You have 150 ml of a solution of benzoic acid in water estimated to contain about 5 g of acid. The distribution coefficient 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. Do the same calculation using one 150 ml extraction with benzene to determine which method is more efficient.

My ans:
k = (concentration of benzoic acid in benzene)/(benzoic acid conc in water) = 10

But I am not sure how to proceed from this. Any help appreciated

To calculate the amount of acid that would be left in the water solution after three 50 ml extractions with benzene, you can use the distribution coefficient (k) and the initial amount of acid in the water solution.

1. Start by calculating the amount of acid in the water solution:
- The concentration of acid in the water solution can be written as:
Concentration of acid = (Mass of acid)/(Volume of solution)
- Given that the water solution contains about 5 g of acid and has a volume of 150 ml, the concentration is:
Concentration of acid = 5 g / 150 ml

2. Calculate the amount of acid in the benzene phase after each extraction:
- After the first extraction, 50 ml of benzene is added to the mixture. The distribution coefficient (k) tells us the ratio of the concentration of acid in the benzene phase to the concentration in the water phase. Therefore, the concentration of acid in the benzene phase after the first extraction is:
Concentration of acid in benzene = k * Concentration of acid in water
- Multiply the concentration of acid in benzene by the volume of benzene (50 ml) to get the amount of acid that moved to the benzene phase after the first extraction.

3. Repeat this process for the second and third extractions:
- For each extraction, add 50 ml of benzene to the mixture and calculate the new concentration and amount of acid in the benzene phase.

4. Calculate the remaining amount of acid in the water phase after three extractions:
- Subtract the total amount of acid that moved to the benzene phase from the initial amount of acid in the water solution.

To compare the efficiency of three 50 ml extractions with one 150 ml extraction, repeat the same calculations using a single extraction with 150 ml of benzene and compare the remaining amount of acid in the water phase. The method with the lower remaining amount of acid in the water phase is more efficient.