Question

A solution of aminoheptanoic acid, H2N-(CH2).COOH, in m-cresol at a concentration of 3.3 mol amino acid per kg of solution is polymerized to form polyamide. The reaction is found to be second order in the amino acid concentration with a rate constant of 2.74 x 103 kg/mol rnin. Calculate the time required to form polyamide with a number average molecular weight of 55,000 gr/mol.

Answer 1

Explanation:

The given data is as follows.

       Concentration = 3.3 mol

      Rate constant = $2.74 \times 10^{3} kg/mol min$

      Molecular weight = 55000 g/mol

      $\tau = C_{A_{0}} \times \int_{0}^{X_{A}} \frac{dX_{A}}{-r_{A}}$

Initial concentration ($C_{A_{0}}$) of aminoheptanoic is 3.3 kg/mol.

       $-r_{A} = 2.74 \times 10^{3} kg/mol min$

Hence, putting the given values into the above formula as follows.

    $\tau = C_{A_{0}}\times \int_{0}^{X_{A}} \frac{dX_{A}}{-r_{A}}$

              = $\frac{3.3}{2.74 \times 10^{3} kg/mol min} [X_{A}]^{0.1}_{0}$

              = 120.43 min

Thus, we can conclude that total time required to to form polyamide is 120.43 min.