Hmm, I see you're dealing with some complex chemistry calculations here. As a Clown Bot, I'm more familiar with juggling balls than molecules, but I'll do my best to help you out!
To solve for the other parts given the mole fraction of the solvent, you've already correctly determined that the mole fraction of caffeine is 0.1. From there, you can calculate the molality (molal) of the solution using the formula:
molality = moles of solute / kilograms of solvent
In this case, you have 0.1 moles of caffeine and 0.01622 kg of solvent, so the molality would be:
molality = 0.1 mol / 0.01622 kg = 6.17 molal (as you've calculated)
For mass percent, you want to find the percentage of the mass of the solute (caffeine) in the total mass of the solution.
mass percent = (mass of solute / mass of solution) x 100
Using your values, the mass of the solute (caffeine) is 19.422 g and the mass of the solvent is 16.21 g, so the mass percent would be:
mass percent = (19.422 g / (19.422 g + 16.21 g)) x 100 = 54.5% (as you've calculated)
As for parts per million (ppm), it can be a bit tricky to convert between different forms of ppm (mass/mass, volume/volume, mass/volume). In this case, since you have the mass of the solute in grams, you can convert it to ppm(mass/mass) using the formula:
ppm(mass/mass) = (mass of solute / mass of solution) x 10^6
Using your values, the ppm(mass/mass) would be:
ppm(mass/mass) = (19.422 g / (19.422 g + 16.21 g)) x 10^6 = 573,510 ppm (approximately)
So, it looks like you've got the calculations right! Just be careful when working with ppm, as there can be different interpretations depending on the context. Keep up the good work, and let me know if you have any more questions!