Copolymerisation Questions and Answers

Answer: D

The mole fraction of vinyl chloride is about 0.86.

The average mass per repeat unit is 10520/160 = 65.75 g/mol. The repeat unit masses are about 62.5 g/mol for vinyl chloride (C₂H₃Cl) and 86.1 g/mol for vinyl acetate (C₄H₆O₂). With f the mole fraction of vinyl chloride:

\[ \begin{aligned} 62.5f + 86.1(1 - f) &= 65.75 \\ 23.6f &= 20.35 \\ f &\approx 0.86 \end{aligned} \]

0.14 is the mole fraction of vinyl acetate, the complement. 0.30 and 0.70 do not satisfy the average mass; a 70 percent vinyl chloride copolymer would have a mean repeat mass of about 69.6 g/mol.

Answer: A

Alternating copolymers form when \(r_{A} = r_{B} = 0\).

The reactivity ratio \(r_{A} = k_{AA}/k_{AB}\) compares how fast a chain ending in A adds another A with how fast it adds B. If both ratios are zero, a chain end never adds its own monomer, so each A must be followed by a B and each B by an A: a perfectly alternating chain.

\(r_{A} = r_{B} = 1\) is the ideal case, where each chain end adds either monomer equally and the copolymer is random. If both ratios exceed 1 each end prefers its own monomer, giving long runs (block-like) or separate homopolymers. Both below 1 gives a tendency to alternate, but strict alternation needs the limit of zero.

Answer: B

The probability of reaction \(P_2\) is \(\frac{1}{r_1F + 1}\).

A growing \(M_1^{*}\) radical can add either \(M_1\) (step \(P_1\)) or \(M_2\) (step \(P_2\)). The probability of \(P_2\) is its rate divided by the total rate of the two competing steps:

\[ \begin{aligned} p_{12} &= \frac{k_{12}[M_2]}{k_{11}[M_1] + k_{12}[M_2]} \\ &= \frac{1}{r_1F + 1} \end{aligned} \]

after dividing through by \(k_{12}[M_2]\). \(\frac{r_1}{r_1F + 1}\) has the wrong numerator. \(\frac{1}{r_2 + F}\) and \(\frac{r_2}{F + r_2}\) describe the steps of an \(M_2^{*}\) radical, \(P_3\) and \(P_4\), not \(P_2\).