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definition of pKa

Migrated topic.
afterwards said:
Now I'm wondering what the Ka of a substance is at 50% dissociation. If Ka=[A-][H+]/AH then e.g. if you have 6 moles of acetic acid and it's 50% dissociated, then you would have 3 moles of H+ and 3 moles of CH3CO2. Wouldn't that mean 3x3/6?
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If you start with 6 mol/l of acetic acid (lets call it HA) and 50% dissociates, that would leave 3 mol/l HA and add 3 mol/l A- and 3 mol/l H+. Note that I write add because there may have been any amount of H+ present in the solution.

If we assume that there is no other source of H+, the formula [A-]x[H+]/[HA]
would yield: 3x3/3. The pKa for the hypothetical HA is 10log(3), or about 0.477
 
Ok - so back to DMT --

I would have thought that the DMT salt (in 1L water) would be the "acid" HA in the equation and DMT base would be the conjugate base. So then, if you have 6 moles of DMTHCl and 50% dissolution, then you would have 3 moles of DMT as the conjugate base, 3 moles of H+, and 3 moles of DMTHCl. Then the Ka would be 3x3/3=3.

If that isn't the case, then what would be HA, and A- ? In any case, it wouldn't seem like you would get a pKa of 0 at 50% dissolution.
 
Mindlusion said:
Ka= [DMT][H3O+]/[DMTH+]
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Yes I was basically thinking that. So the Cl- ends up joined to whatever base is being used -- so like it becomes NaCl if NaOH is used and the H+ joins the OH.
Understand that pH is inherent into this equation THE->> [H3O+] and from this alone, if 50% of DMTH+ dissociates, it does not equal 1.
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So then the pKa at 50% couldn't be 0 and that's another mistake in the wiki.
 
Mindlusion said:
the keyword (or symbol) here is the '+' or '-' sign

If you notice in that graph the x-axis is actually pH - Pka, not pKa

the pka of DMT is 8.68, so at a pH of 8.68, it is in the center of the equilibrium, 50% protonated 50% deprotonated
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So, it would be better for the wiki to explain that pKa +0 is referring to to the Henderson–Hasselbalch equation and is not the pKa?

Also, could you explain what is the difference between PKa and pKa? The graph says "pH - pKa" under the x-axis.

Thanks.
 
This is my suggestion for rewording the wiki:

The pKa is equal to the same number as the pH when 50% of the alkaloid is in salt form and 50% is freebased. The pH and pKa at which this occurs for DMT is 8.68. I.e., the pKa=8.68 and the pH=8.68.

At pH 6.68 (pKa minus 2) 1% is freebased and 99% is salted
At pH 7.68 (pKa minus 1) 10% is freebased and 90% is salted
At pH 8.68 (pKa +/- 0) 50% is freebased and 50% is salted
At pH 9.68 (pKa plus 1) 90% is freebased and 10% is salted
At pH 10.68 (pKa plus 2) 99% is freebased and 1% is salted
 
The preceding post is possibly going to be posted to the wiki in the next few days. I would welcome any suggestions or comments, additions, etc.

Thanks to everyone for your help.
 
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