Suppose a compound Z had a partition coefficient of 8.0 in ether-water. If 10.0 g of Z was dissolved in 100 mL of water, and if the water solution was extracted with two 100 mL portions of ether, answer the following questions. show your calculation.

a) What is the total amount of Z contained in the 200 mL of ether extract after the two extractions?

b) Instead of using two 100ml portions of ether. a single extraction had been carried out using one 200 mL portion of ether. What weight of Z would be contained in the ether solution under these conditions?

Ko/d = ( in organic layer)/(in water layer)

Let x = Z in organic layer., then 10-x = Z in water layer. Then
8.0 = (x/100mL ether)/[(10-x)/100 mL water]

Solve for x, and go through a second extraction, add the two to find total Z in both ether extracts.

For b part redo with 200 mL instead of 100 mL.
Show your work if you get stuck.

I got x= 8.88 g

the second extraction you mean the same solve, that means I should do 8.88+8.88= total of z?

a) To find the total amount of Z in the 200 mL of ether extract after the two extractions, we need to calculate the amount of Z extracted in each portion of ether and then add them together.

Given:
Partition coefficient (P) = 8.0
Amount of Z dissolved in water = 10.0 g
Volume of water used = 100 mL
Volume of ether used in each extraction = 100 mL

First, let's find the amount of Z in the water solution:
Amount of Z in water = Amount of Z dissolved in water = 10.0 g

Next, let's find the amount of Z extracted in one portion of ether:
Amount of Z extracted in one portion of ether = P * Amount of Z in water
= 8.0 * 10.0 g
= 80.0 g

Since there were two extractions, the total amount of Z in the 200 mL of ether extract is:
Total amount of Z in ether extract = Amount of Z extracted in one portion of ether * Number of extractions
= 80.0 g * 2
= 160.0 g

Therefore, the total amount of Z contained in the 200 mL of ether extract after the two extractions is 160.0 grams.

b) If a single extraction had been carried out using one 200 mL portion of ether, we can calculate the amount of Z in the ether solution under these conditions.

Amount of Z extracted in one 200 mL portion of ether = P * Amount of Z in water
= 8.0 * 10.0 g
= 80.0 g

Therefore, the weight of Z contained in the ether solution under these conditions is 80.0 grams.

To answer these questions, we need to calculate the distribution of the compound Z between water and ether based on the given partition coefficient. The partition coefficient (P) is defined as the ratio of the concentration of the compound in one phase to its concentration in the other phase. In this case, P is given as 8.0.

Let's start with the first question:

a) What is the total amount of Z contained in the 200 mL of ether extract after the two extractions?

To calculate this, we need to determine the amount of Z extracted in each extraction and then add them together.

First, we know that 10.0 g of Z was dissolved in 100 mL of water. Therefore, the initial concentration in water (Cw) can be calculated by taking the ratio of the mass of Z to the volume of water:
Cw = 10.0 g / 100 mL = 0.1 g/mL

Using the partition coefficient (P), we can calculate the concentration in ether (Ce) after the first extraction:
Ce1 = Cw / P = 0.1 g/mL / 8.0 = 0.0125 g/mL

To calculate the amount extracted in the first extraction, we multiply the concentration in ether by the volume of ether used (100 mL):
Amount extracted in the first extraction = Ce1 * Volume of ether = 0.0125 g/mL * 100 mL = 1.25 g

Since we used two portions of ether, we repeat the above calculations for the second extraction:
Cw2 = Cw - Amount extracted in the first extraction = 0.1 g/mL - 1.25 g / 100 mL = 0.1 g/mL - 0.0125 g/mL = 0.0875 g/mL
Ce2 = Cw2 / P = 0.0875 g/mL / 8.0 = 0.01094 g/mL
Amount extracted in the second extraction = Ce2 * Volume of ether = 0.01094 g/mL * 100 mL = 1.094 g

Now, we can find the total amount of Z in the 200 mL of ether extract after the two extractions by summing up the amounts extracted in each extraction:
Total amount of Z = Amount extracted in the first extraction + Amount extracted in the second extraction
Total amount of Z = 1.25 g + 1.094 g = 2.344 g

Therefore, the total amount of Z contained in the 200 mL of ether extract after the two extractions is 2.344 grams.

b) Instead of using two 100 mL portions of ether, a single extraction had been carried out using one 200 mL portion of ether. What weight of Z would be contained in the ether solution under these conditions?

With a single extraction using 200 mL of ether, we just need to calculate the concentration in ether and multiply it by the volume of ether used.

Cw = 0.1 g/mL (from the previous calculations)

Ce_single = Cw / P = 0.1 g/mL / 8.0 = 0.0125 g/mL

Amount of Z in the ether solution with a single extraction = Ce_single * Volume of ether = 0.0125 g/mL * 200 mL = 2.5 g

Therefore, the weight of Z contained in the ether solution with a single extraction using 200 mL of ether is 2.5 grams.