4. A 300-ml aqueous solution containing 40 g compound A is to be extracted with ether. The solubility of compound A in either at room temperature is 20 g per 100 ml and in water is 13.3 g per 100 ml. calculate the weight of the compound that would be recovered by extraction with (a) two 150 ml portions of ether and (b) one 300-ml portion of ether.
First, determine K.
Ko/a = 20/13.3
Then K = (org layer)/(aq layer)
For part b.
Let x = grams in org layer; then 40-x = grams in aq layer. Then
(organic layer) = x/300
(aqueous layer) = (40-x)/300
K = (x/300)/(40-x)/300
Solve for x and 40-x.
For part a use the same set up but go through the equation twice with 150 mL each. Two extractions with half the amount will ALWAYS extract more.
To calculate the weight of the compound that would be recovered by extraction, we need to consider the solubilities of the compound in ether and water and the volume of the solution.
Let's break down the problem and solve it step by step:
Step 1: Calculate the volume of compound A in the initial solution.
Given:
- Volume of the initial solution = 300 ml
- Mass of compound A in the initial solution = 40 g
We know that the density of water is 1 g/ml. So the mass of water in the initial solution is:
Mass of water = Volume of initial solution - Mass of compound A
Mass of water = 300 ml - 40 g = 260 g
Step 2: Calculate the mass of compound A that would dissolve in water.
Given:
- Solubility of compound A in water = 13.3 g per 100 ml
To calculate the mass of compound A that would dissolve in water, we can use the following proportion:
Mass of compound A / Volume of water = Solubility of compound A in water / 100 ml
Mass of compound A = (Solubility of compound A in water / 100 ml) * Volume of water
Mass of compound A = (13.3 g/100 ml) * 260 g = 34.58 g
Step 3: Calculate the mass of compound A that would dissolve in ether.
Given:
- Solubility of compound A in ether = 20 g per 100 ml
To calculate the mass of compound A that would dissolve in ether, we can use the same proportion as in step 2:
Mass of compound A in ether = (Solubility of compound A in ether / 100 ml) * Volume of ether
(a) If we use two 150 ml portions of ether:
Mass of compound A in ether = (20 g/100 ml) * 150 ml + (20 g/100 ml) * 150 ml = 60 g
(b) If we use one 300 ml portion of ether:
Mass of compound A in ether = (20 g/100 ml) * 300 ml = 60 g
Therefore, the weight of the compound that would be recovered by extraction is:
(a) 60 g when using two 150 ml portions of ether
(b) 60 g when using one 300 ml portion of ether.