Carbon A is  hybridized because this carbon is only bonded to two other atoms. Carbon B is bonded to four atoms, and would therefore be  hybridized.

Keep in mind that a carbon involved in a triple bond will always be hybridized, a carbon involved in a double bond will be hybridized, and a carbon involved only in single bonds will be hybridized.

The stability of a bond can be compared to others by determining the hybridization of the bond. It helps to remember that the bond with the most s character is considered the most stable.

Carbon dioxide has a carbon that is connected to two oxygens by two double bonds. This means that the carbon has sp hybridization. Since the bond has 50% s character, it is the most stable out of the available compounds.

Methane contains only single bonds and will have an sp³ hybridized carbon, with only 25% s character. Acetone and ethene each contain one double bond and will contain an sp² hybridized carbon with 33% s character.

The initially chiral carbon has an  hybridization. Once treated with ,an oxidizing agent, the secondary alcohol in the compound is oxidized to a ketone. The central carbon is no longer a chiral center (a carbon with a double bond cannot be chiral), and the double bond (pi-bond) formed between carbon and oxygen gives the molecule an  hybridization.

 hybridization is formed with triple bonds, and an  hybridization does not exist. 

In organic chemistry, the trend is that bond length is inversely proportional to bond energy. Shorter bonds result in a higher bond energy. The double bond in ethene is the shortest bond out of all the others. As a result, it has the highest bond energy.

Note that in benzene there are three double bonds and three single bonds between carbons, however, resonance means that each of these only has partial double bond character, and is therefore longer than a pure double bond.

The allyl cation involves resonance, as the double bond is delocalized; thus, each carbon-carbon bond will have an identical length somewhere between a pure single and pure double bond. The average bond length will be the average of a single bond and double bond, which is 1.44 Angstroms.

It helps to remember that bond energy is inversely proportional to bond length. In other words, the shorter the bond, the higher the bond energy.

Bond length is shortened when pi bonds are involved, so double and triple bonds are much shorter than simple sigma bonds. The bond length between the carbons in ethyne is the shortest out of all options because they are triple bonded to one another. This also makes it the most stable bond, and gives it the largest bond energy.

Benzene and 1,3-butadiene will have relatively high energy stored in double bonds, but will be unable to match a triple bond. Propane has only single bonds and will have the lowest bond energy of these answers.

The C–N bond is a single bond, and the carbonyl bond is a double bond. Double bonds are stronger and shorter than single bonds.

Both ammonia and methane display sp³ hybridization, however, methane is surrounded by four hydrogens, while nitrogen is surrounded by three hydrogens and a lone electron pair. Lone electron pairs in a molecule require more room compared to bonding atom pairs, as they generate more electron repulsion. As a result, the lone pair in ammonia will make the bond angles in ammonia smaller than the bond angles in the methane molecule. 

 *Extra information: the bond angles in methane are 109.5^o, while ammonia has bond angles of 107^o.

Recall that electronic structure refers to the geometry of the atoms and lone pairs around the central atom, while the molecular structure refers strictly to the geometry of the atoms of the molecule. , , and  all adopt a tetrahedral electronic geometry; however, when considering just the atoms, only NH₃ has a trigonal pyramidal geometry.  is trigonal planar, while is linear.

Acetic acid has the formula . This compound is common enough that the IUPAC name will rarely be given, and you will need to recognize it by common name alone.

The carbonyl carbon exhibits  hybridization, and has no lone electron pairs. There are three atoms bonded around the carbon. In order for the atoms to be farthest away from one another, they will all orient themselves at  angles within the same plane. This results in a trigonal planar geometry.

An atom with four bonds and no lone pairs will show tetrahedral geometry. An atom with two bonds and one lone pair will be bent. Trigonal pyramidal geometry results from three bonded atoms and one lone pair.