Question

Suppose you have three monodisperse polymer samples, A, B, and C, with molar masses of 100,000 g/mol, 200,000 g/mol, and 300,000 g/mol, respectively. Calculate the number average and weight-average molar mass of a blend obtained by mixing A, B, and C as follows: a) in equal proportions by weight b) in the molar ratio 1:1:1

Answer 1

Answer:

a) Number-average molar mass: 163,700g/mol

Weight-average molar mass: 200,000g/mol

b) Number-average molar mass: 200,000g/mol

Weight-average molar mass: 233,300g/mol

Explanation:

The number-average molar mass is based on mole% and weight-average molar mass is based on weight%, thus:

a) In equal proportions by weight:

number-average molar mass:

1g A×$\frac{1mol}{100,000g}$ = 1x10⁻⁵ moles A

1g B×$\frac{1mol}{200,000g}$ = 5x10⁻⁶ moles B

1g C×$\frac{1mol}{300,000g}$ = 3,33x10⁻⁶ moles C

Total moles are:

1x10⁻⁵ A + 5x10⁻⁶ B + 3,33x10⁻⁶ C = 1,833x10⁻⁵ moles.

Percent A: $\frac{1x10^{-5}}{1,833x10^{-5}}$×100 = 54,5%

Percent B: $\frac{5x10^{-6}}{1,833x10^{-5}}$×100 = 27,3%

Percent C: $\frac{3,33x10^{-6}}{1,833x10^{-5}}$×100 = 18,2%

number-average molar mass:

0,545*100,000g/mol + 0,273*200,000g/mol + 0,182*300,000g/mol = 163,700g/mol

weight-average molar mass:

0,333*100,000g/mol + 0,333*200,000g/mol + 0,333*300,000g/mol = 200,000g/mol

b) In molar ratio 1:1:1

weight-average molar mass:

1mol A×$\frac{100,000g}{1mol}$ = 100,000g A

1mol B×$\frac{200,000g}{1mol}$ = 200,000g B

1mol C×$\frac{300,000g}{1mol}$ = 300,000g C

Total mass is:

100,000 A + 200,000 B + 300,000 C = 600,000 g.

Percent A: $\frac{100,000}{600,000}$×100 = 16,7%

Percent B: $\frac{200,000}{600,000}$×100 = 33,3%

Percent C: $\frac{300,000}{600,000}$×100 = 50,0%

Weight-average molar mass:

0,167*100,000g/mol + 0,333*200,000g/mol + 0,500*300,000g/mol = 233,300g/mol

number-average molar mass:

0,333*100,000g/mol + 0,333*200,000g/mol + 0,333*300,000g/mol = 200,000g/mol

I hope it helps!