(CO2) (O2) (He) (N2) (CH4) (Imagine these are balloons with the specified gas inside)

Above are five identical balloons, each filled to the same volume at 25°C and 1.0 atm

Which balloon contains the molecules with the greatest average speed? Which has the Lowest average speed?

Highest speed: He

Lowest speed: CO2

Explanation:

The rms speed (average speed) of the molecules/atoms in an ideal gas is given by:

where

R is the gas constant

T is the absolute temperature of the gas

M is the molar mass of the gas, which is the mass of the gas per unit mole

From the equation, we see that at equal temperatures, the speed of the molecules in the gas is inversely proportional to the molar mass: the higher the molar mass, the lower the speed, and vice-versa.

In this problem, we have 5 gases:

(CO2) (O2) (He) (N2) (CH4)

Their molar mass is:

CO2: 44 g/mol

O2: 16 g/mol

He: 4 g/mol

N2: 14 g/mol

CH4: 16 g/mol

The gas with lowest molar mass is Helium (He): therefore, this is the gas with greatest average speed.

The gas with highest molar mass is CO2: therefore, this is the gas with lowest average speed.