From this post:

There is a cute little number called Loschmidt, the number of molecules in a cubic meter of air at 1 atm and 0° C, 2.6867774(47) x 10²⁵ molecules/m³ …

Eli Rabett provides a neat way to see why, even if the mix of CO₂ in atmosphere seems low, there are a whopping number of them holding on to excess Earth-generated infrared.

On average a 15 micron photon at the surface will travel a couple of meters before it is absorbed[.]

See the linked text above for the details.

Update, 2016-04-12

More fun from Eli, where he dissects Dr Peter Ward, who posted alternative-ish one and alternative-ish two. The discussion with Ward where this came up is illuminating. In short, he claims, essentially, that all physical calculations pertaining to atmosphere are now being done incorrectly, and he knows the right direction, but none of the details. For example, from JohnMashey‘s summary in comments:

There has been a fundamental misunderstanding in physics about what radiant energy is and how it should be calculated. Natural philosophers and scientists have debated for 2400 years whether light travels as waves or as particles. New observations show that light and other forms of electromagnetic radiation travel simply as frequency, in a manner similar to the signal from your cellphone or a radio station, and that the thermal energy involved is simply equal to frequency times a constant, representing the energy of the atomic oscillators which are the sources of radiation. It turns out that the energy of ultraviolet B radiation is actually 48 times greater -48 times “hotter”- than the energy of infrared radiation, confirming common experience. There simply is not enough energy involved with greenhouse gases for them to play a significant role in global warming.

Sorry, Dr Ward, an alternative scientific hypothesis does not rise to the level of worth-spending-time-on until the proponent does all the details. Otherwise the present science, which does offer a reproducible means of doing calculations which are corroborated by observation and make sense in physical theory, continues to win.