The NMR spectrum of a compound can reveal whether the atoms within the
molecule are equivalent or different. For example, the hydrogen atoms in
\(\mathrm{CH}_{2}=\mathrm{CH}_{2}\) are equivalent: they all exist in an
identical environment. However, in \(\mathrm{CH}_{2}=\mathrm{CHCl}\), the two
hydrogen atoms attached to the same carbon atom are equivalent, but different
from the hydrogen atom on the other carbon atom. Predict how many different
types of hydrogen atoms can be identified in the \({ }^{1} \mathrm{H}\) NMR
spectrum of each of the following molecules: (a) \(\mathrm{C}_{2}
\mathrm{H}_{2}\); (b) cis- \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\); (c)
trans- \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\);
(d) \(\mathrm{CH}_{3} \mathrm{OH}\). (c) In the molecule \(\mathrm{C}_{2}
\mathrm{H}_{5} \mathrm{Cl}\), the hydrogen atoms would all be different if the
molecule existed in only one conformation. However, only two types of hydrogen
atoms are detected. Propose an explanation.