Question

The speed of sound in a diatomic gas is measured at 20°C and found to be 215m/s. What is the molecular weight of this gas? What is the most probable composition of this gas?

Answer 1

The speed of sound in a diatomic gas is

$$v=\sqrt{\frac{\gamma RT}{\Mu}}.$$

For a diatomic gas, with $f=5$ degrees of freedom, the heat capacity ratio is

$$\gamma=1+\frac{2}{f}=1.4.$$

Therefore, we can express and calculate the molecular weight M:

$$\Mu=\frac{\gamma RT}{v^2}=\frac{1.4\cdot8.314\cdot(273+20)}{215^2}=0.074\text{ kg/mol}.$$

The most probable composition of this gas is two atoms of chlorine.