Nylon 6,6 may be formed by means of a condensation polymerization reaction in which hexamethylene diamine \(\left[\mathrm{NH}_{2}-\left(\mathrm{CH}_{2}\right)_{6}-\right.\) \(\mathrm{NH}_{2}\) ] and adipic acid react with one another with the formation of water as a by-product. What masses of hexamethylene diamine and adipic acid are necessary to yield \(37.5 \mathrm{~kg}\) of completely linear nylon 6,6 ? (Note: the chemical equation for this reaction is the answer to Concept Check 15.12.)

The balanced chemical equation for the formation of nylon 6,6 from hexamethylene diamine and adipic acid is given below: $$\mathrm{NH}_{2}\left(\mathrm{CH}_{2}\right)_{6}\mathrm{NH}_{2} + \mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{4}\mathrm{COOH} \rightarrow [\mathrm{NH}\left(\mathrm{CH}_{2}\right)_{6}\mathrm{NHCO}\left(\mathrm{CH}_{2}\right)_{4}\mathrm{CO}]_{n} + 2\mathrm{H}_{2}\mathrm{O}$$

We will find the molar masses using the atomic masses of the elements in each compound: Hexamethylene diamine (C6H16N2): Molar mass = 6(12.01) + 16(1.01) + 2(14.01) = 116.20 g/mol Adipic acid (C6H10O4): Molar mass = 6(12.01) + 10(1.01) + 4(16.00) = 146.14 g/mol Nylon 6,6 (C12H22N2O2): Molar mass = 12(12.01) + 22(1.01) + 2(14.01) + 2(16.00) = 226.32 g/mol

Given the mass of nylon 6,6 produced (37.5 kg) and its molar mass (226.32 g/mol), we can calculate the amount (in moles) using the formula: Amount (in moles) = Mass (g) / Molar mass (g/mol) First, let's convert the mass to grams: 37.5 kg = 37,500 g Now, we can calculate the moles of nylon 6,6: Amount (in moles) = 37,500 g / 226.32 g/mol = 165.68 mol

From the balanced chemical equation, the stoichiometry of the reaction is 1:1 for both reactants and product. This means that for each mole of nylon 6,6 produced, 1 mole of hexamethylene diamine and 1 mole of adipic acid are required. Amount (in moles) of hexamethylene diamine needed = 165.68 mol Amount (in moles) of adipic acid needed = 165.68 mol Now, we convert the moles of each reactant to mass using their molar masses: Mass of hexamethylene diamine needed = 165.68 mol × 116.20 g/mol = 19,262.94 g (or 19.26 kg) Mass of adipic acid needed = 165.68 mol × 146.14 g/mol = 24,200.31 g (or 24.20 kg) Thus, to produce 37.5 kg of completely linear nylon 6,6, 19.26 kg of hexamethylene diamine and 24.20 kg of adipic acid are necessary.