The molar atomic mass of iodine is 127 g. A standing wave in a tube filled with iodine gas at 400 K has nodes that are 6.77 cm apart when the frequency is 1000 Hz. We have to determine from these data whether iodine gas is monatomic or diatomic.
|
Solution: Click For PDF Version We will first determine the speed of sound from the data on the standing waves set up in a tube filled with the gas the iodine gas. It is given that the standing waves have nodes that are 6.77 cm. Therefore, the wavelength of the sound waves of frequency 1000 Hz is
Frequency of the sound waves is
Therefore, the speed of sound in the iodine gas is
Speed of
sound is a macroscopic thermodynamic property of molecules. It
depends on the ratio of specific heats,
As the molar mass of the iodine is 127 g, the molar mass of the iodine gas will be
where
We know use the property that for monatomic gas
and for diatomic gas
We have found
that
|
,
temperature, T, and
the molar mass of the molecules, M,
and is given by the relation
if the gas is monatomic, and
if the gas is diatomic. We calculate the value of
,
.
,
therefore