Question

The number-average molecular weight of a poly(styrene-butadiene alternating copolymer is 1,350,000 g/mol; determine the average number of styrene and butadiene repeat units per molecule.

Answer 1

Given:

No. average molecular weight, $\bar{M_{n}}$ = 1350000 g/mol

Formulae to be used:

1) m = $n_{1}A_{C} + n_{2} A_{H}$                  (1)

2) $D_{p} = \frac{\bar{M_{n}}}{m}$                  (2)

where,

m = total average weight of the combination

$A_{C}$ = Atomic weight of carbon

$A_{H}$ = Atomic weight of hydrogen

$D_{p}$ = Degree of polymerization

Solution:

No. of both the types of repeat unit is sameas it is a copolymer.

For styrene, there are 8 carbon and 8 hydrogen atoms and for buta di-ene repeat unit, there are 4 carbon and 6 hydrogen atoms.

Therefore, the average weight of the combined unit is given by eqn (1)

m = 12(12.01) + 14(1.008) = 158.23 g/mol

Using eqn (2) to calculate average of repeat units per molecule:

$D_{p}$ = $\frac{1350000}{158.23}$ = 8531.77 ≈ 8532

Answer 2

Following are the calculation of the molecule:  

Given:

Poly(styrene-butadiene) alternating copolymer average molecular weight $= 1350000\ \frac{g}{mol}$

To find:

molecule=?

Solution:

Calculating the styrene's molecular weight$= 104\ \frac{g}{mol}$

Calculating the butadiene molecular weight $= 54 \ \frac{g}{mol}$

Calculating the weight for the repeating unit $= (104+54) \ \frac{g}{mol} = 158 \ \frac{g}{mol}$

$\therefore$

Calculating the amount of repeating molecules per unit:

$\to \frac{1350000}{158} \\\\\to \frac{675000}{79} \\\\ \to \frac{675000}{79} \\\\ \to 8544.30 \approx 8544$

Therefore, the final answer is "8544".

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