Question

Would water molecules in Venus’ atmosphere, whose temperature is 740 K, escape into outer space? A water molecule has a mass that is 18 times that of a hydrogen atom. Recall that gas eventually will escape if the average velocity of its atoms is greater than 1/6 times the escape velocity of the planet. The escape velocity of Venus is 10 km/s.

Answer 1

The water molecule cannot escape, since the average velocity of the water molecules is less than one sixth of the escape velocity of venus.

Step-by-step explanation:

The average speed of gas molecules is given by:

`v_(rms)=\sqrt{(3RT)/(M)}`

R is the gas constant, T is the temperature and M the molar mass of the gas.

We know that a water molecule has a mass that is 18 times that of a hydrogen atom:

`M_H=1.01*10^(-3)(kg)/(mol)\\M_(H2O)=18M_H=0.02(kg)/(mol)`

So, we have:

`v_(rms)=\sqrt{(3(8.314(J)/(mol \cdot K))740K)/(0.02(kg)/(mol))}\\v_(rms)=960.65(m)/(s)*(1km)/(1000m)=0.96(km)/(s)`

The water molecule cannot escape, since the average velocity of the water molecules is less than one sixth of the escape velocity of venus:

`10(km)/(s)*(1)/(6)=1.6(km)/(s)\\0.96(km)/(s)<1.6(km)/(s)`