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

Step-by-step explanation:

The given data is as follows.

Concentration = 3.3 mol

Rate constant =
`2.74 * 10^(3) kg/mol min`

Molecular weight = 55000 g/mol

`\tau = C_{A_(0)} * \int_(0)^{X_(A)} (dX_(A))/(-r_(A))`

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

`-r_(A) = 2.74 * 10^(3) kg/mol min`

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

`\tau = C_{A_(0)}* \int_(0)^{X_(A)} (dX_(A))/(-r_(A))`

=
`(3.3)/(2.74 * 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.