Question

PVA (Poly(vinyl alcohol))

1) Show that the average strand of PVA (MW 78,000) contains approximately 1800 monomer units.

2) Calculate the approximate length of PVA assuming that each monomer unit contributes two carbon atom diameters to the length (1 carbon atom diameter = 154 pm).

3) Show that 1.00 L of 4% (40g/L) PVA contains approximately 3 x 10^20 PVA strands.

Answer 1

1)

To calculate the average strand of PVA use the following expression:

Average strand = MW of polymer / formula weight of monomer

Here; MW of polymer = 78000 and formula weight of monomer; - CH2-CHOH = 44

Then

Average strand = 78000 / 44 = 1772.7 or 1800 monomer units.

2)

Here, polymer contains 1800 monomer units.

One monomer (-CH2-CHOH-) contains = 2 C atoms

1800 monomer units will contain = 2C * 1800 = 3600 C atoms

Given that;

Each monomer unit contributes two carbon atom diameters to the length.

1 carbon atom diameter = 154 pm

3600 C atoms diameter = 154 pm *3600 = 554400 pm

Now convert it into meter:

1 picometer = 1.0 × 10^-12 meters

554400 pm * 1.0 × 10^-12 meters / 1.00 pm = 5.544 *10^-7 m

3)

PVA is (C4H8O2)n = (-CH2-CHOH-) *2 ;

The degree of polymerization of polyvinyl alcohol typically is 100 to 5000.
4% PVA = 40g / L

Molar mass C4H8O2 = 88g/mol
40g = 40/86 = 0.45 mol
Number of molecules unpolymerised PVA = 0.45 *6.022*10^23 = 2.7 *10^23

If n = 1 in the above formula, then there would be 2.7 *10^23 particles
If n = 100 in the above formula, then there would be (2.7*10^23)/100 = 2.7*10^21 particles or strands
If n = 5000 in the above, then there would be (2.7 *10^23)/5000 = 5.4*10^19 particles or strands.

If n = 933.3 then there would be (2.7*10^23)/933.3 = 3*10^20 particles or strands