Domain: Polymer statistics

In a polymerization of \\(H_2N(CH_2)_{10}COOH\\) to form \\(nylon-11\\), \\(95\%\\) of the functional groups is known to have reacted. Calculate (a) the amount of monomer (in terms of weight fraction) remaining in the reaction mixture, (b) the weight fraction of the reaction mixture having a number-averaged degree of polymerization equal to \\(100\\), and (c) the extent of reaction at which the \\(100-mer\\) has the maximum yield by weight. Provide  the final answer in the form of simplest ratio \((a:b:c\\)).

Grading rubric:
criterion: The solution correctly states that the chain-length distribution follows Flory’s most-probable distribution derived from independent functional-group reaction probabilities.
weight: 10
criterion: The solution recognizes that AB-type monomer eliminates the need for stoichiometric imbalance correction factors present in AA–BB systems.
weight: 20
criterion: The solution interprets that Flory–Carothers statistics apply due to equal reactivity of functional groups, absence of cyclization or branching.
weight: 10
criterion: The solution uses joint probability of two unreacted functional groups to justify w1 = (1 − p)^2 rather than treating monomer as single-event survival.

weight: 20
criterion: The solution uses that the normalization condition Σ(wx) = 1 is satisfied by the Flory weight distribution used.

weight: 20
criterion: The solution derives p_max = (x − 1)/(x + 1) from balancing chain-growth probability against depletion of unreacted groups.
weight: 10
criterion: The solution reports final answer as a simplest integer ratio equivalent to 5 : 3 : 1960.
weight: 10

Answer:
5 : 3 : 1960