Final answer:
The number of cycloalkanes with the molecular formula C6H12 that do not show cis-trans isomerization is 2: cyclohexane and methylcyclopentane.
Step-by-step explanation:
The question is asking for the number of cycloalkanes with the molecular formula C6H12 that cannot exhibit cis-trans isomerization. Cis-trans isomerism requires the presence of two different groups attached to carbons on a cycloalkane that are in either the same side (cis) or opposite sides (trans) of the ring.
However, for a molecule to show such isomerism, certain structural features must be present. For instance, if a cycloalkane has all similar substituents or is symmetrical, it cannot show cis-trans isomerism since flipping the molecule does not produce a different isomer.
In the case of C6H12, the cycloalkanes that cannot show cis-trans isomerization are cyclohexane and methylcyclopentane, as both are symmetrical. Other derivatives of C6H12 where the substituents are the same or the molecules are symmetrical will also not show cis-trans isomerization.
The cycloalkanes that do have the potential for cis-trans isomerization are ones with at least two different substituents on the ring that can be on the same side (cis) or opposite sides (trans). Examples of these include 1-methylcyclopentane (where the methyl group can be axial or equatorial), but it will not count toward our total since it does not have a second different substituent to create cis-trans isomers.
Thus, the correct answer is option A) 2, because only cyclohexane and methylcyclopentane meet the criteria of not having cis-trans isomerization among the C6H12 cycloalkanes.