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A Polymer has the following composition: 100 Molecules of molecular mass 1000, 200 molecules of molecular mass 2000 and 500 molecules of molecular mass 5000. Calculate the number and weight average of molecular weight and the polydispersity index. (P…

Q.3 (a) A Polymer has the following composition: 100 Molecules of molecular mass 1000, 200 molecules of molecular mass 2000 and 500 molecules of molecular mass 5000. Calculate the number and weight average of molecular weight and the polydispersity index. (PI)

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Best answer

Given:

NiMiNiMiNiMi2
10010001.0 × 1051.0 × 108
20020004.0 × 1058.0 × 108
500500025.0 × 105125.0 × 108
Σ = 80030.0 × 105134.0 × 108

Number-average molecular weight:

\( \bar M_n = \dfrac{\sum N_iM_i}{\sum N_i} = \dfrac{3.0\times10^6}{800} = 3750 \)

Weight-average molecular weight:

\( \bar M_w = \dfrac{\sum N_iM_i^2}{\sum N_iM_i} = \dfrac{1.34\times10^{10}}{3.0\times10^6} = 4466.67 \)

Polydispersity index:

\( PDI = \dfrac{\bar M_w}{\bar M_n} = \dfrac{4466.67}{3750} = 1.19 \)

M̄n = 3750; M̄w ≈ 4467; PDI ≈ 1.19. PDI is greater than 1, so the polymer is polydisperse.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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