Question

Nylon 6,6 is synthesized by the reaction of adipic acid and hexamethylene diamine. If the extent of reaction is 95% for the equimolar feed ratio of the monomers, then the number average degree of polymerization is:

• A. 95
• B. 20
• C. 50
• D. 100

Hint:

The Carothers Equation highlights why high molecular weights are difficult to achieve in step-growth polymerization. You need an extremely high extent of reaction (\(>99%\)) to get very long chains. At \(p = 0.99\), \(\bar{X}_n\) would jump to 100!

Answer 1

The Correct Option is B

Concept: For step-growth polymerization (like the formation of Nylon 6,6), the number average degree of polymerization (\(\bar{X}_n\)) is related to the extent of reaction (\(p\)) by the Carothers Equation.

Step 1: Identify the parameters.
The Carothers Equation for an equimolar ratio is: \[ \bar{X}_n = \frac{1}{1 - p} \] Where \(p\) is the extent of reaction (the fraction of functional groups that have reacted).

Step 2: Calculate \(\bar{X}_n\).
Given the extent of reaction is 95%, we have \(p = 0.95\). \[ \bar{X}_n = \frac{1}{1 - 0.95} = \frac{1}{0.05} \] \[ \bar{X}_n = 20 \]