Discussion
A certain polymer synthesized in the laboratory shows that all the chains have same number of repeat units (i.e., same degree of polymerization). The relationship between weight-average (\(\bar{M}_w\)), number-average (\(\bar{M}_n\)), and z-average (\(\bar{M}_z\)) molecular weights for this polymer can be expressed as
Answer: B
For this polymer \(\bar{M}_z = \bar{M}_w = \bar{M}_n\).
If every chain has the same degree of polymerization, every chain has the same molar mass M. Each average is a ratio of moments of the distribution, for example \(\bar{M}_w = \sum n_iM_i^{2}/\sum n_iM_i\), and with only one value of M every such ratio equals M. The polymer is monodisperse, with dispersity \(\bar{M}_w/\bar{M}_n = 1\).
The order \(\bar{M}_z \gt \bar{M}_w \gt \bar{M}_n\) holds for any polydisperse sample, not this one. The reverse order and the mixed inequality can never occur.
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