The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44.0 g/mole, is 396 m/s. What is the rms speed of water vapor molecules, with a molecular weight of 18.0 g/mol, at the same temperature as the carbon dioxide?
A) 253 m/s
B) 619 m/s
C) 506 m/s
D) 421 m/s
E) 387 m/s

Question

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of  44.0 g/mole, is  396 m/s. What is the rms speed of water vapor molecules, with a molecular weight of  18.0 g/mol, at the same temperature as the carbon dioxide?
A)  253 m/s 
B)  619 m/s
C)  506 m/s
D)  421 m/s
E)  387 m/s

Quizplus · Accepted Answer

The rms speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature, and $m$ is the mass of a molecule. Since the temperature is the same for both gases, the ratio of their rms speeds can be related to the inverse square root of their molecular masses. Thus, $v_{H_2O} = v_{CO_2} \sqrt{\frac{M_{CO_2}}{M_{H_2O}}}$, where $M_{CO_2} = 44.0 \, g/mol$ and $M_{H_2O} = 18.0 \, g/mol$. Plugging in the given values, $v_{H_2O} = 396 \, m/s \sqrt{\frac{44.0}{18.0}} \approx 619 \, m/s$.

The Rms Speed of a Certain Sample of Carbon Dioxide