# the molar atomic mass of lodine is 127 g. A standing wave in a tube filled with iodine gas ta 400 K has nodes that are 6.77 cm apart when the frequency is 1000 Hz. Determine from these data whether iodine gas is monatomic or diatomic.

Deepak Patra
8 years ago
To know iodine gas is monoatomic or diatomic, we have to find out the value of adiabatic gas constant γ.
First we have to find out the speed v of the sound in the iodine gas.
The wavelength λ will be,
λ = 2×6.77 cm
= (2×6.77 cm) (10-2 m/1 cm)
=2×0.0677 m
= 0.1354 m
To obtain the speed v of the sound in the iodine gas, substitute 1000 Hz for f and 0.1354 m for λ in the equation v = fλ,
v = fλ
= (1000 Hz) (0.1354 m)
= (1000 Hz) (1/1 s/1 Hz)(0.1354 m)
= 135 m/s
To obtain the value of adiabatic gas constant γ, substitute 127 g/mol for m, 135 m/s for v, 8.31 J/mol.K for R and 400 K for T in the equation γ = nmv2/RT,
γ = nmv2/RT
= n (127 g/mol) (135 m/s2)2/(8.31 J/mol.K) (400 K)
= n (127 g/mol) (10-3 kg/1 g) (135 m/s2)2/(8.31 J/mol.K) (400 K)
= n (0.696)
As γ is greater than 1, thus n≥2.
If n= 2, then,
γ = n (0.696)
= 2 (0.696)
= 1.39 (which is consistent)
If n= 3, then,
γ = n (0.696)
= 3 (0.696)
= 2.08 (which is not consistent)
From the above observation we conclude that, iodine gas is diatomic.