The data for the various molecular weight range for polystyrene is given below; Molecular Weight Range ‘mol) 50,000 100,000 100,000 150,000 150,000 200,000 200,000 250,000 250,000 300,000 300,000 350,000 350,000 400,000 Mean g/mol) 75,000 125,000 175,000 225,000 275,000 325,000 375,000 0.09 0.14 0.23 0.24 0.19 0.08 0.03 Calculate the average molecular weight of polystyrene Determine the degree of polymerization of polystyrene. (2+2 marks) Draw the stress and strain curve diagram of an ELASTOMER. Briefly explains on how the mechanical properties (point of sample breaks_ tensile strength, toughness and Youngs Modulus) of the elastomer can be determined from the diagram marks)
The Correct Answer and Explanation is:
To calculate the average molecular weight and the degree of polymerization, we can proceed with the following steps:
1. Calculate the Average Molecular Weight:
The molecular weight is given for different ranges, along with their respective weight fractions. To calculate the average molecular weight, we use the weighted average formula:Mavg=∑i=1n(Mean Molecular Weight of Rangei×Weight Fraction of Rangei)M_{avg} = \sum_{i=1}^n \left( \text{Mean Molecular Weight of Range}_i \times \text{Weight Fraction of Range}_i \right)Mavg=i=1∑n(Mean Molecular Weight of Rangei×Weight Fraction of Rangei)
From the data:
| Molecular Weight Range (g/mol) | Mean Molecular Weight (g/mol) | Weight Fraction (w_i) |
|---|---|---|
| 50,000 – 100,000 | 75,000 | 0.09 |
| 100,000 – 150,000 | 125,000 | 0.14 |
| 150,000 – 200,000 | 175,000 | 0.23 |
| 200,000 – 250,000 | 225,000 | 0.24 |
| 250,000 – 300,000 | 275,000 | 0.19 |
| 300,000 – 350,000 | 325,000 | 0.08 |
| 350,000 – 400,000 | 375,000 | 0.03 |
Now, calculate the weighted average molecular weight:Mavg=(75,000×0.09)+(125,000×0.14)+(175,000×0.23)+(225,000×0.24)+(275,000×0.19)+(325,000×0.08)+(375,000×0.03)M_{avg} = (75,000 \times 0.09) + (125,000 \times 0.14) + (175,000 \times 0.23) + (225,000 \times 0.24) + (275,000 \times 0.19) + (325,000 \times 0.08) + (375,000 \times 0.03)Mavg=(75,000×0.09)+(125,000×0.14)+(175,000×0.23)+(225,000×0.24)+(275,000×0.19)+(325,000×0.08)+(375,000×0.03)Mavg=6,750+17,500+40,250+54,000+52,250+26,000+11,250=207,000 g/molM_{avg} = 6,750 + 17,500 + 40,250 + 54,000 + 52,250 + 26,000 + 11,250 = 207,000 \, \text{g/mol}Mavg=6,750+17,500+40,250+54,000+52,250+26,000+11,250=207,000g/mol
2. Degree of Polymerization:
The degree of polymerization (DP) can be calculated by dividing the molecular weight of polystyrene by the molecular weight of the monomer (styrene). The molecular weight of styrene (C8H8) is 104.15 g/mol.DP=MavgMolecular weight of Styrene=207,000104.15≈1,987DP = \frac{M_{avg}}{\text{Molecular weight of Styrene}} = \frac{207,000}{104.15} \approx 1,987DP=Molecular weight of StyreneMavg=104.15207,000≈1,987
Thus, the degree of polymerization is approximately 1,987.
3. Stress-Strain Curve of an Elastomer:
Elastomers are materials that exhibit significant elastic deformation. A typical stress-strain curve for an elastomer looks as follows:
- Initial Linear Region (Elastic Region): The material behaves like a typical solid, following Hooke’s Law (stress is proportional to strain). This is where the Young’s Modulus is measured.
- Yield Point: The point where the material starts to deform plastically and no longer returns to its original shape.
- Elongation: As stress continues, the material stretches without breaking. Elastomers can undergo large strains before breaking.
- Breaking Point (Fracture): The point where the material eventually breaks after undergoing maximum strain.
Mechanical Properties Determined from the Stress-Strain Curve:
- Tensile Strength: The maximum stress the material can withstand before breaking (the peak of the curve).
- Toughness: The area under the stress-strain curve. It represents the energy the material can absorb before failure.
- Young’s Modulus: The slope of the linear portion of the stress-strain curve, indicating the stiffness of the material. In the case of elastomers, this is often low compared to metals.
Conclusion:
From the stress-strain diagram of an elastomer, we can determine its tensile strength, toughness, and Young’s Modulus, which are critical in assessing the material’s suitability for various applications, especially in flexible and resilient components.
