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?

Question

Kendrick Ibarra

Chemistry

19 February, 23:50

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?

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Jordon Mitchell · 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