Calculate the molecular weight of a gas that has a root mean square velocity of 269 m s^-1 at 381 K. A) 131 g mol^-1 B) 83.8 g mol^-1 C) 39.9 g mol^-1 D) 20.2 g mol^-1 E) 4.00 g mol^-1

Question

Quizplus · Accepted Answer

The root mean square velocity of a gas is given by the equation:$$v_{rms}=\sqrt{\frac{3RT}{M}}$$where:* $$v_{rms}$$ is the root mean square velocity* $$R$$ is the gas constant* $$T$$ is the temperature* $$M$$ is the molar massWe can rearrange this equation to solve for the molar mass:$$M=\frac{3RT}{v_{rms}^2}$$Plugging in the given values, we get:$$M=\frac{3(8.314 J/mol K)(381 K)}{(269 m/s)^2}=39.9 g/mol$$Therefore, the molecular weight of the gas is 39.9 g/mol.

Calculate the Molecular Weight of a Gas That Has a Root