I am about to do an extraction experiment, and needed help with a question to improve my understanding. Any help appreciated.
1. You have 150 ml of a solution of benzoic acid in water estimated to contain about 5g of the acid. The distribution coeffcient of benzoic acid in benzene and water is approx. 10. Calculate the amount of acid that would be left in the water solution after three 50 ml extractions with benzene. SO the same calculation using one 150ml extraction with benzene to determine which method is more efficient.
Also I was wondering why three small extractions are more efficient than one large extraction, and how can this be proven?
a. The main reason that three extractions are more efficient than one large one is that the first extraction takes out a portion, the second extraction STARTS with less than the first and the third extraction starts with even less. It's the same process as transferring a solution quantitatively from one beaker to another. You can fill the beaker with water and pour into the other beaker with one transfer OR you can wash with four or five 5-mL portions and pour each rinse into the other beaker. You will get quantitative transfer (meaning all of it) with four or five SMALL rinses but you will not get quantitative transfer with just one large (or small) rinse.
b. The way you prove this is to do it.
To calculate the amount of benzoic acid left in the water solution after three 50 ml extractions with benzene, you need to consider the distribution coefficient and the initial amount of benzoic acid in the water solution.
Let's break down the calculation step by step:
1. Calculate the amount of benzoic acid extracted in each extraction:
- In the first extraction, 10% (distribution coefficient of 10) of the benzoic acid will be extracted by benzene, which is 5g * 0.10 = 0.5g.
- In the second extraction, another 10% of the remaining benzoic acid will be extracted, which is (5g - 0.5g) * 0.10 = 0.45g.
- In the third extraction, another 10% of the remaining benzoic acid will be extracted, which is (5g - 0.5g - 0.45g) * 0.10 = 0.405g.
2. Calculate the final amount of benzoic acid left in the water solution after three extractions:
- The initial amount of benzoic acid in the water solution is 5g.
- After the first extraction, 0.5g is removed, so the remaining amount is 5g - 0.5g = 4.5g.
- After the second extraction, 0.45g is removed, so the remaining amount is 4.5g - 0.45g = 4.05g.
- After the third extraction, 0.405g is removed, so the final amount in the water solution is 4.05g - 0.405g = 3.645g.
To compare the efficiency of three small extractions with one large extraction, you need to calculate the amount of benzoic acid left in the water solution after a single 150 ml extraction with benzene.
1. Calculate the amount of benzoic acid extracted in the large extraction:
- In a single 150 ml extraction, the total amount of benzoic acid in the water solution is extracted.
- 10% (distribution coefficient of 10) of the initial 5g of benzoic acid will be extracted, which is 5g * 0.10 = 0.5g.
2. Calculate the final amount of benzoic acid left in the water solution after the large extraction:
- The initial amount of benzoic acid in the water solution is 5g.
- After the extraction, 0.5g is removed, so the final amount in the water solution is 5g - 0.5g = 4.5g.
In conclusion, after three 50 ml extractions with benzene, the amount of benzoic acid left in the water solution is 3.645g. In comparison, after a single 150 ml extraction with benzene, the amount of benzoic acid left in the water solution is 4.5g.
Three small extractions are more efficient than one large extraction because each small extraction removes a portion of the benzoic acid, reducing its concentration in the water solution. This lowers the driving force for further extraction, which means less benzoic acid will be left in the water after each subsequent extraction.
On the other hand, a single large extraction removes a significant amount of benzoic acid in one step, which saturates the benzene solution faster and decreases the extraction efficiency. This can leave more benzoic acid in the water solution compared to multiple small extractions.
This can be proven by performing the extractions experimentally and quantifying the amount of benzoic acid left in the water solution for different extraction methods. By comparing the results, you can determine which method is more efficient in terms of benzoic acid removal.