Question

If the number-average degree of polymerization for polystyrene obtained by the bulk polymerization of styrene at 60 (C) is 1000, what would be the number-average degree of polymerization if the polymerization were conducted in a 10% solution in toluene (900 g of toluene per 100 g of styrene) under otherwise identical conditions? The molecular weights of styrene and toluene are 104.12 and 92.15, respectively. State any assumptions that are needed.

Answer 1

To find the number-average degree of polymerization when the polymerization is conducted in a 10% solution in toluene, we can use the equation P2 / P1 = (W1 / W2) * (MW2 / MW1). Assuming the weight of toluene is negligible compared to the weight of styrene, the number-average degree of polymerization in the 10% solution in toluene would be 886.5.

Step-by-step explanation:

To find the number-average degree of polymerization when the polymerization is conducted in a 10% solution in toluene, we can use the equation:

P2 / P1 = (W1 / W2) * (MW2 / MW1)

Where P1 is the number-average degree of polymerization in the bulk polymerization, W1 is the weight of styrene in the bulk polymerization, MW1 is the molecular weight of styrene, P2 is the number-average degree of polymerization in the solution polymerization, W2 is the weight of styrene in the solution polymerization, and MW2 is the molecular weight of the toluene.

Assuming that the weight of toluene is negligible compared to the weight of styrene, we can simplify the equation to:

P2 / P1 = MW2 / MW1

Using the given information, the molecular weights of styrene and toluene are 104.12 and 92.15, respectively. Therefore, the number-average degree of polymerization in the 10% solution in toluene would be:

P2 = P1 * (MW2 / MW1) = 1000 * (92.15 / 104.12) = 886.5

Answer 2

Step-by-step explanation:

Formula to calculate degree of polymerization is as follows.

Degree of polymerization (DP) =
`\frac{\text{Number average molecular weight}}{\text{Average unit molecular weight}}`

DP =
`\frac{\bar{M_(n)}}{m}`

1000 =
`\frac{\bar{M_(n)}}{104.12}`

`\bar{M_(n)}` = 104150

Formula to calculate average repeat molecular weight of co-polymer is as follows.

`\bar{m} = \sum{f_(j)m_(j)}`

where,
`f_(j)` = mole fraction of each component

Moles of styrene =
`\frac{mass}{\text{molar mass}}`

=
`(100 g)/(104.12 g/mol)`

= 0.96 mol

Moles of toulene =
`(900 g)/(92.15 g/mol)`

= 9.77 mol

Therefore, mole fraction will be calculated as follows.

`f_(1) = (0.96)/(0.96 + 9.77)`

= 0.0895

`f_(2) = (9.77)/(0.96 + 9.77)`

= 0.910

`\bar{m} = 0.0895 * 104.12 g/mol + 0.910 * 92.15 g/mol`

= 93.22 g/mol

Hence, DP =
`\frac{\bar{M_(n)}}{\bar{m}}`

=
`(104150)/(93.22 g/mol)`

= 1117

Thus, we can conclude that the number-average degree of polymerization is 1117.