Titan, the largest satellite of Saturn has a radius of 2,575 km and a mass of $1.36\times {10}^{23} \mathrm{kg}$. The
NASA Cassini probe has measured its average surface temperature to be $–178°C$. Which of the
following gases would you expect to remain in the atmosphere of Titan (A rule-of-thumb among
astronomers is that if the average speed is below $1/6$ of the escape velocity. The gas will remain for the age of the solar system)

The escape velocity $v_e$ of an object from a planet of radius R is obtained by setting the kinetic energy of the object near the surface equal to the gravitational potential energy difference between the surface and infinity. As the mass of the atoms and molecules m in this case is much smaller than the mass of the satellite, we don’t need to use the reduced mass of the system in the calculation.

$\frac{\mathrm{m}{v}_{\mathrm{e}}^2}{\mathrm{w}}-\frac{\mathrm{GMm}}{\mathrm{R}}=0$

$\Rightarrow v_{\mathrm{e}}={\left[\frac{2\mathrm{GM}}{\mathrm{R}}\right]}^{1/2}=2655\mathrm{m}/\mathrm{s}$

The speed of a gas molecule or atom follows the Maxwell-Boltzzmann distribution. Their average speed, as a function of temperature is given by

$\frac{\mathrm{m}{v}^2}{2}=\frac{3\mathrm{kT}}{2}$

where k is Boltzmann’s constant and T the temperature in Kelvin. The following table
gives the masses and average velocity for the gases in the question.

As the Maxwell-Boltzmann distribution has a long tail in the direction of higher speeds, even though the average speed is below the escape velocity, some molecules (atoms) of gas will escape. A rule-of-thumb among astronomers is that if the average speed is below 1/6 of the escape velocity, the gas will remain for the
age of the solar system. 

So ammonia and methane will remain on Titan, helium would for a shorter time but hydrogen (molecular or atomic) will escape more quickly.