Question

Calculste the r.m.s. speed of hydrogen molecules at s.t.p.

Answer 1

The kinetic theory can be used to calculate the r.m.s. velocity of gas molecules. 

Kinetic energy of a gas molecule = ½ mc2,

where m is the mass and c is the velocity.

Kinetic energy of a gas =   ½ mN c' 2, where N is the number of molecules and c' the root mean square velocity.

In the equation PV =  (1/3) mN c' 2, substitute PV = RT for one mole of a gas and mN = M the molar mass of the gas in kg. 

For hydrogen, mN = M = 2.02 x 10-3 kg/mol, 

Substituting in PV =  (1/3) mN c' 2 = RT we get

c'2 = 3 x 8.31 x 273 /( 2.02 x 10-3 )

The r.m.s. velocity c' = [ 3 x 8.31 x 273 /( 2.02 x 10-3 )]½. 
                                 = 1.84 x 103 m/s.