Question

The escape velocity required for gas molecules to overcome the earth's gravity and go off to outer space is 1.12 *10^3 m/s at 15 degrees Celsius. Calculate the molar mass of a species with that velocity. Would you expect He or H2 molecules in the earth's atmosphere? How about argon atoms?

Answer 1

The escape velocity required for gas molecules to overcome the Earth's gravity and go off to outer space is 1.12x10^3 m/s at 15 degrees Celcius.

We need to calculate the rms or root mean speed of the gas. So, the velocity of the gas must be 1.12x10^3 m/s.

v = √((3RT)/M)

where R = gas constant
T = temperature of the gas in Kelvin
M = molar mass of the gas

1.12x10^3 m/s = √((3*8.314*(15+273))/M)

Solve for M