The above answer @A.R Karbassi is correct. To add some more details, following are the generally used conversion methods for greenhouse gas accounting:
1 kg CH4-C = (16/12)*1 kg CH4 = 1.33 kg CH4
1 kg CO2-C = (44/12)*1 kg CO2 =3.67 kg CO2
1 kg N2O-N = (44/28)*1 kg N2O = 1.57 kg N2O
CH4 and N2O emissions rates can be converted to CO2 equivalents using the ‘100-yr global warming potential’ factors as follows:
1 kg N2O = 298 kg CO2 equivalents
1 kg CH4 = 25 kg CO2 equivalents
Please note that, according the most recent IPCC report (IPCC, 2013), the conversion of CH4 into CO2eq. should be:
1 kg CH4 = 34 kg CO2 equivalents
Reference cited:
IPCC (2013) Climate change 2013: the physical science basis. Intergovernmental Panel on Climate Change. Available at https://www.ipcc.ch/report/ar5/wg1/
Dr. Susantha has clearly elaborated. I think you also want to say species are different, then also why it should be expressed in terms of carbon. There are two things: the first one is expressing all radiatively active gases in same unit of stable form to quantify the impact and second comparison of impact.
Carbon is a chemical element which is present in many gases and compounds. For example, carbon combines with oxygen to make carbon dioxide (CO2), and combines with hydrogen to make methane (CH4). The term “carbon” is used in a variety of ways when talking about greenhouse gas emissions, and therefore tends to be ambiguous and potentially confusing. “Carbon” is sometimes used as a shorthand for referring to CO2, or greenhouse gases in general, and it can also be used to express CO2 emissions in terms of the amount of carbon in the CO2. The atomic weight of a carbon atom is 12 and the atomic weight of oxygen is 16, so the total atomic weight of CO2 is 44 (12 + (16 * 2) = 44). This means that a quantity of CO2 can be expressed in terms of the amount of carbon it contains by multiplying the amount of CO2 by 0.27 (12/44). E.g. 1kg of CO2 can be expressed as 0.27kg of carbon, as this is the amount of carbon in the CO2.