrium has a negligible effect on the pH.  

We can now calculate for pH:   
     pOH = -log [OH-] = -log (4.30×10^-5 M) = 4.37 
     pH = 14 - pOH = 14 - 4.37 = 9.63