Answer:
The water molecule cannot escape, since the average velocity of the water molecules is less than one sixth of the escape velocity of venus.
Explanation:
The average speed of gas molecules is given by:
[tex]v_{rms}=\sqrt{\frac{3RT}{M}}[/tex]
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:
[tex]M_H=1.01*10^{-3}\frac{kg}{mol}\\M_{H2O}=18M_H=0.02\frac{kg}{mol}[/tex]
So, we have:
[tex]v_{rms}=\sqrt{\frac{3(8.314\frac{J}{mol \cdot K})740K}{0.02\frac{kg}{mol}}}\\v_{rms}=960.65\frac{m}{s}*\frac{1km}{1000m}=0.96\frac{km}{s}[/tex]
The water molecule cannot escape, since the average velocity of the water molecules is less than one sixth of the escape velocity of venus:
[tex]10\frac{km}{s}*\frac{1}{6}=1.6\frac{km}{s}\\0.96\frac{km}{s}<1.6\frac{km}{s}[/tex]
