The intrinsic viscosity $[\eta]$ of a polymer solution obeys the Mark-Houwink equation $[\eta] = K M^{a}$ with $K = 1.2 \times 10^{-4}\ \text{dL g}^{-1}$ and $a = 0.75$. An experimental measurement gives $[\eta] = 0.85\ \text{dL g}^{-1}$.

(i) Determine the number‑average molecular weight $M_n$ of the polymer.

(ii) If the polymer is formed by step‑growth polymerisation of a monomer of molar mass $M_0 = 100\ \text{g mol}^{-1}$, calculate the average degree of polymerisation $DP_n$.

Question

The intrinsic viscosity $[\eta]$ of a polymer solution obeys the Mark-Houwink equation $[\eta] = K M^{a}$ with $K = 1.2 \times 10^{-4}\ \text{dL g}^{-1}$ and $a = 0.75$. An experimental measurement gives $[\eta] = 0.85\ \text{dL g}^{-1}$.

(i) Determine the number‑average molecular weight $M_n$ of the polymer.

(ii) If the polymer is formed by step‑growth polymerisation of a monomer of molar mass $M_0 = 100\ \text{g mol}^{-1}$, calculate the average degree of polymerisation $DP_n$.

Accepted Answer

(i) $M_n \approx 1.36\times10^{5}\ \text{g mol}^{-1}$\n(ii) $DP_n \approx 1.36\times10^{3}$ (about 1360).

Gce Model Questions Vol1 2021 Chemistry Question 34

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