Complete the following table for aqueous solutions of caffeine, C8H10O2N4.
a) molality
b) mass percent solvent
c) Ppm solute

All we're given is Mole fraction solvent= .900. How do I solve for the other parts with only this??

It XH2O = 0.9, then
Suppose we have 0.1 mol caffeine and 0.9 mol H2O, we would have those mol fractions listed.
That is Xcaffeine= 0.1/(0.1+0.9) = 0.1.
The same reasoning applies to mols fraction H2O.
Therefore, a solution containing 0.1 mol caffeine (molar mass is 194.2 so 0.1 mol = 19.42 g) and 0.9 mols H2O (18.02 x 0.9 = 16.22 g H2O).
So a solution containing 0.1 mol caffeine + 0.01622 kg solvent is ?? molal.
Check my thinking.
mass percent and ppm solute then should be a piece of cake.

Would you mind checking what I did to make sure I understood this correctly?
I calculated that the solution was 6.17 molal.
To find mass percent, I did
.100 mol x 194.22 g caffeine/1 mol= 19.422 g solute
.900 mol x 18.02 g solvent/1 mol= 16.21 g solvent
19.422/(16.21 + 19.422) x 100= 54.5%
Then to find ppm,
19.422 x 10^6= 1.9422 x 10^7
Is that right?

mass percent is fine.
I don't know what to tell you about ppm. It is used so much in the U.S. and in many many cases incorrectly. The problem is that we can express ppm as grams of solute per million grams of water OR grams of solute per million grams of solution. In dilute solutions that doesn't make much difference because the density of a very dilute solution is the same as that of water, essentially, so the ppm (mass) and the ppm (volume) is the same. It is MUCH better, in analytical chemistry, to express it as milligrams per liter of solution (mg/L) and that way everyone knows what we are talking about.
So 19.42 g/16.22 mL H2O = quite a concentrated solution, the density will not be 1.0 I am sure, so a liter of solution will weigh ?? and ?????.
You have mass percent so that is part caffeine per 100 g solution. That converted to ppm(mass/mass) = 54.5% (I obtained 54.49) is 54.5 grams/100 g solution = 54.5 x 1 x 10^6/100 = 54.5 x 10^4 = 5.45 x 10^5 grams solute per million grams solution or 5.45E5 ppm(mass/mass). In trace element analysis, for example, I may find 1 x 10^-3 g (1 mg) Cu in a liter of solution so I express (Cu)=1 mg/L and I would use that interchangeably with 1 ppm because the difference between the mass of 1 L of water and 1 L of solution is not worth the time of day. I hope I haven't confused you. Wikipedia does a good job of differentiating with this statement (which is not quoted exactly). Many don't bother to define parts per notation because they believe their field is the most important in science; therefore, others read the publicstion and misinterpret the results.

So if I were to go backwards, from a number in ppm to I guess g of solvent (per 100 g of solution), would I be correct in dividing the number given by 10^4 (or 10^6/100)?

yes. Percent by mass is changed to ppm(mass/mass) by multiplying by 10^4.

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