A polymer solution obeys the Mark-Houwink relationship $[\eta] = K M^{a}$ with $K = 1.2\times10^{-4}\,\text{dL g}^{-1}$ and $a = 0.75$. The intrinsic viscosity measured for a 0.5 % (w/v) solution is $[\eta] = 0.85\,\text{dL g}^{-1}$.

(a) Determine the number‑average molecular weight $M_{n}$ of the polymer.

(b) If the repeat unit has a molar mass of 113 g mol$^{-1}$, calculate the degree of polymerisation (DP), rounding to the nearest integer.

Question

A polymer solution obeys the Mark-Houwink relationship $[\eta] = K M^{a}$ with $K = 1.2\times10^{-4}\,\text{dL g}^{-1}$ and $a = 0.75$. The intrinsic viscosity measured for a 0.5 % (w/v) solution is $[\eta] = 0.85\,\text{dL g}^{-1}$.

(a) Determine the number‑average molecular weight $M_{n}$ of the polymer.

(b) If the repeat unit has a molar mass of 113 g mol$^{-1}$, calculate the degree of polymerisation (DP), rounding to the nearest integer.

Accepted Answer

M_n ≈ 1.36×10^5 g mol⁻¹; DP ≈ 1204

Gce Model Questions Vol1 2023 Chemistry Question 48

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