A little orgo for me and you?

[NexusMD]

Ok, so I am taking orgo 1 right now and I am completely stumped. Any one have any ideas on how to answer this lab question?

A crude sample has a mass of 3.4 grams; 3.1 grams of this sample are compound P [the desired material] and 0.3 grams of impurity I. A student in an organic chemistry lab was assigned the project of purifying compound P by the technique of recrystallization.
Compound P and impurity I have the following solubility properties in the recrystallization solvent. These solubility properties of compound P and impurity I in the recrystallization solvent are for these two components individually and in the presence of one another.
Solubility in Recrystallization Solvent
Compound P 0.4g/mL 75oC
Impurity I 0.3g/mL 75oC
Compound P 0.1g/mL 10oC
Impurity I 0.1g/mL 10oC
Based upon the above information, what is the percent recovery of compound P? Calculate the percent recovery of compound P on the amount of compound P in the initial crude sample.

How would I solve this problem? If it seems trivial to you, I apologize. I am just really confused

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[Disinence2]

O chem lab sucks...

 

[punkindrublic]

I may be off here, as I've never seen a question like this before (our course is highly anti-math), but here goes:

First you want to find the mimimum amount of solvent necessary to dissolve the compound, which comes out to 7.75mL (3.1g/0.4ml/g). You don't need to worry about the impurity because it will all be dissolved since the properties are the same for each alone or together.

Now you've got everything dissolved at 75c so you let it cool to room temp, then toss 'er into the ol' ice bath until it hits 10c. At that point, only 0.1g of product will remain in solution per mL solvent, so with 7.75mL, 0.775g of product will remain in solution, and we can see that all of the impurity will be as well since the solubility is the same. When it's all said and done, you have:

(3.1-0.775)/3.1*100 = 75% yield.

Recrystallization sucks.