Do realistic gravitational differences affect chemistry? Would the lesser gravity of the moon, the microgravity of the space station and lack of Earth's atmosphere make a difference in atomic or chemical reactions?
 A: Any chemistry that relies on convection to mix the constituents is clearly affected by zero gravity.
A candle flame will self-extinguish;  see https://www.youtube.com/watch?v=9zdD7lfB0Fs
When the Apollo-13 astronauts wanted to warm the contents of their liquid oxygen tank, they first needed to turn on the electrically driven stirring motors.  Oops...
Residents on the ISS need fans running all the time to remove exhaled air from around them as they sleep. 
A: Yes. Pressure matters. Pressure on Earth is often a result of gravity. 
Water boils at room temperature in a vacuum. Diamond is stable deep in the earth. At the surface, it (very slowly) turns to graphite. 
A: Just to be contrary to @mmesser314's answer, No. That is, pressure effects aside, see, e.g., http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/couple.html#c5 where it shows that the gravitational force between an electron and proton is some $10^{39}$ times weaker than the electromagnetic force between them. And that's a real small perturbation by anybody's standards (i.e., a little technically, solutions to any kind of pde's involving Hamiltionians wouldn't be measurably affected).
For example, the Earth's mass is $\sim6\times10^{24}\mbox{kg}$, so one part in $10^{39}$ is like adding $\sim10^{-11}\mbox{gm}$ to the Earth, which is about the mass of a single E.Coli bacterium (as per https://hypertextbook.com/facts/2003/LouisSiu.shtml). So you might somewhat loosely compare the effect of gravity on chemical reactions to the effect of a single E.Coli bacterium on the Moon's orbit around the Earth.
And for a kind of converse example, if the electromagnetic force were as weak as gravity, then the (first Bohr) radius of hydrogen atom (about $5.3\times10^{-11}\mbox{m}$) would instead be roughly the distance from Earth to the nearest star (besides the Sun).
