a mixture contains two crystalline solid X and Y. Decide if pure X can be obtained by a proper recrystallization using solvent A. Include the exact volumes of solvent used and the amount of pure X obtained.
GIVEN:
Solubility of X in boiling A :200mg/ml
solubility of X at room temp.: 20mg/ml
solubility of Y at boiling A : 200mg/ml
solubility of Y at room temp.: 20mg/ml
amount of X in mixture: 400mg
amount of Y in mixture: 30mg
Suppose you take 2 mL of boiling A.
X = 2 mL x 200 mg/mL = 400 mg so all of X will dissolve.
Y = 2 mL x 200 mg/mL = 400 mg so all of Y will dissolve.
Now cool the solution to room temperature. How much X and Y will recrystallize?
2 mL x 20 mg/mL = 40 mg X will stay in solution; 400 - 40 = 360 mg X will crystallize.
For Y,
2 mL x 20 mg/mL = 40 mg Y will stay in solution; you had only 30 so none will crystallize.
I'm guessing that 2mL of boiling A came from (400mg)(1mL/200mg)= 2mL
So we don't have worry about the Y at boiling A? which will be 0.15mL if we do the calculation.
You add enough boiling A to dissolve all of X (of course it will dissolver all of Y, too). Using 0.15 mL of boiling A will dissolve all of Y and some of X. In fact I suppose you could get pure X this way, too, although it isn't the usual way we think of recrystallization.
200 mg/mL x 0.15 mL = 30 mg X will dissolve leaving 400-30 = 370 mg X behind, BUT
1. 0.15 mL is a small volume to be working with, and you would have trouble controlling the volume and losing volume as it sticks to the walls of the vessel,
2. I would want to add just a little more than 0.15 because this JUST barely gets all of Y in solution.
3. I doubt this is the way your prof expects you to answer.
I was also thinking so we can't add the two volume of A together? So like for X in boiling A there is 2mL and in Y there is 0.15ml. So all together solvent A would be 2.15mL.
all of Y would still be gone but for X instead of 360mg i would get 357mg
In general, we assume that we need only one volume. In this case, however, an extra 0.15 mL couldn't hurt anything. As you point, however, it affects the yield.
To determine if pure X can be obtained by recrystallization using solvent A, we need to compare the solubility of X and Y in solvent A at different temperatures.
1. Calculate the maximum amount of X that can dissolve in solvent A at boiling temperature:
Solubility of X in boiling A: 200 mg/ml
Volume of solvent used: Let's assume V ml
Therefore, the maximum amount of X dissolved = 200 mg/ml * V ml
2. Calculate the maximum amount of X that can dissolve in solvent A at room temperature:
Solubility of X at room temperature: 20 mg/ml
Volume of solvent used: Let's assume V ml
Therefore, the maximum amount of X dissolved = 20 mg/ml * V ml
3. Calculate the minimum volume of solvent A required to dissolve all the Y:
Amount of Y in the mixture: 30 mg
Solubility of Y at boiling A: 200 mg/ml
Minimum volume of solvent A required to dissolve Y = 30 mg / 200 mg/ml
If the minimum volume of solvent A required to dissolve Y is greater than the maximum volume of solvent A required to dissolve X at both boiling and room temperature, then it is possible to obtain pure X by recrystallization using solvent A. Otherwise, it is not possible.
4. Calculate the amount of pure X obtained:
Amount of X in the original mixture: 400 mg
Amount of X that can dissolve in solvent A: Minimum of the maximum amount of X dissolved at boiling and room temperature
Amount of pure X obtained = 400 mg - (maximum amount of X dissolved)
Remember to round the volumes and amounts to the appropriate number of significant figures.
By following these steps, you can determine if pure X can be obtained using solvent A and calculate the exact volumes of solvent used and the amount of pure X obtained.