GATE 2023 CY – Question 61
Polystyrene in toluene has intrinsic viscosity 84 cm$^3$/g at 30 °C. It follows Mark–Houwink with $K=1.05\times10^{-2}$ cm$^3$/g and $a=0.75$. Its molecular weight is ______ $\times10^3$ g/mol (nearest integer).
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Correct answer: 158 to 160
Explanation
Mark–Houwink gives[η]=KM^a.
Thus M=(84/0.0105)^(1/0.75)=8000^(4/3)=160000 g/mol. In the requested 10³g/mol units, this is **160**, inside the official 158–160 interval. The exponent must be inverted when solving for M.