Chemistry - Why don't gases escape Earth's atmosphere?
Solution 1:
The atmosphere actually loses gases to outer space.
The average velocity $\bar v$ of gas molecules is determined by temperature $T$. However, not all the molecules travel with the same velocity. The probability of finding a molecule with a velocity near $v$ is described by the Maxwell distribution of speeds $$\begin{align} f{\left(v\right)}&=4\pi\sqrt{{\left(\frac m{2\pi kT}\right)}^3}v^2\exp\left(-\frac{m{v^2}}{2kT}\right)\\[6pt] &=4\pi\sqrt{{\left(\frac M{2\pi RT}\right)}^3}v^2\exp\left(-\frac{M{v^2}}{2RT}\right) \end{align}$$ where $m$ is the mass of the molecule, $k$ is the Boltzmann constant, $M$ is the molar mass of the gas, and $R$ is the molar gas constant.
Individual molecules may reach escape velocity $v_\mathrm e$ and thus be able to leave the atmosphere.
Escape velocity is the minimum velocity that is sufficient for an object to escape from the gravitational attraction of a massive body. For a planet, the escape velocity may be estimated by using the formula $${v_\mathrm e}=\sqrt{\frac{2Gm_\text{planet}}r}$$ where $G$ is the gravitational constant, $m_\text{planet}$ is the mass of the planet, and $r$ is the distance from the centre of mass of the planet.
Therefore, atmospheric escape depends on the mass of the planet, the temperature of the atmosphere, and the molar mass of the gas.
Solution 2:
Actually some do. There is a problem of helium escaping the earth's atmosphere.
https://en.wikipedia.org/wiki/Atmospheric_escape
There are many other sources about this very problematic occurrence.
Solution 3:
Lighter gases don't go up after they've mixed with the surrounding atmosphere. Buoyancy (like with a balloon filled with $\ce{He}$ rising or $\ce{CO_2}$ from a leak in a line dropping to the floor and filling the room) occurs only with bulk masses.
You need extreme g fields/gradients, like in a ultracentrifuge, to separate gases by weight.
There is a certain net flux of light compounds upwards, because e.g. $\ce{He}$ (from radioactive decay) comes into the atmosphere at the ground and escapes into space from the upper layers (see other answer).