The carbon atoms on ethane are

Analysis of the Question

The question asks for the hybridization state of the carbon atoms in an ethane molecule. To solve this, we need to look at the bonding structure of ethane ($C_2H_6$).

Concept Explanation

Hybridization is the process of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons in chemical bonds.

In organic chemistry, we determine the hybridization of a carbon atom by counting the number of "sigma bonds" and "lone pairs" attached to it (often called the steric number):

• sp³ hybridization: Occurs when a carbon atom is bonded to 4 other atoms (single bonds only). The geometry is tetrahedral.
• sp² hybridization: Occurs when a carbon atom is bonded to 3 other atoms (usually involves one double bond). The geometry is trigonal planar.
• sp hybridization: Occurs when a carbon atom is bonded to 2 other atoms (usually involves a triple bond or two double bonds). The geometry is linear.

Step-by-Step Solution

1. Write the structure of ethane: Ethane has the formula $C_2H_6$. Each carbon atom is bonded to three hydrogen atoms and one other carbon atom. • Structure: $CH_3 - CH_3$
2. Count the bonds on one carbon atom: • Each carbon atom is bonded to 4 atoms (3 hydrogens and 1 carbon). • All these bonds are single bonds (sigma bonds).
3. Apply the rule: Since each carbon atom is involved in 4 single sigma bonds, the carbon atom must undergo $sp^3$ hybridization (mixing one $s$ orbital and three $p$ orbitals).

Conclusion

Because ethane is a saturated hydrocarbon (an alkane) where every carbon atom is bonded to four other atoms via single bonds, the carbon atoms are $sp^3$ hybridized.

Exam Tip: Remember the "Alkane Rule": All carbons in alkanes are always $sp^3$ hybridized. Carbons in alkenes (with a double bond) are $sp^2$ hybridized, and carbons in alkynes (with a triple bond) are $sp$ hybridized. This shortcut will save you time in the exam hall!