Arrange them in order of greatest to least Molar Mass to get most dense to least dense at a given temperature and pressure.
Explanation:
"Given Temperature and Pressure" just tells you that those two variables are being held constant. The Ideal Gas Law (PV = nRT) shows that n (the # of moles) and V (the volume) are variable still. To keep pressure constant, we need to increase the volume so that the force per area is the same which would unfortunately lower the density. The only way for a gas to have the greatest density would be to have the least average kinetic energy to keep the pressure constant at a smaller volume. This is because kinetic energy is equal to KE = 1/2 m v^2, where m is mass in kilograms and v is the velocity. IT IS CRUCIAL TO NOTE THAT ACCORDING TO KINETIC MOLECULAR THEORY, ALL GASES HAVE THE SAME AVG. KINETIC ENERGY WHEN AT THE SAME TEMPERATURE. So since the avg. KE is also constant across these answers due to the temp. being constant, our only way to decrease the velocity (the rate at which the particles are moving per second) and in turn the number of collisions (to repeat, a smaller number of collisions is desired because they are equal to the pressure that must maintained at a constant value at the smallest volume possible to achieve highest density possible) is to increase the molar mass. This is also pretty intutive for the other part of the issue: since Density is a broken heart (m/v), a higher molar mass would ensure a smaller pressure (due to decreased velocity) and smaller volume (due to constant pressure). Okay, now order the gases heaviest to lightest in terms of molar mass and you got your answer. Please gimme brainliest if this helped bc it took 15 minutes to type out. Hope this helped you! :D
