How does the carboxly group bond and why do they bond

Question

Having trouble with this question for a while how do they bond such as "why does bond with carbon with a double bond"

Answer 1

Look at the electron configuration of oxygen:  1s² 2s² 2p² 2p¹ 2p¹ so it has bonding electrons in the 2p_y and 2p_z orbitals. Now look at hybridized carbon, i.e. sp² hydridized carbon.  There are 3 sp² hybridized orbitals. The bond that is formed between C and O is a double bond consisting of 1 sigma bond and a pi bond (the p orbital electrons).  It is difficult to explain in words, but if you look up sp2 hybridized orbitals of carbon, you may be better able to see how this happens.