Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors
Example 9.4: Calculate Xn for Monomers with the Same End Groups
\( n \text{ARA} + n \text{BRB} \longrightarrow A\{RR'\}_n B + (n-1)AB \)
Initially we have 10 polymer molecules of ARA and 10 polymer molecules of BR¢ B, for a total of 20 structural units (10 R and 10R¢ ), a total of 20 A functional groups and 20 B functional groups. At time t there are seven polymer molecules and the distribution of molecules at time t is shown in the table below. Calculate the fractional conversion of functional groups, p, and the number average chain length \( \overline{X}_n \).
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Solution
MA0 = Number of functional groups of A initially = 20
MA = Number of functional groups of A remaining = 7
N0 = Number of polymer molecules initially.
N = Number of polymer molecules remaining at time t
\( p = \frac{M_{A0} - M_A}{M_A} = \frac{20 - 7}{20} = \frac{13}{20} = 0.65 \)
\( \overline{X}_n = \frac{1}{1 - p} = \frac{1}{1 - 0.65} = 2.86 \)
or
\( \overline{X}_n = \frac{N_o}{N} = \frac{20}{7} = 2.86 \)