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Homework Help: PH-rate profile minimum?

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data

    The rate of degradation of a drug D that is subject to hydrolysis is given by the first order equation rate=kobs (D) where Kobs= Kh (H+) + Ko= Koh (OH-) Derive an equation for the pH at the minimum (pH)min of the pH/rate profile.

    3. The attempt at a solution

    From elementary calculus, I know that I need to first differentiate the rate equation, then find the roots of the differentiated equation. Take a second differentiation of the equation, put the roots into it and see whether it gives a positive or a negative value. The positive value gives you the (pH)min.
    However...I'm not too sure how to do that with this sort of equation??

    Last edited: Oct 24, 2007
  2. jcsd
  3. Oct 24, 2007 #2


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    Science Advisor

    Well, since this is not a chemistry or biology forum, you will need to tells us how the functions Kobs= Kh (H+) + Ko= Koh (OH-) are defined! It's been a long time since i took any chemistry.
  4. Oct 24, 2007 #3
    Kobs= observed rate of reaction
    Kh is the concentration of [H+]
    Koh is the concentration of [OH-]
    ko is the constant.

    Rearrange..... k=[H]+ko-[OH-]

    pH=pKa + log [unionized/ionized] where ionized= [OH-] and/or[H+] and ionized [H20]

    Hope this helps....
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