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3.8.5 Example Calculation Involving Intrinsic Viscosity Say we are interested in a fast, approximate molecular weight of a polystyrene sample. We dissolve 0.10 g of the polymer in 100 ml of butanone and measure the flow times at 25°C in an Ubbelhode capillary viscometer. The results are Pure butanone 110 s 0.10% Polystyrene solution 140 s Starting with equation (3.84), and nothing that the flow time is proportional to the viscosity, ?rel = ?/?0 = 140/110 = 1.273 ?sp = ?rel - 1 = 0.273 ?sp/c = 0.273/0.001 ml/g = 2.73x10² ml/g As an approximation, assume that the concentration is near zero, and the [?] = 2.73 × 10² ml/g, equation (3.86). This obviates the extrapolation in Figure 3.14 that is required for more accurate results. Using the Mark–Houwink–Sakurada relation, equation (3.97) and Table 3.11, we have [?] = KMv? 2.73×10² = 39×10?³ Mv?·?? Mv = 4.26×10? g/mol Note that the units of K are irregular, depending on the value of a. Usually the units of K are omitted from tables.

          3.8.5 Example Calculation Involving Intrinsic Viscosity

Say we are interested in a fast, approximate molecular weight of a polystyrene sample. We dissolve 0.10 g of the polymer in 100 ml of butanone and measure the flow times at 25°C in an Ubbelhode capillary viscometer. The results are

Pure butanone 110 s
0.10% Polystyrene solution 140 s

Starting with equation (3.84), and nothing that the flow time is proportional to the viscosity,

?rel = ?/?0 = 140/110 = 1.273
?sp = ?rel - 1 = 0.273
?sp/c = 0.273/0.001 ml/g = 2.73x10² ml/g

As an approximation, assume that the concentration is near zero, and the [?] = 2.73 × 10² ml/g, equation (3.86). This obviates the extrapolation in Figure 3.14 that is required for more accurate results. Using the Mark–Houwink–Sakurada relation, equation (3.97) and Table 3.11, we have

[?] = KMv?
2.73×10² = 39×10?³ Mv?·??
Mv = 4.26×10? g/mol

Note that the units of K are irregular, depending on the value of a. Usually the units of K are omitted from tables.

3.8.5 Example Calculation Involving Intrinsic Viscosity

Say we are interested in a fast, approximate molecular weight of a polystyrene sample. We dissolve 0.10 g of the polymer in 100 ml of butanone and measure the flow times at 25°C in an Ubbelhode capillary viscometer. The results are

Pure butanone 110 s
0.10% Polystyrene solution 140 s

Starting with equation (3.84), and nothing that the flow time is proportional to the viscosity,

?rel = ?/?0 = 140/110 = 1.273
?sp = ?rel - 1 = 0.273
?sp/c = 0.273/0.001 ml/g = 2.73x10² ml/g

As an approximation, assume that the concentration is near zero, and the [?] = 2.73 × 10² ml/g, equation (3.86). This obviates the extrapolation in Figure 3.14 that is required for more accurate results. Using the Mark–Houwink–Sakurada relation, equation (3.97) and Table 3.11, we have

[?] = KMv?
2.73×10² = 39×10?³ Mv?·??
Mv = 4.26×10? g/mol

Note that the units of K are irregular, depending on the value of a. Usually the units of K are omitted from tables.

Added by Michelle C.

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