You have 100 mL of a solution of benzoic acid in water; the amount of benzoic acid in the solution is estimated to be about 0.30 g. The distribution coefficient of benzoic acid in diethyl ether and water is approximately 10. Calculate the amount of acid that would be left in the water solution after four 20-mL extractions with ether. Do the same calculation, using one 80-mL extraction with ether, to determine which method is more efficient.
Kd = 10
Bz = 0.3 in 100 mL H2O
4 20 mL portions ether extraction
fn = [1+kd*(Vo/Va)]^-n
Vo = 20
Va = 100
-n = -4
Solve for fn which is the fraction of benzoic acid remaining in the water layer after 4 extractions. You can go through the math but I found 0.0037 g benzoic acid remaining after four separate extractions.
After 1 extraction I found 0.033 in the water layer; obviously it's more effective with more extractions than with one large extraction.
To calculate the amount of benzoic acid that would be left in the water solution after extractions with ether, we need to know the distribution coefficient and the number of extractions.
The distribution coefficient (Kd) is a measure of how much a compound prefers one solvent over another. For benzoic acid in diethyl ether and water, the Kd is given as approximately 10.
Let's start by calculating the amount of benzoic acid extracted in one extraction using 20 mL of ether:
1. Calculate the volume ratio of water to ether used in the extraction:
- Water volume: 100 mL
- Ether volume: 20 mL
Volume ratio = Water volume / Ether volume = 100 mL / 20 mL = 5
2. Calculate the amount of benzoic acid extracted in one extraction:
- Initial amount of benzoic acid in water: 0.30 g
- Distribution coefficient (Kd): 10
Amount of benzoic acid extracted = Initial amount of benzoic acid in water / (1 + volume ratio x Kd)
= 0.30 g / (1 + 5 x 10)
= 0.30 g / 51
≈ 0.0059 g
Therefore, approximately 0.0059 g of benzoic acid would be extracted in one 20-mL extraction with ether.
Now, let's calculate the amount of benzoic acid left in the water solution after four 20-mL extractions with ether:
1. Calculate the total amount of benzoic acid extracted in four extractions:
- Amount of benzoic acid extracted in one extraction: 0.0059 g
Total amount of benzoic acid extracted = Amount of benzoic acid extracted in one extraction x Number of extractions
= 0.0059 g x 4
= 0.0236 g
2. Calculate the amount of benzoic acid left in the water solution:
- Initial amount of benzoic acid in water: 0.30 g
Amount of benzoic acid left in water = Initial amount of benzoic acid in water - Total amount of benzoic acid extracted
= 0.30 g - 0.0236 g
≈ 0.2764 g
Therefore, approximately 0.2764 g of benzoic acid would be left in the water solution after four 20-mL extractions with ether.
To determine which method (four 20-mL extractions or one 80-mL extraction) is more efficient, we need to compare the amounts of benzoic acid left in the water solution after each method.
For the method with one 80-mL extraction:
1. Calculate the volume ratio of water to ether used in the extraction:
- Water volume: 100 mL
- Ether volume: 80 mL
Volume ratio = Water volume / Ether volume = 100 mL / 80 mL = 1.25
2. Calculate the amount of benzoic acid extracted in one 80-mL extraction:
- Initial amount of benzoic acid in water: 0.30 g
Amount of benzoic acid extracted = Initial amount of benzoic acid in water / (1 + volume ratio x Kd)
= 0.30 g / (1 + 1.25 x 10)
= 0.30 g / 13.25
≈ 0.0226 g
Therefore, approximately 0.0226 g of benzoic acid would be left in the water solution after one 80-mL extraction with ether.
Comparing the amounts of benzoic acid left in the water solution after four 20-mL extractions (0.2764 g) and one 80-mL extraction (0.0226 g), we can see that the method of four 20-mL extractions is more efficient for separating benzoic acid from the water solution.
Please note that these calculations are approximate and based on the given values and assumptions.
yes
Well in order to solve this you must first start by evaluating what 100 mL of benzoic acid will do when mixed with water. But more importantly what to do with water itself because without water in the world, there would be no life. Thus, since we drink water, we come to the conclusion to whether or not we should watch tv or play video games. I normally choose to play games because they're fun.
Hope this helps.