To find the concentration of butanoic acid in each phase (water and benzene), we need to consider the partition coefficient and the initial concentration of butanoic acid.
The partition coefficient (P) is defined as the ratio of the concentration of butanoic acid in benzene (Cbenzene) to the concentration in water (Cwater), so we have:
P = Cbenzene/Cwater
For part (a), when the pH is 4.00, we need to make some assumptions. Butanoic acid is a weak acid, so it will partially dissociate in water to form butanoate ions (C4H7O2-) and hydrogen ions (H+). At pH 4.00, we assume that most of the butanoic acid will be in the undissociated form.
First, calculate the initial concentration of butanoic acid in water (Cwater) using the given volume and molarity:
Cwater = (0.10 M) x (20.0 mL/1000 mL) = 0.002 M
Next, use the partition coefficient to find the concentration of butanoic acid in benzene (Cbenzene):
P = Cbenzene/Cwater
3.0 = Cbenzene/0.002
Cbenzene = 3.0 x 0.002 = 0.006 M
So, the concentration of butanoic acid in water is 0.002 M, and in benzene is 0.006 M for part (a).
For part (b), when the pH is 10, we assume that the butanoate ion will be the prevailing form in water since the pH is higher than the pKa of butanoic acid. Therefore, the concentration of butanoic acid in water (Cwater) is negligible at pH 10.
Using the initial concentration of butanoic acid in water (Cwater) = 0.002 M and the partition coefficient (P = 3.0), we can find the concentration of butanoic acid in benzene (Cbenzene):
P = Cbenzene/Cwater
3.0 = Cbenzene/0 (negligible concentration of butanoic acid in water at pH 10)
Cbenzene = 3.0 x 0 = 0 M
So, the concentration of butanoic acid in water is negligible, and in benzene is 0 M for part (b).
In summary:
(a) When the pH is 4.00, the concentration of butanoic acid is 0.002 M in water and 0.006 M in benzene.
(b) When the pH is 10, the concentration of butanoic acid is negligible in water and 0 M in benzene.