Would the trajectory of a pellet shot from an air rifle be different whether using the same pressure of various gasses, for example charging with air vs. a heavier gas such as carbon dioxide? That is, would the heavier gas impart more energy to the projectile?

How the gas expands will matter, but the relevant energy will be PV. What matters is if the expansion happens with or without heat flow or temperature change, because those will potentially rob the system of some energy, and that's where the molecule will matter. Adiabatic expansion depends on the specific heat values (c_p and c_v) of the gas

 

http://www.ux1.eiu.edu/~cfadd/1150/14Thermo/work.html

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html

The work obtained in adiabatic expansion from the same initial pressure and volume depends on the gas' gamma.

 

For a big expansion factor, the main effect is that the enthalpy available in the gas changes significantly with the gas: bigger with carbon dioxide, which has more degrees of freedom than a diatomic gas like air, hence stores more energy.

 

The second effect is that the conversion of enthalpy to work is slightly less efficient - for a given expansion ratio - if the gas has more degrees of freedom.

Edit already...

 

I implicitly supposed that a small amount of gas is introduced in the rifle and expands much over the bullet's travel.

Swansont may have supposed that gas is replenished during the bullet's travel.

 

Also, depending on the gas pressure in the rifle, carbon dioxide can be very far from an ideal gas, and then the gamma story doesn't hold as is. It gets complicated, and people introduce an artifical gamma which isn't a constant any more. And at 70bar and 300K, carbon dioxide would even be a liquid, nearly critical, which changes everything.

http://encyclopedia.airliquide.com/encyclopedia.asp?GasID=26

http://encyclopedia.airliquide.com/images_encyclopedie/VaporPressureGraph/Carbon_dioxide_Vapor_Pressure.GIF

Thanks for the responses. It seems far more complex than I suspected. Thermodynamics isn't my strong suit.