Thanks for your earlier thoughts. Am still working on the problem and would like to know if you have any thoughts on my approach below:
If I have a set of data that gives the apparent partition coefficient as a function of pH, over a range of pH 2-10, how do I calculate the Ka of the compound?
Dr. Bob222, my thought from what I've read:
myweb.brooklyn.liu.edu/msavva/intropartition.pdf
was to use the following relationship for a weak base:
(1/K') = (1/(K*Ka))*[H+] + 1/K
and graph 1/K' vs pH to get the slope and y-intercept which I could then use to determine the Ka. However, when I graph over the entire pH range, I don't get a linear relationship. Since this is a weak base, do you think I should only be graphing out the data from say pH 7-10, or somewhere around this range (5-10, 6-10, etc), as I do get a linear relationship when I ignore the lower pH values. The issue I have though is I'm not sure what pH I should start at, as when I graph out values for pH 5-10 or 6-10 or 7-10, the values that I get for Ka and K are dramatically different for each range. Thanks for any additional insight you might have.
I found this. It may or may not help but further down the page it talks about log D in terms of pH, Ka, etc.
http://en.wikipedia.org/wiki/Partition_coefficient
Sorry I can't be of more help.
Your approach to calculate the Ka of the compound using the relationship (1/K') = (1/(K * Ka)) * [H+] + 1/K is correct. However, it seems that you are encountering some difficulties with the data and the graph.
The non-linear relationship you are observing when graphing 1/K' vs pH over the entire pH range is likely due to the fact that the equation you're using assumes constant values of K and Ka. This assumption may not hold true for your compound, especially if its properties change significantly at extreme pH values (pH 2 and pH 10).
Since you mentioned that the compound is a weak base, it may be more appropriate to focus on the pH range where the compound is mostly ionized or deprotonated. Starting the graph from around pH 7-10 could be a reasonable approach. However, it's important to ensure that you have enough data points in that range to accurately determine the slope and y-intercept of the linear relationship.
To determine the pH range to use, you could consider looking at the inflection point on the graph or estimate the pH range where the curve starts to exhibit linearity. Another option is to investigate the pKa of the compound, as it provides information about the pH at which the ionization is at its half-maximum. This could guide you in selecting a suitable pH range to focus on.
Regarding the dramatic differences in Ka and K values when using different pH ranges, this could be due to the varying compounds or species present at different pH values. It's important to remember that the Ka value represents the acid dissociation constant for a specific compound under specific conditions, so it can vary depending on the chemical environment.
In summary, consider narrowing down the pH range to focus on where the compound exhibits more linearity in the graph of 1/K' vs pH. Additionally, consult the compound's pKa or consider the compound's behavior to select a suitable pH range. This will help you obtain more accurate estimates of the Ka value.