At room temperature, the rms speed of the molecules of certain diatomic gas is found to be 1930 m/s. The gas is

The correct option is H₂.

To identify the diatomic gas, we can use the formula for the root-mean-square (rms) speed of gas molecules:

$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Where:
• $v_{\text{rms}}$ is the root-mean-square speed ($1930\text{m/s}$)
• $R$ is the universal gas constant ($8.314\text{J/(mol}·\text{K)}$)
• $T$ is the absolute temperature at room temperature, which is approximately $300\text{K}$ (or $27\text{°C}$)
• $M$ is the molar mass of the gas in kg/mol

Rearranging the equation to solve for the molar mass ($M$):

$v_{\text{rms}}^{}{}^2=\frac{3RT}{M}$

$M=\frac{3RT}{v_{\text{rms}}^{}}$

Substitute the given values into the equation:

$M=\frac{3\times 8.314\times 300}{{\left(1930\right)}^2}$

$M=\frac{7482.6}{3724900}$

$M\approx 0.00201\text{kg/mol}$

Converting this to grams per mole (g/mol):

$M\approx 2.01\text{g/mol}$

Since the molar mass of hydrogen gas (H₂) is approximately $2\text{g/mol}$, the gas is H₂.