Question

The molecular weight (M) of a polymer is determined from Mark-Houwink equation by using coefficient \( K = 11.5 \times 10^{-3} \) ml/g and exponent \( a = 0.73 \). If the measured intrinsic viscosity \( [\eta] \) of the solution is \( 6.0 \times 10^2 \) ml/g then the value of \( M \times 10^{-6} \), (rounded off to two decimal places), is \(\underline{\hspace{2cm}}\).

Hint:

Use the Mark-Houwink equation to calculate the molecular weight of a polymer from its intrinsic viscosity and known constants.

Answer 1

Correct Answer: 2.7

The Mark-Houwink equation is given by: \[ [\eta] = K M^a, \] where \( [\eta] \) is the intrinsic viscosity, \( K \) and \( a \) are constants, and \( M \) is the molecular weight. Solving for \( M \), we get: \[ M = \left( \frac{[\eta]}{K} \right)^{1/a}. \] Substituting the given values, we find: \[ M = \left( \frac{6.0 \times 10^2}{11.5 \times 10^{-3}} \right)^{1/0.73} \approx 58.0. \] Thus, the value of \( M \times 10^{-6} \) is \( 58.0 \).