You have a 1:1 mass mixture(with 1 mg/mL, with a total of 2mg/mL) of 50nm and 150nm iron oxide nanoparticles (density = 5.24 g/cm^3) in water. You are interested in separating the larger from the smaller by sedimentation in a 5cm cylinder tube at room temperature (295 K) and collecting a certain fraction from the bottom of the flask. You may assume no flocculation and that the particles are dilute enough to not have multi-particle effects.

1. Please calculate the total fraction height (measured from the bottom) that you should collect to have a new ratio of 3:1 of 150nm to 50nm particles. Show all steps
2. If you collected the same fraction but at a new temperature (say, 350K), would your ratio of particles change? If so, how? You may prove this mathematically or prove it conceptually, but you must justify your answer.