Final answer:
The ranking of the flask contents in terms of pressure, average molecular kinetic energy, diffusion rate, total kinetic energy, density, and collision frequency depends on the molecular weights and molar quantities of CH4, Helium (He), and Hydrogen (H2). All are the same temperature and volume, so molecular weight plays a significant role in ranking most properties, except for average molecular kinetic energy, which is the same for all three gases.
Step-by-step explanation:
To rank three 8-L flasks containing 4 g of CH4, He, and H2 gas respectively at 284 K in terms of various properties, we use the ideal gas law and kinetic molecular theory.
(a) Pressure
The pressure of a gas is determined by the number of moles, temperature, and the volume it occupies. Given that all gases are at the same temperature and volume, the number of moles will determine the pressure. In our case, He has the smallest molar mass, followed by H2, then CH4. Since each flask has the same mass of gas, He will have the most moles and thus the highest pressure, and CH4 will have the least. Therefore, the order is B > C > A.
(b) Average Molecular Kinetic Energy
Average molecular kinetic energy is determined by the temperature alone and is identical for all gases at a given temperature by virtue of kinetic molecular theory. Therefore, the order is A = B = C.
(c) Diffusion Rate after Valve is Opened
The diffusion rate is inversely related to the square root of the molar mass of gas (Graham's Law). Helium having the lowest molar mass will diffuse fastest, followed by H2 and then CH4. The order thus is B > C > A.
(d) Total Kinetic Energy of the Molecules
Total kinetic energy of the gas is the sum of kinetic energies of all molecules and is proportional to the temperature and amount (moles) of gas. Since all gases are at the same temperature and we have equal masses of different gases, the gas with the lowest molar mass (He) will have the most moles and thus the highest total kinetic energy. The order is B > C > A.
(e) Density
Density is mass divided by volume. Since each flask has the same mass and volume, density will be determined by the molar mass of the gas. CH4 has the highest molar mass and thus the highest density, whereas He has the lowest. The order is A > C > B.
(f) Collision Frequency
Collision frequency is determined by the speed of the molecules and frequency of collisions with the walls of the container. Since all gases have the same kinetic energy (and thus similar speeds) and are in equal-sized containers, the collision frequency is determined by molecular size and quantity. Helium, being smaller and more abundant in the same volume, will collide more often. The order is B > C > A.