  Additive submonoids of $\mathbb{Q}_{\ge 0}$, also known as Puiseux monoids,
are not unique factorization monoids (UFMs) in general. Indeed, the only unique
factorization Puiseux monoids are those generated by one element. However, even
if a Puiseux monoid is not a UFM, it may contain nonzero elements having
exactly one factorization. We call such elements molecules. Molecules were
first investigated by W. Narkiewicz in the context of algebraic number theory.
More recently, F. Gotti and the first author studied molecules in the context
of Puiseux monoids. Here we address some aspects related to the size of the
sets of molecules of various subclasses of Puiseux monoids with different
atomic behaviors. In particular, we positively answer the following recent
realization conjecture: for each $m \in \mathbb{N}_{\ge 2}$ there exists a
numerical monoid whose set of molecules that are not atoms has cardinality $m$.
