7. Gases

Determine which gas would have a root mean square speed of 515.59 m/s at 405 K.

The root mean square speed of gas molecules is 283.0 m/s at a given temperature T when the recorded molar mass is 42.0 g/mol. What would be the root mean square speed for a gas with a molar mass of 152.0 g/mol?

The “escape velocity” for an object to escape from the top of Earth’s atmosphere is 7.1 km/s.

a. At what temperature would the rms speed of a He atom equal this value?

b. The actual temperature at the top of the atmosphere is approximately 200 K. Thus, only a small proportion of He atoms at this temperature are moving fast enough to potentially escape from Earth. Calculate the rms speed of a He atom at 200 K.

c. Calculate the rms speed of a hydrogen molecule at 200 K.

d. Which gas—hydrogen or helium—is more likely to escape Earth’s atmosphere?