Chemistry High School

The following polymer sample is composed of: 15% 90-mers, 25% 100- mers, 30% 120-mers, 25% 140-mers, and 5% 155-mers. The repeat unit molecular weight of the polymer is 105 g mol-¹. Calculate each of the following values a) The number-average molecular weight (Mn).. b) The weight-average molecular weight (Mw) c) The dispersity (D)- "

Answers

Answer 1

To calculate the number-average molecular weight (Mn), weight-average molecular weight (Mw), and dispersity (D), we need to use the following formulas:

a) Number-average molecular weight (Mn):

Mn = (Σ(Ni * Mi)) / Σ(Ni)

Where:

Ni = Number of polymer chains with molecular weight Mi

b) Weight-average molecular weight (Mw):

Mw = (Σ(Ni * Mi^2)) / Σ(Ni * Mi)

c) Dispersity (D):

D = Mw / Mn

Given the composition of the polymer sample, we can calculate these values as follows:

For Mn:

Mn = (15% * 90) + (25% * 100) + (30% * 120) + (25% * 140) + (5% * 155)

= 13.5 + 25 + 36 + 35 + 7.75

= 117.25 g/mol

For Mw:

Mw = (15% * 90^2) + (25% * 100^2) + (30% * 120^2) + (25% * 140^2) + (5% * 155^2)

= 18225 + 25000 + 51840 + 68600 + 12022.5

= 175,687.5 g/mol

For D:

D = Mw / Mn

= 175,687.5 / 117.25

≈ 1497.13

Therefore, the calculated values are:

a) Mn = 117.25 g/mol

b) Mw = 175,687.5 g/mol

c) D ≈ 1497.13

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Related Questions

why is china so scientific?

Answers

China's scientific prowess is the result of a combination of historical legacy, government support, a strong education system, global competitiveness, and a commitment to international collaboration.

China's emphasis on science and scientific advancements can be attributed to several factors:

1. Historical Legacy: China has a rich history of scientific discoveries and innovations dating back centuries. Ancient Chinese contributions include inventions such as papermaking, gunpowder, compass, and the development of traditional Chinese medicine. This legacy has instilled a cultural appreciation for scientific knowledge and inquiry.

2. Government Support: The Chinese government recognizes the importance of science and technology for economic development and national progress. It has implemented policies and initiatives to promote scientific research, innovation, and education. Significant investments have been made in research and development, infrastructure, and the establishment of scientific institutions and universities.

3. Education System: China has a rigorous education system that places a strong emphasis on science, technology, engineering, and mathematics (STEM) education. There is a focus on producing a skilled scientific workforce to drive innovation and economic growth. The country has numerous prestigious universities and research institutions that attract talented students and researchers from both within China and internationally.

4. Global Competitiveness: China's rise as a global economic power has led to a desire to enhance its scientific capabilities and compete with other advanced nations. It recognizes that scientific advancements are key to technological innovation, industrial competitiveness, and addressing societal challenges.

5. International Collaboration: China actively engages in international scientific collaborations and partnerships. It recognizes the value of exchanging knowledge, sharing resources, and collaborating with researchers worldwide. This approach facilitates access to cutting-edge research, global networks, and diverse perspectives.

Overall, China's scientific prowess is the result of a combination of historical legacy, government support, a strong education system, global competitiveness, and a commitment to international collaboration. These factors have contributed to China's significant scientific advancements and its position as a scientific powerhouse.

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