Deriving the pH at the Minimum of a pH/Rate Profile for Drug Degradation

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Homework Statement

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.

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??

Thanks!

 

[HallsofIvy]

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.

 

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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...