Tensile Strength (MPa) Number-Average Molecular Weight (g/mol) 82 12,700
156 28,500
The tensile strength and number-average molecular weight for two polyethylene materials given above. Estimate the number-average molecular weight that is required to give a tensile strength required above. Using the data given find TS (infinity) in MPa.

Explanation:

The question can be well structured in a table format as illustrated below:

Tensile Strength (MPa)            Number- Average Molecular Weight  (g/mol)

82                                                  12,700

156                                                 28,500

The tensile strength and number-average molecular weight for two polyethylene materials given above.

Estimate the number-average molecular weight that is required to give a tensile strength required above. Using the data given find TS (infinity) in MPa.

SOLUTION:

We know that :

where;

= Tensile Strength

= Tensile Strength (Infinity)

= Number- Average Molecular Weight  (g/mol)

SO;

From equation (1) ; collecting the like terms; we have :

From equation (2) ; we have:

So;

Then;

Solving by L.C.M

By cross multiplying ; we have:

Collecting like terms ; we have

Dividing both sides by 15800:

A = 1695208.861

From equation (1);

Replacing A = 1695208.861 in the above equation; we have:

From equation(2);

Replacing A = 1695208.861 in the above equation; we have:

We are to also estimate the number- average molecular weight that is required to give a tensile strength required above.

If the Tensile Strength (MPa) is 82 MPa

Definitely the average molecular weight will be = 12,700 g/mol

If the Tensile Strength (MPa) is 156 MPa

Definitely the average molecular weight will be = 28,500 g/mol

But;

Let us assume that the Tensile Strength (MPa) = 181 MPa for example.

Using the same formula:

Then:

Collecting like terms ; we have:

1695208.861= 34.481

Dividing both sides by 34.481; we have:

=