The MALDI-TOF mass spectrum of a sample of poly(methylphenylsilane) was recorded in a matrix containing potassium chloride, KCl.  Peaks corresponding to polymer chains with 5, 6, 7 and 8 monomer units were observed at masses of 785, 905, 1025 and 1145 g mol^–1 respectively.  Which of the following structures is consistent with these observations?

Calculate the value of the dispersity index for a sample of poly(ethylene oxide) given that the number average and weight average molar masses are 4.44 kg mol^–1 and 4.53 kg mol^–1 respectively.  .

Analysis of a sample of poly(styrene) in benzene solution showed the following distribution of chain lengths.  Use the data to calculate the dispersity index of the sample.

Molar mass interval
/ (kg / mol^–1) 5–10

10–15

15–20

20–25

25–30

Mass of sample falling within interval / g

10.8

12.2

9.6

5.4

3.1

Calculate the contour length of a poly(methylmethacrylate) polymer chain of 500 monomer units if the monomer length is 2.23 Å.

The root-mean-square distance between the ends of a polymer chain was found to be 6.2 nm. Estimate the number of monomers in the chain, given that the length of each monomer unit is 2.1 Å.

Calculate the radius of gyration for a poly(vinylchloride), –(C₂H₃Cl)_n–, with a molar mass of 450 kg mol^–1_. Assume that the length of a monomer unit is 160 pm.

Calculate the change in the conformational entropy when the length of a polymer chain consisting of N monomer units is compressed by the equivalent of 20% of its length.

What is the magnitude of the restoring force exerted when an elastomer chain is extended by 25% at 25 °C?  Assume that the length of each bond within the elastomer backbone is 154 pm.

Calculate the work done at standard pressure in forming a spherical air bubble of radius 2.0 cm from a droplet of a soap solution with a surface tension of 25.5 mN m^–2.

When a cylindrical capillary column of internal radius 0.25 mm is inserted into glycerol, C₃H₅(OH)₃, at 25°C the liquid rises to a height of 4.1 cm up the tube.  Determine the surface tension of glycerol at this temperature, given that its density is 1.261 g cm^–3.