Assuming that 1.00 L of 4% PVA solution Is spread out to form a thin sheet of th
ID: 1065630 • Letter: A
Question
Assuming that 1.00 L of 4% PVA solution Is spread out to form a thin sheet of thickness equal to the average length of a PVA strand, calculate the total area of the liquid sheet. Then calculate the average area of the sheet of solution per strand of PVA. Assuming this area Is a little square, the squareroot of this area gives the edge length of the square which Is approximately the average distance between PVA strands. Show that this distance Is about ten times the estimated diameter of a PVA strand (0.2-0.3 nm).Explanation / Answer
Solution:
One unit of PVA (monomer) looks like is -(C4H6O2)n-.
The degree of polymerization of polyvinyl acetate (PVA) is typically 100 to 5000.
4% PVA = 40g per litre
Molar mass C4H6O2 = 86g/mol
40g = 40/86 = 0.465 mol
Number of molecules of un-polymerised PVA = 0.465x6.022x1023 = 2.8x1023
If n = 1 in the above formula, then there would be 2.8x1023 particles or strands
If n = 100 in the above formula, then there would be (2.8x1023)/100 = 2.8x1021 particles or strands
If n = 5000 in the above, then there would be (2.8x1023)/5000 = 5.6x1019 particles or strands.
If n = 933.3 then there would be (2.8x1023)/933.3 = 3x1020 particles or strands
Where n = the degree of polymerization, which is not given in the question, but it is quite reasonable to have 3x1020 strands of PVA, n = 933 that fits neatly into the range of n = 100 to 5000.
Given the diameter of the PVA strand or particle, d = 0.3x10-9 m
Therefore total length = no. of strands x d = 3x1020x0.3x10-9 = 9x10-10 m
A square has 4 nos. of equal length sides. Therefore the length of the one side (edge length), a = 9x10-10/4 = 2.25x10-10 m
Let the area (total area), A = a2, a = edge length of the square
Or, A = (2.25x10-10)2 = 5x10-20 m2
Therefore, area per strand is, a12 = 5x10-20/3x1020 = 1.66x10-40 m2
Or, a1 = 1.28x10-20 m