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?

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