Answer
8.49 kg
Work Step by Step
Required:
How much ethylene glycol must be added to 20.0 kg of dimethyl terephthalate to produce a linear chain structure of poly(ethylene terephthalate) according to Equation 15.9.
Solution:
ethylene glycol- 2 carbons, 6 hydrogens, 2 oxygens
dimethyl terephthalate - 8 carbons, 10 hydrogens, 4 oxygens
Computing the molecular weights of each material:
$MW_{ethylene glycol} = 2(A_{C}) + 6(A_{H}) + 2(A_{O}) = 2(12.011 g/mol) + 6(1.008 g/mol) + 2(16.00 g/mol) = 62.07 g/mol$
$MW_{dimethyl terephthalate} = 6(A_{C}) + 10(A_{H}) + 4(A_{O}) = 6(12.011 g/mol) + 10(1.008 g/mol) + 4(16.00 g/mol) = 146.15 g/mol$
The 20.0 kg mass of dimethyl terephthalate is equal to 20,000 g, or $\frac{20,000 g}{146.15 g/mol} = 136.85 mol$. From Equation 15.9, each mole of dimethyl terephthalate requires one mole ethylene glycol, so:
$(136.85 mol)(62.07 g/mol) = 8,494.28 g = 8.49 kg$
