I am not sure how to understand when pH will affect a given problem regarding extraction. For example, in a problem given that K$_D$ of the reaction is $1.86$ I am asked to calculate:
(a) How much propionic acid is left in octanol if you shake $100$ ml of octanol as contains $1.0$ mM propionic acid with a $50$ ml aqueous solution buffered to pH $2$?
(b) How much propionic acid is left in octanol if you shake $100$ ml of octanol as contains $1.0$ mM propionic acid with a $50$ ml aqueous solution buffered to pH $7$?
For these problems it is stated that "At pH $2$, only AH will be formed in water and we can ignore the proton equilibrium, so that n$_0$ = [AH]$_{aq}$ V$_{aq}$ + [AH]$_{org}$ V$_{org}$" but " At pH $7$, A- is no longer negligible and n$_0$ = [AH]$_{aq}$ V$_{aq}$ + [AH]$_{org}$ V$_{org}$ +[A-]$_{aq}$ V$_{aq}$"
How does one know this?
The same is goes for the problem:
Propionic anhydride can be extracted from cyclohexane to water. The distribution equilibrium can be written as:
PRANH (org) <-> PRANH (H2O) K = $0.82$
In aqueous solution, propionic anhydride can be hydrolyzed to propionic acid (PRIC ACID) according to the following equilibrium:
PRANH + H2O <-> 2 PRIC ACID K = $0.0023$ M (at pH <$3.0$)
A cyclohexane solution contains 1$0$ mM propionic anhydride. At what volume ratio of cyclohexane to water will $80$% of the propionic anhydride be extracted over to the aqueous phase (pH $2$) with a shake?
Here I assume that I should either get if the pH doesn't matter:
$1-p = \frac{1}{1+ K_D V_{aq}/V_{org}}$
Or if pH matters then n$_0$ = [PRANH]$_{aq}$ V$_{aq}$ + [PRANH]$_{org}$ V$_{org}$ +[PRIC ACID]$_{aq}$ V$_{aq}$ and I would get that:
$1-p = \frac{1}{1+ K_D* V_{aq}/V_{org}+ [PRIC ACID]_{aq}/[PRANH]_{org}*V_{aq}/V_{org}}$
where $1$-p=$1$-$0.8$=$0.2$
I would assume that the second is correct (if either is correct) since it is given that PRANH hydrolyzes at pH<$3$ so if we're at pH=$2$ then that should occur. But am I correct in assuming that? But then what happens to the equilibrium constant given for the hydrolyzation, do I use that for something or should I only take into account the K$_D$ = $0.82$ for the extraction process?
Thankful for all help!
