suppose solute A has a partition coefficient of 4.0 between diethyl ether and water. Demonstrate that if 100mL of solution of 5.0g of A in water were extracted with two 25mL portion of diethyl ether, a smaller amount of A would remain in the water than if the solution were extracted with one 50mL portion of diethyl ether.
Ko/a = (organic)/(aqueous)
o = organic
a = aqueous
5/100 = aqueous phase to start.
Let x = g in organic phase in 25 mL ether; then (x/25) = concn in organic phase and
(5-x)/100 = the amount left in the water phase.
4.0 = (x/25)/(5-x)/100
x will give you the amount in the organic phase, evaluate 5-x to determine the amount left in the water, then do the extraction again (on paper) to find the final concn in the water phase. Then redo with the different numbers for the single extraction. Compare. Two extractions with a smaller amount of solvent(25 each time) is more effective than a single extraction with 50 mL.
Post your owrk if you get stuck.
Where Did the 4.0 come from?
3. 4.0 = (x/25)/(5-x)/100
x= -1/3
16/3 left in the water
To demonstrate this, we need to understand how the partition coefficient works and how it affects the distribution of the solute between two immiscible liquids (such as diethyl ether and water) during extraction.
The partition coefficient (P) measures the distribution of a solute between two phases. In this case, it shows how much solute A prefers one phase over the other. A higher partition coefficient indicates a greater affinity of the solute for the first phase, while a lower partition coefficient indicates a greater affinity for the second phase.
Let's look at the scenario described:
1. Extraction with two 25mL portions of diethyl ether:
- We have 100mL of a solution containing 5.0g of solute A in water.
- The partition coefficient of A between diethyl ether and water is 4.0.
- We separate this solution into two equal portions of 50mL each.
- We perform the extraction twice using 25mL of diethyl ether for each extraction.
When we extract with diethyl ether, solute A will distribute itself between water and diethyl ether based on their relative affinities. In the first extraction, 25mL of diethyl ether will come into contact with 50mL of the solution. Initially, the partitioning ratio will be 2:1 (50/25), as the volumes are in the same ratio. However, due to the partition coefficient (P) of 4.0, the actual distribution will differ.
In the first extraction process:
- A fraction of A will dissolve in 25mL of diethyl ether.
- A fraction of A will also remain in 50mL of water.
- The ratio of the distribution can be calculated using the partition coefficient (P) as follows:
Distribution in diethyl ether: X
Distribution in water: Y
X/Y = (volume of diethyl ether)/(volume of water) * P
X/Y = 25mL/50mL * 4.0
X/Y = 2.0
This means that solute A will be two times more concentrated in the diethyl ether layer compared to the water layer after the first extraction.
For the second extraction:
- We take another 25mL of diethyl ether and mix it with the remaining 50mL of water from the first extraction.
- The partitioning ratio is the same: 2:1 (25/50).
- However, the distribution will be affected by the remaining A concentration in each layer after the first extraction.
Since the initial concentration of A was higher in the diethyl ether layer than in the water layer, when we perform the second extraction, a fraction of A will move from the water to the diethyl ether layer to attain equilibrium. The P value helps determine this distribution.
Now let's calculate the distribution in the second extraction:
Distribution in diethyl ether: X'
Distribution in water: Y'
X'/Y' = (volume of diethyl ether after the first extraction)/(volume of water after the first extraction) * P
X'/Y' = 25mL/25mL * 4.0
X'/Y' = 4.0
After the second extraction, solute A will be four times more concentrated in the diethyl ether layer compared to the water layer.
Comparing the two scenarios:
- Extraction with two 25mL portions of diethyl ether: 2.0 concentration ratio in favor of diethyl ether after the first extraction, followed by a 4.0 concentration ratio after the second extraction.
- Extraction with one 50mL portion of diethyl ether: 4.0 concentration ratio in favor of diethyl ether.
Therefore, a smaller amount of solute A will remain in the water layer if the solution is extracted with two 25mL portions of diethyl ether compared to extracting it with one 50mL portion of diethyl ether.