First slide

Rms speed

Question

At room Temperature , a diatomic gas is found to have an rms speed of 1930 m/s. The gas is

Moderate

A

H₂
B

Cl₂
C

O₂
D

F₂

Solution

We have
$v_{rms} = \sqrt{\frac{3 RT}{M}} \Rightarrow M = \frac{3 RT}{{v^{2}}_{rms}} \Rightarrow M = \frac{3 \times 8.314 \times 300}{1930 \times 1930} kg / mol = \frac{3 \times 8.314 \times 300}{1930 \times 1930} \times 1000 g / m = 2 g / mol$
Therefore, the gas is H₂

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