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What causes methane to have 25 times higher global warming potential than $\ce{CO2}$?

I think it has to do with $\ce{CH4}$ being a less massive molecule, but I'm not sure.

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First we have to look how the greenhouse effect works for all gases:

Light with a wavelength not absorbed by the atmosphere gets absorbed by the soil and heats up the earth. Because of black body radiation for 300K the earth starts to emit light itself with a maximum in the IR spectrum. Light with this frequency gets readily absorbed by vibrational excitation of molecules. But one has to keep in mind that intensity of absorption between different molecules and even between different vibration in one molecule differs a lot. This can not be explained with mass, or just vibration itself you actually have to look at https://en.wikipedia.org/wiki/Transition_dipole_moment or https://en.wikipedia.org/wiki/Selection_rule

But just believe me for a moment, methane is actually very bad at absorbing infrared light. Especially its by far worse than Water or $CO_2$.

But then there is another effect. You can not absorb more light than there actually is. So if you practically absorb 100% of the light for a given frequency then there is no effect in increasing the concentration of the molecule absorbing this frequency.

Both water and $CO_2$ absorb with nearly 100% in their frequency range (compare fig. 1 which shows the IR absorption of the atmosphere). So in order to absorb more light you have to absorb in other frequency ranges.

IR absorption of the atmosphere

This is where methane gets its role. If you look at figure 2 and keep in mind to change the wavenumber into wavelengths you will see that it absorbs in a frequency range that is covered neither by water nor by $CO_2$.

IR spectrum of methane

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Yeah I found answer It is because methane is able to absorb the infrared radiation that pass through carbon dioxide, which causes the molecule to vibrate and generate heat

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    $\begingroup$ Just keep in mind that all molecules vibrate and hence all molecules absorb some infrared radiation, only in different frequency ranges. Methane just happens to cover the range which is important to us. $\endgroup$ – Ivan Neretin Sep 24 '15 at 6:17

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