The composition of planetary atmospheres is determined in part by the speeds of the molecules of the constituent gases because the faster-moving molecules can reach escape velocity and leave the planet. Calculate the mean speed of CH4 molecules at 77K and 1500K.

At T = 77k, V = 2.69m/a

At T = 1500K, V = 11.86m/s

Explanation:

Hello,

We're required to find the root mean speed (RMS) of a gas and to do that, we'll have to relate the energy of a gas and its kinetic energy

Ek = 3/2 RT

Ek = ½mv²

½mv² = 3/2 RT

Solve for V

MV² = 3RT

V² = 3RT / M

V = √(3RT/M)

V = velocity or speed of the gas

R = ideal gas constant

T = temperature of the gas

M = molarmass mass of the gas

Molar mass of CH4 = 12 + 4 = 16g/mol

At T = 77k

V = √[((3/2) × 77) / 16]

V = √7.216

V = 2.69m/s

At T = 1500K

V = √[((3/2) × 1500) / 16]

V = √140.625

V = 11.86m/s