Question

A mixture of gasses at STP is 42.0% nitrogen, 26.5% oxygen, and 31.5% carbon dioxide by volume.

1st choice	N2
2nd choice	O2
3rd choice	CO2

Part A: Rank these gasses in order of increasing average kinetic energy
Part B: Rank these gasses in order of increasing rms velocity (average molecular speed)
Part C: Rank these gasses in order of increasing time required to diffuse across a room

Answer 1

Part A : According to the kinetic theory of gases the expression for average kinetic energy of gas is given by,

Average Kinetic Energy = (3RT/2) , where R is the universal gas constant and T is the temperature of the gas.

Therefore, kinetic energy of a gas is independent of the molar mass of the gas and only depends upon the temperature of the gas. Since, here all the gases are at same temperature, so the average kinetic energy of all three gases will be same.

Therefore, average kinetic energy of N₂ = O₂ = CO₂

Part B : According to the kinetic theory of gases the expression for root mean square velocity (rms) of gas is given by,

rms velocity = (3RT/M)^1/2 , where R is the universal gas constant, T is the temperature and M is the molar mass of the gas.

So, rms velocity of a gas is inversely proportional with the square root of molar mass of the gas. Higher the molar mass of the gas lower is the rms velocity at constant temperature.

Now, molar mass of N₂ = 28 g/mol, molar mass of O₂ = 32 g/mol and molar mass of CO₂ = 44 g/mol.

Since, the molar mass of N₂ < O₂ < CO₂ thus the rms velocity order will be as - CO₂ < O₂ < N₂

Part C : According to the Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the molar mass of the gas at constant temperature. So, higher the molar mass of the gas , lower the rate of diffusion of the gas.

Since, the molar mass of N₂ < O₂ < CO₂ thus the rate of diffusion  order will be as - CO₂ < O₂ < N_2.