Page 24 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:35 9in x 6in b985-ch01 Elementary Physical Chemistry

State of Matter. Properties of Gases 9

proportional to the square root of the density, ρ.Thatis

D 1/D 2 = (ρ 2 /ρ 1) (1.17)
Since for an ideal gas PV =(m/M)RT ,where m is the total mass of the
gas and M its molecular weight, we can write

P =(m/V )(RT/M)=(ρ/M)RT (1.18)
It follows that for two gases at a given P and T ,

ρ 2 /ρ 1 = M 2 /M 1 (1.19)
and thus

D 1/D 2 = (M 2/M 1) (1.20)

1.10. Molecular Basis of Graham’s Law
It is natural to suppose that the rate of diffusion is proportional to the

2
root-mean-square velocity, that is, D is proportional to c or to c.
Accordingly,
D 1 /D 2 = c 1 /c 2

= { (3RT/M 1)/ (3RT/M 2)}

= M 2/M 1 (1.21a)
It follows also that for the same gas at different temperatures,

D 1 /D 2 = (T 1 /T 2 ) (1.21b)
and for different gases at the same P and T ,

D 1/D 2 = (M 2/M 1) (1.21c)
in accordance with the kinetic theory of gases.

Example 1.3.

a) Calculate the root-mean-square speed (in ms −1 )ofaH 2 molecule at

T = 298.15 K. The root-mean-square speed is c = (3RT/M). Taking
2 −2
R in Joule (1 J = kg m s )and M in kg mol −1 ,we get
−1
2 −2
c = (3 × 8.3145 kg m s × 298.15 K/0.028 kgmol −1 ) = 515.4m s