# PH-rate profile minimum?

1. Oct 24, 2007

### paperclip

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??

Thanks!

Last edited: Oct 24, 2007
2. Oct 24, 2007

### HallsofIvy

Staff Emeritus
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.

3. Oct 24, 2007

### paperclip

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....