The question asks, "Butanoic acid has a partition coeff of 3.0 when distributed b/t water and benzene. Find the formal concentration of butanoic acid in each phase when 100 mL of 0.10 M aqueous butanoic acid is extracted with 25 mL of benzene at pH 10.00."
I know that the first step is to find D, where D = K(Ka)/[(Ka+[H+)].
So I calculated:
D = 3.0(1.52x10^-5)/[(1.52x10^-5+10^-10)].
The answer should have been D = 1.97 x 10^-5, but I didn't get this.
You answered: If the question is worded correctly, then Kd water/benzene = 3.0
However, the distribution coefficient USUALLY is listed as organic/water.
So my question is, what do I need to do to get 1.97 x 10^-5? Where did I go wrong?
Th question is asking for the concn of butanoic acid in the water phase and in the benzene phase? Is the answer you are looking up either of these concentrations or does it say specificially that D = 1.97....?
Yes. That's all I am given on the question. The answer key says that D = 1.97 x 10^-5.
To determine the formal concentration of butanoic acid in each phase, you need to use the distribution coefficient (Kd) given for water and benzene. The equation you mentioned, D = K(Ka)/[(Ka+[H+)], is not applicable in this scenario.
Given that the partition coefficient is Kd = 3.0 for water/benzene, we can calculate the concentration of butanoic acid in each phase by following these steps:
1. Calculate the moles of butanoic acid initially present in the aqueous phase:
Moles of butanoic acid = volume (in L) × concentration (in M)
= 0.1 L × 0.10 M
= 0.01 moles
2. Determine the amount of butanoic acid that partitions into the benzene phase:
Moles of butanoic acid in benzene = Kd × moles of butanoic acid in water
= 3.0 × 0.01 moles
= 0.03 moles
3. Calculate the volume of the benzene phase:
Volume of benzene = 25 mL ÷ 1000 mL/L
= 0.025 L
4. Determine the concentration of butanoic acid in the benzene phase:
Concentration in benzene = moles of butanoic acid in benzene ÷ volume of benzene
= 0.03 moles ÷ 0.025 L
= 1.2 M
5. Calculate the volume of the aqueous phase:
Volume of water = 100 mL ÷ 1000 mL/L
= 0.1 L
6. Determine the concentration of butanoic acid in the aqueous phase:
Concentration in water = (moles of butanoic acid - moles of butanoic acid in benzene) ÷ volume of water
= (0.01 moles - 0.03 moles) ÷ 0.1 L
= -0.2 M
The negative concentration in water indicates that all the butanoic acid has partitioned into the benzene phase. Please note that negative concentrations are not physically meaningful. Therefore, the final concentration of butanoic acid in each phase is:
Concentration in water: -0.2 M (meaning none present)
Concentration in benzene: 1.2 M
This suggests that all the butanoic acid has partitioned into the benzene phase due to the high partition coefficient.
To find the correct distribution coefficient and formal concentrations, let's break down the steps.
First, let's clarify the terminology used in the question:
- Kd (distribution coefficient) usually represents the ratio of solute concentrations in two immiscible solvents (organic/water in most cases).
- Ka represents the acid dissociation constant.
- [H+] represents the hydrogen ion concentration (pH-dependent).
Now, let's go through the correct steps to obtain the desired answer:
Step 1: Calculate the distribution coefficient (Kd) using the correct ratio of solute concentrations. In this case, Kd water/benzene = 3.0, as given in the question.
Step 2: Calculate the concentration of butanoic acid in the aqueous phase before extraction:
Concentration in water before extraction = initial concentration = 0.10 M
Step 3: Calculate the concentration of butanoic acid in the organic (benzene) phase:
Concentration in benzene after extraction = (Kd) x (Concentration in water before extraction)
= (3.0) x (0.10 M)
= 0.30 M
Step 4: Determine the concentration of butanoic acid in the aqueous phase after extraction:
Concentration in water after extraction = (Initial concentration) - (Concentration in benzene after extraction)
= 0.10 M - 0.30 M (all transferred to benzene)
= -0.20 M (This negative value means that all of the acid transferred to the benzene phase)
It seems there might be a discrepancy in the given answer (1.97 x 10^-5) and the values obtained from the calculations. Please double-check the information provided in the question to ensure accuracy.
If you have any other questions or need further clarification, feel free to ask!