A 20 g mixture containing 95% (by weight) of A and 5% of B is recrystallized in toluene (b.p. 110 C). Solubility for compound A is 1.5 g @20 degrees and 10 g @ 110 degrees. For compound B solubility is 0.5 g @20 degrees and 8 g @ 110 degrees. What amount of solvent is needed to obtain pure A and how much pure A will be recovered?
Nowhere in your problem do you say what the volume is for the solubility. In most cases it is quoted as 100 mL; therefore, I ASSUME that 1.5 g @ 20 C MEANS 1.5 grams A will dissolve in 100 mL toluene at 20 C, etc.
20 g sample is
95%A or 20 x 0.95 = 19 grams A.
5% B or 20 x 0.05 = 1 grams B.
How much toluene do we need to dissolve the 19 g A? It is 100 mL x (19/10) = 190 mL toluene needed to dissolve 19 grams A @ 110 C. Will that dissolve all of the B? Yes, because you have only 1 g B and the solubility of B at 110 C is 8 grams.
Now we cool the 190 mL toluene to 20 C. How much A comes out?
1.5 g x (190/100) = 2.85 grams A dissolve; thus, 19-2.85 = ?? grams recrystallize so your percent recovery (although the problem doesn't ask for that) is (16.15/20)*100 = ??
You may want to check to see if it will be contaminated with B. We had the 1 g B dissolved in 190 mL toluene at 110 C. At 20 C, B dissolves to the extent of
0.5 x (190/100) = 0.95. Since we had 1.0 g B, all of it will stay in solution at the lower temperature. Check my thinking.
yes
now
we need 200 mL, because we want to dissolve all B. To revover pure A
Oh, chemistry, you always know how to make my brain feel "elementary!" Alright, let's crunch some numbers and sprinkle some humor into this chemical concoction.
To obtain pure A, we need to dissolve the 20 g mixture in toluene at its boiling point. But how much toluene should we use? Well, let's check out the solubilities.
At 20 degrees, compound A has a solubility of 1.5 g in 1 g of toluene. So, to dissolve 20 g of compound A, we would need about 13.33 g of toluene. (20 g ÷ 1.5 g/g = 13.33 g)
Similarly, at 110 degrees, compound A has a solubility of 10 g in 1 g of toluene. So, to dissolve 20 g of compound A, we would only need 2 g of toluene. (20 g ÷ 10 g/g = 2 g)
Now let's do the math for compound B!
At 20 degrees, compound B has a solubility of 0.5 g in 1 g of toluene. So, we would need about 10 g of toluene to dissolve the 20 g of compound B. (20 g ÷ 0.5 g/g = 40 g)
At 110 degrees, compound B has a solubility of 8 g in 1 g of toluene. So, we would only need 2.5 g of toluene to dissolve the 20 g of compound B. (20 g ÷ 8 g/g = 2.5 g)
So, to dissolve the entire mixture and obtain pure A, we would need the larger amount of toluene, which is 40 g. (Because we need 13.33 g for A and 40 g for B.)
Now, how much pure A can we recover from this process? Well, we dissolved 20 g of the mixture in 40 g of toluene, so we will have a solution with a total weight of 60 g.
Since compound A initially made up 95% of the mixture by weight, in this solution of 60 g, A will still make up 95% of the total weight.
Therefore, we can recover 57 g of pure A. (60 g × 0.95 = 57 g)
Voila! With 40 g of toluene as our trusty solvent, we can dissolve the mixture and retrieve a delightful 57 g of pure compound A. Happy chemistry-ing, my friend!
To determine the amount of solvent needed to obtain pure A and the amount of pure A that will be recovered, we need to understand the solubility behavior of compounds A and B at different temperatures.
Let's break down the problem step by step:
1. Calculate the amount of A and B in the initial mixture:
- Total weight of the mixture = 20 g
- Percentage of A in the mixture = 95%
- Percentage of B in the mixture = 5%
- Weight of A in the mixture = 0.95 * 20 g = 19 g
- Weight of B in the mixture = 0.05 * 20 g = 1 g
2. Determine the solubility of A and B at the lower temperature (20 degrees Celsius):
- Solubility of A at 20 degrees = 1.5 g
- Solubility of B at 20 degrees = 0.5 g
3. Calculate the minimum solvent required to dissolve all of compound A:
- We want to completely dissolve 19 g of compound A, so we divide it by the solubility at 20 degrees: 19 g / 1.5 g = 12.67 (approximately)
- Therefore, we need at least 12.67 times the solubility volume of the solvent to dissolve all of A.
4. Determine the solubility of A and B at the higher temperature (110 degrees Celsius):
- Solubility of A at 110 degrees = 10 g
- Solubility of B at 110 degrees = 8 g
5. Calculate the maximum amount of A that can be recovered:
- The solubility of A at 110 degrees is greater than the initial weight of A (19 g), indicating that A is completely soluble at this temperature.
- Therefore, we can recover the entire amount of A during recrystallization.
In summary, to obtain pure A, you would need at least 12.67 times the solubility volume of the solvent. During recrystallization, you can recover the entire 19 g of pure A.