Answer:
a) The mean repeat unit molar mass for PEVA is 30.72 g/mol
b) degree of polymerization of the copolymer is 1300
Explanation:
Given that;
the wt% of copolymer consist of 12.9 wt% of vinyl acetate and 87.1 wt% Ethylene.
Basis: 100 g of PEVA consist of 12.9 of vinyl acetate and 87.1g of Ethylene.
now we calculate the mole fraction of vinyl acetate Ethylene in the copolymer;
the molecular weights of vinyl acetate and ethylene are 86.09 g/mol and 28.05 g/mol respectively
so
moles of vinyl acetate = wt. of vinyl acetate / molecular weights of vinyl acetate
moles of vinyl acetate = 12.9 g / 86.09 g/mol
moles of vinyl acetate = 0.1498 mol
moles of Ethylene = wt. of Ethylene / molecular weights of Ethylene
moles of Ethylene = 87.1 g / 28.05 d/mol
moles of Ethylene = 3.1052 mol
Total moles = 0.1498 mol + 3.1052 mol = 3.255 mol
Next we calculate the mole percent;
mole percent of vinyl acetate [tex]X_{V}[/tex] = moles of vinyl acetate / total moles
[tex]X_{V}[/tex] = (0.1498 mol / 3.255 mol) × 100
[tex]X_{V}[/tex] = 4.6%
mole percent of Ethylene [tex]X_{E}[/tex] = moles of Ethylene / total moles
[tex]X_{E}[/tex] = (3.1052 mol / 3.255 mol) × 100
[tex]X_{E}[/tex] = 95.397% ≈ 95.4%
we know that, mean repeat unit molar mass for a sample = ∑[tex]X_{i}[/tex][tex]M_{i}[/tex]
where [tex]X_{i}[/tex] is the fraction ratio and [tex]M_{i}[/tex] is the molecular weight
so or the PEVA
mean repeat unit molar mass M = ( [tex]X_{V}[/tex][tex]M_{V}[/tex]) + ( [tex]X_{E}[/tex][tex]M_{E}[/tex])
so we substitute
M = ( 4.6% × 86.09) + ( 95.4% × 28.05 )
M = 3.96014 + 26.7597
M = 30.72 g/mol
Therefore, The mean repeat unit molar mass for PEVA is 30.72 g/mol
b)
Degree of polymerization
[tex]DP_{n}[/tex] = [tex]\frac{M_{n} }{M}[/tex]
where [tex]M_{n}[/tex] is the number average molecular weight ( 39,870 g/mol )
so we substitute
[tex]DP_{n}[/tex] = 39,870 g/mol / 30.72 g/mol
[tex]DP_{n}[/tex] = 1297.85 ≈ 1300 { 3 significance figure }
Therefore, degree of polymerization of the copolymer is 1300